GLOBAL OPTIMIZATION CONFERENCE

GOC-2017

Dedicated in Memory of Professor Christodoulos A. Floudas

March 30–April 1, 2017

Annenberg Presidential Conference Center

College Station, TX

CristÒdouloj Acilleύj FloÚdaj

ProfessorChristodoulos A. Floudas

Recognitions and Honors

Education

Final Appointments

National Academy of Inventors 2015Academy of Athens, Corresponding Member 2015P.V. Danckwerts Memorial Lecture 2015Thomson Reuters Highly Cited Researcher 2015 (for 2003-2013)Constantin Caratheodory Prize 2015Thomson Reuters Highly Cited Researcher 2014 (for 2002-2012)Texas A&M University Institute for Advanced Study Fellow and Eminent Scholar 2013-14National Award and HELORS Gold Medal 2013AIChE Fellow 2013National Academy of Engineering 2011Graduate Mentoring Award, Princeton University 2007AIChE Computing in Chemical Engineering Award 2006AIChE Andreas Acrivos Award for Professional Progress in Chemical Engineering 2001

Ph.D. in Chemical EngineeringThesis: “Synthesis and Analysis of Flexible Energy Recovery Systems”Advisor: Professor I. E. GrossmannCarnegie Mellon University 1986

Diploma of Chemical EngineeringAristotle University of Thessaloniki 1982

h-index Google Scholar 83 Web of Science 62Citations 12,235Journal Articles >335

Texas A&M UniversityDirector Texas A&M Energy InstituteErle Nye ‘59 Chair Professor for Engineering Excellence Artie McFerrin Department of Chemical Engineering

Princeton UniversityStephen C. Macaleer ‘63 Professor in Engineering and Applied Science, Emeritus Professor of Chemical and Biological Engineering, Emeritus1959 - 2016

CONFERENCE PROGRAMOrganizersSergiy Butenko and Efstratios Pistikoloulos(Texas A&M University, USA)

Program CommitteePanos M. Pardalos (USA), Hoang Tuy (Vietnam),Claire S. Adjiman (UK), Charles Audet (Canada),Adil Bagirov (Australia), Balabhaskar Balasundaram(USA), Paul I. Barton (USA), Ernesto G. Bir-gin (Brazil), Immanuel Bomze (Austria), Altan-nar Chinchuluun (UK), Wanpracha Art Chaovalit-wongse (USA), Yu-Hong Dai (China), Aris Dani-ilidis (Spain), Ding-Zhu Du (USA), Mirjam Dür(Germany), Matthias Ehrgott (Australia), Shu-CherngFang (USA), Inmaculada Garcı́a Fernández (Spain),Dalila Fontes (Portugal), János Fülöp (Hungary),Boris Goldengorin (USA), Chrysanthos E. Gounaris(USA), Ignacio E. Grossmann (USA), Yongpei Guan(USA), Nicolas Hadjisavvas (Greece), Eligius M. T.Hendrix (Spain), Jeya Jeyakumar (Australia), Don-ald R. Jones (USA), Igor Konnov (Russia), PavloKrokhmal (USA), Simge Küçükyavuz (USA), ErhunKundakcioglu (Turkey), Takahito Kuno (Japan), LeoLiberti (France), Marco Locatelli (Italy), AngeloLucia (USA), Jérôme Malick (France), Lina Mal-lozzi (Italy), Antonino Maugeri (Italy), Juan EnriqueMartı́nez-Legaz (Spain), Frédéric Messine (France),Kaisa Miettinen (Finland), Athanasios Migdalas(Greece & Sweden), Alexander Mitsos (Germany),Boris Mordukhovich (USA), Lewis Ntaimo (USA),Jiming Peng (USA), Janos D. Pinter (USA), LeonidasPitsoulis (Greece), Oleg Prokopyev (USA), Themisto-cles M. Rassias (Greece), Steffen Rebennack (USA),Mauricio G. C. Resende (USA), Jean-Philippe P.Richard (USA), Dolores Romero Morales (Denmark),Berc Rustem (UK), Nikolaos V. Sahinidis (USA),Fabio Schoen (Italy), Yaroslav D. Sergeyev (Italy),Thomas C. Sharkey (USA), Ruey-Lin Sheu (Tai-wan), Anthony Man-Cho So (China), Mohit Tawar-malani (USA), Kok Lay Teo (Austrialia), Fengqi You(USA), Tapio Westerlund (Finland), Henry Wolkow-icz (Canada), Graham Wood (Australia), Zelda Zabin-sky (USA), Anatoly Zhigljavsky (UK), Antanas Zilin-skas (Lithuania), Julius Zilinskas (Lithuania)

Schedule at a Glance

Wednesday, March 29

• 6:00-8:00 PM Welcome ReceptionThe Stables, Cavalry Court Hotel

Thursday, March 30

• 08:00-08:20 Registration and Coffee, Lobby• 08:20-08:30 Welcome Remarks, 1011C• 08:30-10:00 Session T1, 1011C• 10:00-10:30 Coffee Break, Lobby• 10:30-12:00 Sessions T2-A (1011B), T2-B (PDR)• 12:00-01:30 Lunch, 1011C• 12:00-01:30 JOGO Editorial Board Meeting, PDR• 01:30-03:00 Sessions T3-A (1011B), T3-B (PDR)• 03:00-03:30 Coffee Break, Lobby• 03:30-05:00 Sessions T4-A (1011B), T4-B (PDR)

Friday, March 31

• 08:00-09:00 Registration and Coffee, Lobby• 09:00-10:00 Carathéodory Prize Session, 1011C• 10:00-10:30 Coffee Break, Lobby• 10:30-12:00 Sessions F2-A (1011B), F2-B (PDR)• 12:00-01:30 Lunch, 1011C• 01:30-03:00 Sessions F3-A (1011B), F3-B (PDR)• 03:00-03:30 Coffee Break, Lobby• 03:30-05:00 Sessions F4-A (1011B), F4-B (PDR)• 06:30 Dinner at The Stables, Cavalry Court Hotel

Saturday, April 1

• 09:00-01:00 “Floudas Cup” soccer tournament,field 10 of Penberthy Sports Complex

• 09:00-01:00 George Bush Presidential Library andMuseum tour

Acknowledgements

The conference has been organized with the financialsupport and technical assistance from• Texas A&M Energy Institute• Department of Industrial and Systems Engineering,

Texas A&M University• INFORMS Student Chapter at Texas A&M

Session T1: Advances in Selected TopicsThursday, 8:30-10:00, 1011CChair: Panos M. Pardalos

On Objective Function Representation Methods inGlobal Optimization, Panos M. Pardalos, Universityof Florida, Gainesville, FL, USA. E-mail: parda-los@ufl.edu.

The problem of representation (or decomposition) of a con-tinuous function and its use in global optimization has beenwell studied. The most well known and used methods includethe representation of functions as the difference of two convexfunctions (CD optimization) or difference of two monotonicallyincreasing functions (Monotonic Optimization). Other tech-niques include reduction to separability (total or partial), andmethods based on Kolmogorov’s superposition theorem.

After a summary of existing work, the talk will focus onDC discrete optimization. In particular, we are going to dis-cuss details for the solution of degree-constrained fault-tolerantspanning subgraph problem by DC optimization.

Tuning BARON Using Derivative-Free Optimiza-tion Algorithms, Jianfeng Liu, Nikolaos Ploskas,Nikolaos V. Sahinidis, Carnegie Mellon University, USA.E-mail: sahinidis@cmu.edu.

Optimization solvers include many options that allow users tocontrol algorithmic aspects that may have a considerable impacton solver performance. Tuning solver options is often necessaryto reduce execution time and improve solution quality. Previ-ous studies of solver tuning techniques have focused on mixed-integer linear programming and local nonlinear programmingsolvers. In this paper, we investigate the potential of tuninga global optimization solver for mixed-integer nonlinear pro-gramming problems. In particular, derivative-free optimization(DFO) algorithms are used to find optimal values for optionsof the global optimization solver BARON. A set of 126 prob-lems from the GLOBALLib and MINLPLib collections are uti-lized in a computational study from which we conclude thattuning options can improve the default performance of BARONfor individual problems. Additionally, we present a system-atic comparison of 27 DFO solvers in terms of their ability toimprove the performance of the global solver. We find that sev-eral DFO implementations are much better than others in termsof finding optimal tuning parameters.

DIRECT-based Global Optimization Algorithmsand Their Comparison with Metaheuristics,Yaroslav Sergeyev, Dmitri E. Kvasov, Marat S.Mukhametzhanov, Università della Calabria, Rende(CS), Italy and Lobachevsky State University of NizhniNovgorod, Russia. E-mail: yaro@si.dimes.unical.it.

Deterministic Lipschitz DIRECT-based global optimizationalgorithms are considered in this lecture. Several modifica-tions are presented and compared with widely used multidi-mensional metaheuristic global optimization methods – geneticalgorithms, differential evolution, particle swarm optimization,artificial bee colony algorithms, and firefly algorithms. For this

purpose, there has been introduced a methodology allowing oneto compare stochastic methods with deterministic ones by usingoperational characteristics originally proposed for working withdeterministic algorithms only. As a result, a visual compari-son of methods having different nature on classes of randomlygenerated test functions becomes possible. A detailed descrip-tion of the new methodology for comparing, called “operationalzones”, is given and results of wide numerical experiments arereported.

Finding Critical Links for Closeness Centrality,Oleg Prokopyeva, Alexander Veremyev, Eduardo L.Pasiliao, aUniversity of Pittsburgh, USA. E-mail:adroleg@pitt.edu.

Closeness centrality is a class of distance-based measures in thenetwork analysis literature to quantify reachability of a givenvertex (or a group of vertices) by other network agents. Inthis talk, we consider a new class of critical edge detectionproblems, where given a group of vertices that represent animportant subset of network elements of interest (e.g., serversthat provide an essential service to the network), the decision-maker is interested in identifying a subset of critical edgeswhose removal maximally degrades the closeness centrality ofthose vertices. We develop a general optimization framework,where the closeness centrality measure can be based on anynon-increasing function of distances between vertices, which,in turn, can be interpreted as communication efficiency betweenthem. Our approach includes three well-known closeness cen-trality measures as special cases: harmonic centrality, decaycentrality and k-step reach centrality. Furthermore, for quan-tifying the centrality of a group of vertices we consider threedifferent approaches for measuring the reachability of the groupfrom any vertex in the network: minimum distance to a vertex inthe group, maximum distance to a vertex in the group, and theaverage centrality of vertices in the group. We study the the-oretical computational complexity of the proposed models anddescribe the corresponding mixed integer programming formu-lations. For solving medium- and large-scale instances of theproblem, we first develop an exact algorithm that exploits the“small-world” property of real-life networks, and then proposetwo conceptually different heuristic algorithms. Finally, weconduct computational experiments with real-world and syn-thetic network instances under various settings, which revealinteresting insights and demonstrate the advantages and limita-tions of the proposed models and algorithms.

Session T2-A: Convexification TechniquesThursday, 10:30-12:00, 1011BChair: M. M. Faruque Hasan

Edge-Concavity based Underestimation and GlobalOptimization of General C2-continuous NonlinearNonconvex Problems, M. M. Faruque Hasan, TexasA&M University, USA. E-mail: hasan@tamu.edu.

Many optimization problems of practical interest are nonlinear,nonconvex and have multiple local solutions. Convex under-estimators are often used to obtain a guaranteed bound on theglobal solution of a nonconvex problem. However, a key chal-lenge with convex underestimators is that the resulting relax-ation is not always tight if the original function is highly non-convex. The tightness of the relaxation is central to the effec-tiveness of a branch-and-bound algorithm, since a tighter relax-ation leads to less number of nodes to be explored and fasterconvergence. In this presentation, we will describe a new relax-ation technique for the deterministic global optimization of gen-eral nonconvex and C2-continuous problems, which marks adeparture from the convexity-based optimization approaches.Instead of using a convex underestimator, the relaxation is basedon an underestimator which is edge-concave (componentwiseconcave). The underestimator is constructed by subtracting apositive quadratic expression such that all non-edgeconcavitiesin the original function is overpowered by the added expres-sion. Next, we use the linear facets of the vertex polyhedralconvex envelope of the edge-concave underestimator to obtaina linear programming (LP)-based relaxation of general noncon-vex functions. The method will be presented with theoreticalresults and will be compared with convexification/ underesti-mation techniques such as αBB and its variants through testexamples. Future directions in the area of edge-concavity basedglobal optimization of nonconvex problems will be also dis-cussed.

Implications of Anchoring and Interval Extensionson Tightness of Convex and Concave Relaxations,Jaromił Najman, Alexander Mitsos, RWTH Aachen Uni-versity, Germany. E-mail: Amitsos@alum.mit.edu.

We call a convex relaxation f cv of f anchored at a point z if thevalues of the function at z are equal. First, we consider anchor-ing of convex and concave relaxations at corner points of thedomain of the function. We present results showing that anchor-ing at corner points is a useful property but neither necessary nora sufficient one for favorable Hausdorff and pointwise conver-gence order of a relaxation. Next, we investigate the tightnessand convergence behavior of McCormick relaxations in specificcases. McCormick relaxations have at least quadratic Haus-dorff and pointwise convergence order [1,3] which is a favor-able property in light of the so-called cluster problem [2,4] butsimple branch-and-bound algorithms may require very smallnode width in order to terminate. We prove that the problemcan be partially handled if we use tighter underlying intervalextensions for the construction of McCormick relaxations.Acknowledgements: We would like to thank the late ChrisFloudas who motivated us to look into anchoring.

[1] A. Bompadre and A. Mitsos. Convergence rate ofMcCormick relaxations. Journal of Global Optimization,52(1):1–28, 2012.

[2] K. Du and R. B. Kearfott. The cluster problem in multi-variate global optimization. Journal of Global Optimiza-tion, 5(3):253–265, 1994.

[3] J. Najman and A. Mitsos. Convergence analysis of mul-tivariate mccormick relaxations. Journal of Global Opti-mization, 66(4):597–628, 2016.

[4] A. Wechsung, S. D. Schaber, and P. I. Barton. The clus-ter problem revisited. Journal of Global Optimization,58(3):429–438, 2014.

Differentiable Convex Underestimators for Paramet-ric ODE Solutions, Kamil A. Khan, McMaster Univer-sity, Canada. E-mail: khank11@mcmaster.ca

Established methods for deterministic global optimization typi-cally compute useful global bounding information by construct-ing and minimizing convex underestimators of process mod-els. Convex underestimators are also useful in their own right,for design centering and for reachable set descriptions. How-ever, generating useful convex underestimators for dynamicsystems is difficult; dynamics obscure our intuition about thedependence of a model on its parameters, and the strength ofGronwall’s Inequality in practice suggests that any discrep-ancy between a dynamic model and its convex underestima-tor is likely to grow exponentially with system time. Nev-ertheless, there is significant room for improvement; supply-ing tighter convex underestimators for dynamic models wouldbroaden the class of dynamic optimization problems that can besolved to global optimality with given computational resources,as would reducing the computational effort required for sub-gradient evaluations. This presentation describes a new proce-dure for constructing tight, useful convex underestimators fordynamic models that are described as parametric systems ofordinary differential equations (ODEs). This work harnessesseveral recent advances in global optimization: a method andframework for convex relaxation generation by Tsoukalas andMitsos [4] that improves on McCormick’s classical technique[2], a recent variant [1] of this method that yields continuouslydifferentiable relaxations, and a technique by Scott and Barton[3] for describing convex relaxations for parametric ODE sys-tems as solutions of hybrid discrete/ continuous systems whosecontinuous dynamics are constructed using McCormick’s relax-ations. Combining these approaches and overcoming severaltheoretical obstacles that emerge yield dynamic convex relax-ations that are unique solutions of auxiliary ODE systems withcontinuously differentiable right-hand sides. These new under-estimators have several useful properties: they may be inte-grated using off-the-shelf ODE solvers, they converge rapidly tothe original model as the parameter domain of interest shrinks,they may be computed automatically and accurately with theoriginal model as input, and they are amenable to treatmentby efficient adjoint sensitivity analysis techniques, to reducethe computation required for subgradient computation in globaloptimization. Implications and examples are discussed.

[1] K.A. Khan, H.A.J. Watson, and P.I. Barton, DifferentiableMcCormick relaxations, J. Glob. Optim., in press. DOI:10.1007/s10898-016-0440-6.

[2] G.P. McCormick, Computability of global solutions tofactorable nonconvex programs: Part I – convex under-estimating problems, Math. Program., 10:147-175, 1976.

[3] J.K. Scott and P.I. Barton, Improved relaxations for theparametric solutions of ODEs using differential inequali-ties, J. Glob. Optim., 57:143-176, 2013.

[4] A. Tsoukalas and A. Mitsos, Multivariate McCormickrelaxations, J. Glob. Optim., 59:633-662, 2014.

Tightening Convex Relaxations for Nonlinear Pro-grams via Adaptive, Multivariate Partitioning,Harsha Nagarajana, Mowen Lub, Site Wangb, RussellBenta, aLos Alamos National Laboratory, NM, USA,bClemson University, SC, United States. E-mail: har-sha@lanl.gov.

A primary requirement for the global optimization of non-convex mixed-integer multi-linear programs is the computationof a tight lower bound for the objective function being mini-mized. Classically, applying convex under and over-estimatorshierarchically on multi-linear functions lead to good lowerbounds provided the variable bounds are tight. Further, apply-ing the well-known spatial branch-and-cut methods lead toglobal optimality.

In this work, we propose a two-stage approach to strengthenpiecewise convex relaxations for mixed-integer nonlinear pro-grams (MINLP) with multi-linear terms. In the first stage,we exploit Constraint Programing techniques to contract thevariable bounds. We apply feasibility-based bound contrac-tion methods iteratively until a fixed point with respect to thebounds are achieved. In the second stage, we partition thevariables domains using an adaptive multivariate partitioningscheme. Instead of equally partitioning the domains of variablesappearing in multi-linear terms (predominantly common in theliterature), we construct sparser partitions yet tighter relaxationsby iteratively partitioning the variable domains in regions ofinterest (a parametrized partition around the current solutionof lower-bounding MILP). This approach decouples the num-ber of partitions from the size of the variable domains, leadsto a significant reduction in computation time, and limits thenumber of binary variables that are introduced by the parti-tioning. We further apply polyhedral cutting plane methodsto handle convex relaxations of higher-order monomial terms.Through the solution of several benchmark problems from theMINLPLib and Pooling problems literature, we demonstrate thesuperiority in the performance of our algorithm compared to thestate-of-the-art, commercial and open-source global optimiza-tion solvers (most recent versions). Further, we also general-ize our methods to a class of hard alternating-current optimalpower ow instances (NP-hard) with transcendental functions.For these instances, we provide global optimal solutions whosebest-known optimality gaps were 15%.

Session T2-B: Global Search StrategiesThursday, 10:30-12:00, PDRChair: Shi Pu

A Flocking-based Approach for Distributed Stochas-tic Optimization, Shi Pu, Alfredo Garcia, Univer-sity of Florida, Gainesville, FL, USA. E-mail: agar-cia@ise.ufl.edu.

In recent years, the paradigm of cloud computing has emergedas an architecture for computing that makes use of distributed(networked) computing resources. In this paper, we consider adistributed computing algorithmic scheme for stochastic opti-mization which relies on modest communication requirementsamongst processors and most importantly, does not require syn-chronization. Specifically, we analyze a scheme with N > 1independent threads implementing each a stochastic gradientalgorithm.

The threads are coupled via a perturbation of the gradient(with attractive and repulsive forces) in a similar manner tomathematical models of flocking, swarming and other groupformations found in nature with mild communication require-ments. When the objective function is convex, we show thata flocking-like approach for distributed stochastic optimizationprovides a noise reduction effect similar to that of a centralizedstochastic gradient algorithm based upon the average of N gra-dient samples at each step. The distributed nature of flockingmakes it an appealing computational alternative. We show thatwhen the overhead related to the time needed to gather N sam-ples and synchronization is not negligible, the flocking imple-mentation outperforms a centralized stochastic gradient algo-rithm based upon the average of N gradient samples at eachstep. When the objective function is not convex, the flocking-based approach seems better suited to escape locally optimalsolutions due to the repulsive force which enforces a certainlevel of diversity in the set of candidate solutions. Here again,we show that the noise reduction effect is similar to that associ-ated to the centralized stochastic gradient algorithm based uponthe average of N gradient samples at each step.

Solving Constrained Global Optimization Problemsby DIRECT and the Filter Method, M. FernandaP. Costa, Ana Maria A.C. Rocha, Edite M.G.P. Fer-nandes, University of Minho, Portugal. E-mail:arocha@dps.uminho.pt.

This paper presents a DIRECT-type method that incorporates afilter methodology to assure convergence to a feasible and opti-mal solution of nonsmooth and nonconvex constrained globaloptimization problems. The filter methodology is used to han-dle the general constraints of the problem by giving priority tothe selection of hyperrectangles with feasible center points, fol-lowed by those with infeasible and non-dominated center pointsand finally by those that have infeasible and dominated centerpoints. During hyperrectangles division, special rules to definea “preference point” by dimension and a “preference order” areproposed. Numerical results showing that the new DIRECTalgorithm is competitive when compared with other DIRECT-type methods are presented.

Frequency Domain Time Delay Estimation withOptimization Over Randomly Selected Lines,Ismet Sahina∗, Nuri Yilmazerb, aTexas Southern Uni-versity, Houston, TX, USA, bTexas A&M University-Kingsville, USA. E-mail: ∗ismet.sahin@tsu.edu.

Estimation of time delays between multiple signals which aredelayed and noisy forms of a transmitted signal has manyimportant applications in seismology, communication systems,and biology. A previous paper achieved subsample precisionin estimating time delays by minimizing the sum of pairwisephase-shifted DFTs of the signals. However the accuracy of thisapproach depends on the choice of initial time delays which areoften not known a priori. In particular deterministic optimiza-tion methods starting with an initial delay vector that is far fromthe true delay vector often leads to an erroneous time delayvector. This paper proposes a population based optimizationapproach which slices the search space along randomly selectedlines and then performs one dimensional searches along theselines. This approach also involves mutation and crossover oper-ations in order to avoid local minima. Comparison of thisapproach to the Differential Evaluation method and our previ-ous successive minimization method demonstrates that the pro-posed approach produces superior estimation results, in partic-ular for signals with low signal to noise ratios.

[1] Ismet Sahin, Marwan A. Simaan, and Anthony J. Kears-ley, Successive Frequency Domain Minimization for TimeDelay Estimation, Signal Processing, vol. 98, pp. 96-101,2014.

[2] Ismet Sahin, Random Lines: A Novel PopulationSet-based Evolutionary Global Optimization Algorithm,Lecture Notes in Computer Science, Springer, vol.6621/2011, pp. 97-107, 2011.

[3] G. Clifford Carter, Coherence and time delay estimation:an applied tutorial for research, development, test, andevaluation engineers, IEEE Press, 1993.

[4] Ismet Sahin, Nuri Yilmazer, and Marwan A. Simaan,A Method for Subsample Fetal Heart Rate EstimationUnder Noisy Conditions, IEEE Transactions on Biomedi-cal Engineering, 57(4):875-883, April 2010.

Coordinated Branching in Interval Algorithms forGlobal Optimization, Min Sun, The University ofAlabama, Tuscaloosa, AL, USA. E-mail: msun@ua.edu.

Interval algorithms have become one of well-known types ofsearch methods for global optimization. Branching in the searchdomain is considered as a standard approach adopted in thebranch part of the interval method. Based on a very limitedamount of prior trials of branching in the function value space,this article reports some preliminary results of a more system-atic investigation of coordinated branching in both the searchdomain and the function value space. The investigation aimsat identifying advantages and disadvantages of this approach.A fair amount of numerical experiments are conducted to illus-trate our preliminary conclusions.

Session T3-A: Algorithms and ApplicationsThursday, 1:30-3:00, 1011BChair: Fengqi You

Distributionally Robust Mixed-Integer Linear Pro-grams with Moment Information: Global Optimiza-tion Strategy and Scheduling Applications, ChaoShang, Fengqi You∗, Cornell University, Ithaca, NY,USA. E-mail: ∗fengqi.you@cornell.edu.

Mixed-integer linear programming (MILP) has pervasive appli-cations associated with resource-assigning problems. Param-eters uncertainties, however, exert immense influences on thesolution performance, and even compromise the feasibility ofconstraints of special interests. A distributionally robust mixed-integer linear programming model is proposed in this work.Uncertain parameters are assumed to follow ambiguous distri-butions with known second-order moments, which can be esti-mated from historical data with relative ease. It also enablesinjections of support information, which is typically utilized byrobust optimization. To control the risk of constraint violations,chance constraints along with conditional value-at-risk (CVaR)approximations are adopted. By disentangling the relationshipbetween discrete variables and continuous variables, chanceconstraints are tractably reformulated as linear matrix inequal-ities (LMIs). Then the entire problem reduces to a mixed-integer semi-definite program (MISDP). A tailored generalizedBenders decomposition algorithm is developed to approach theglobal optimum of the MISDP by leveraging strong duality ofpositive semi-definite cones inherited to subproblems, alongwith its implementation issues investigated. A process schedul-ing example demonstrates that the proposed approach enablesan improved utilization of information within massive data andyields a reasonable data-driven solution to resource-assigningproblems.

Packing Disks in a Circular Container via VoronoiDiagram, Joonghyun Ryu, Mokwon Lee, Donguk Kim,Kokichi Sugihara, Deok-Soo Kima∗, aHanyang Uni-versity, Korea, Gangneung-Wonju National University,Korea, Meiji Institute for Advanced Study of Mathemati-cal Sciences, Japan. E-mail: ∗dskim@hanyang.ac.kr.

Given the disks in the plane, the disk packing problem is to findthe smallest container which encloses all the disks without anyoverlap. There are some options: Disk size may be either equalor unequal; Container may be a circle, a rectangle, or a simplepolygon. We present the packing of the unequal-sized disks ina circular container, which is to determine the center and radiusof the smallest container and the centers of the correspondingdisks.

The disk packing problem can be formulated as a nonlin-ear program with a linear objective function and quadratic con-straints. This problem is proved NP-hard and thus heuristicalgorithms are inevitable. Due to its theoretical and practicalimportance, the disk packing problem has been studied by manyprevious researchers. It turns out that the vacancy information(called void clearance) around disks could be exploited to getgood feasible solutions from the previous studies.

We develop an efficient heuristic to solve the disk packingproblem using the Voronoi diagram (VD). The VD of disks is

the tessellation of the space such that each cell of the tessellationconsists of the locations closer to the corresponding disk thanothers. Given the VD, various spatial reasoning around diskscan be done very conveniently and efficiently. The proposedalgorithm computes the void clearance around disks using VDwhich is used to find the candidate location of each disk. Hencethe efficient construction of the VD facilitates the proposed diskpacking heuristic. We develop an efficient algorithm to con-struct the VD in case that each disk is incrementally changedand apply this algorithm to the disk packing heuristic. It turnsout that the proposed algorithm very efficiently computes theimproved solution compared to the previous studies.

A Biased Random-key GA for a 2-Dimension Cut-ting Problem with Defects, José Fernando Gonçalves,Universidade do Porto, Portugal. E-mail:jfgoncal@fep.up.pt.

In this paper, we address a two-dimensional (2D) non-guillotinecutting problem, where a fixed set of small rectangles is to becut from a large stock rectangle with defects so as to maximizethe value of the rectangles cut. A hybrid approach combininga placement procedure with a biased random-key genetic algo-rithm (BRKGA) is used. The approach is tested on a set ofbenchmark instances taken from the literature and comparedwith other approaches. The experimental results validate thequality of the solutions and the effectiveness of the proposedBRKGA approach. Supported by Project “NORTE-01-0145-FEDER-000020” financed by the North Portugal RegionalOperational Programme (NORTE 2020), under the PORTU-GAL 2020 Partnership Agreement, and through the EuropeanRegional Development Fund (ERDF).

Joint Production and Transportation Schedul-ing in Flexible Manufacturing Systems,Dalila B.M.M. Fontesa, Seyed Mahdi Homayounia,b,aUniversidade do Porto, Porto, Portugal, bIslamic AzadUniversity, Esfahan, Iran. E-mail: fontes@fep.up.pt.

This work addresses the problem of simultaneous schedulingproduction and transportation activities. Production schedulingrefers to sequencing operations on machines, while transporta-tion scheduling refers assigning to Automated Guided VehiclesAGVs the transportation of jobs between machines. Since pro-duction scheduling in flexible manufacturing systems is highlydependent on the material handling system these two prob-lems should be addressed simultaneously (Sabuncuoglu andHommertzheim 1992; Bilge and Ulusoy 1995; Le-Anh andDe Koster 2006; Zhen et al, 2014). Although productionscheduling and AGVs scheduling problems have been vastlyresearch, there are not many contributions on the simultane-ous scheduling of AGVs and production activities. Since bothmachine scheduling and AGVs scheduling problems are NP-hard (Ulusoy et al, 1997), the simultaneous scheduling prob-lem is also NP-hard. Therefore, it is not surprising that thesolution approaches proposed are heuristic in nature. Actu-ally, thus far only two MIP models (Bilge and Ulusoy, 1995;Zhen et al, 2014) have been proposed and only for one ofthem the authors report having solved it. There is contro-versy regarding the 82 benchmark problem instances proposedby Bilge and Ulusoy (1995). According to Abdelmaguid et al(2004) some of the results reported by Ulusoy et al (1997) are

invalid and according to Zhen et al (2014) those of Babu etal (2010) are doubtful, as for 32 of the instances they reportobjective function values lower than the lower bounds reportedby Ulusoy et al (1997). In addition, optimal solutions to theseproblem instances have yet to be reported. (Although, Abdel-maguid et al (2004) state that the ones produced by a slidingtime window heuristic reported in Bilge and Ulusoy (1995)are optimal.) Therefore, we propose a new MIP formulationand to solve it to optimality for some of these instances.

[1] Abdelmaguid, T. F., A. O. Nassef, B. A. Kamal, andM. F. Hassan. 2004. A Hybrid GA/Heuristic Approachto the Simultaneous Scheduling of Machines and Auto-mated Guided Vehicles. International Journal of ProductionResearch 42 (2): 267281.

[2] Bilge, Ü., and G. Ulusoy. 1995. A Time Window Approachto Simultaneous Scheduling of Machines and MaterialHandling System in an FMS. Operations Research 43 (6):10581070.

[3] Babu, A. G., J. Jerald, A. N. Haq, V. M. Luxmi, and T.P. Vigneswaralu. 2010. Scheduling of Machines and Auto-mated Guided Vehicles in FMS Using Differential Evolu-tion. International Journal of Production Research 48 (16):46834699

[4] Le-Anh, T., and M. B. M. De Koster. 2006. A Review ofDesign and Control of Automated Guided Vehicle Systems.European Journal of Operational Research 171: 123.

[5] Sabuncuoglu, I., and D. L. Hommertzheim. 1992. DynamicDispatching Algorithm for Scheduling Machines and Auto-mated Guided Vehicles in a Flexible Manufacturing Sys-tem. International Journal of Production Research 30 (5):10591079.

[6] Ulusoy, G., F. Sivrikaya-Şerifoǧlu, and Ü. Bilge, A geneticalgorithm approach to the simultaneous scheduling ofmachines and automated guided vehicles. Computers &Operations Research, 1997. 24(4): p. 335-351.

[7] Zheng, Y., Y. Xiao, and Y. Seo. 2014. A tabu search algo-rithm for simultaneous machine/AGV scheduling prob-lem, International Journal of Production Research, 52(19):5748-5763.

Session T3-B: Biochemical/Energy SystemsThursday, 1:30-3:00, PDRChair: Angelo Lucia

Metabolic Pathway Analysis Using a Nash Equilib-rium Approach, Angelo Luciaa, Peter A. DiMaggiob,Diego Alonso Martinezb, aUniversity of RhodeIsland, USA, bImperial College London, UK. E-mail:aalucia@uri.edu.

A novel approach to metabolic network analysis using a NashEquilibrium (NE) formulation is proposed in which enzymesare considered players in a multi-player game. Each player hasits own payoff function with the objective of minimizing theGibbs free energy associated with the biochemical reaction(s) itcatalyzes subject to elemental mass balances while the networkobjective is to find the best solution to the sum of the player pay-off functions. As a result, any NE solution may not be best forall players. Key advantages of the NE approach include the abil-ity to model (1) sub-networks as closed systems, (2) aqueouselectrolyte solution behavior, (3) the consumption/productionof co-factors, (4) regulatory controls, and (5) charge balancing.Unlike conventional flux balance analysis (FBA) formulationswhich rely on linear programming, the proposed Nash equi-librium formulation results in a set of nonlinear programming(NLP) sub-problems that guarantee thermodynamic consistencyand are more demanding to solve. A direct substitution solutionmethodology for converging feedbacks is described. Results forthe Krebs cycle and the mevalonate pathway are used to demon-strate the efficacy of the NE approach while comparisons withboth FBA and a wide range of experimental metabolic indi-cators are used to show that it represents a paradigm shift inmetabolic network analysis.

Constrained Grey-Box Multi-Objective Opti-mization Framework for Optimal Design ofEnergy Systems, Burcu Beykal, Fani Boukouvala,Christodoulos A. Floudas , Efstratios N. Pistikopou-

los, Texas A&M University, USA. E-mail: bur-cubeykal@tamu.edu.

Energy systems are characterized by large, diverse num-ber of components in which they form an integrated com-plex multi-scale network. The complexity of these multi-scalemodels is further amplified with the generation of large num-ber of data, which makes them harder to express with mech-anistic formulations. In such models, derivative informationis often unavailable or unreliable, and the direct use of opti-mization methods is usually rather prohibitive [1]. Thus, theglobal optimization of complex energy systems from an eco-nomic and sustainability perspective poses a formidable chal-lenge. Derivative-Free Optimization (DFO) methods are com-monly utilized for the optimization of models that lack theclosed-form equations or models that strongly rely on input-output data. We have previously introduced the constrainedgrey-box optimization algorithm called ARGONAUT [2] thatcouples tractable surrogate approximations, which accuratelyrepresent any unknown correlations, with the state-of-the artMixed-Integer Nonlinear Programming (MINLP) global opti-mization solver ANTIGONE [3]. In this work, we further

expand the existing algorithm to handle mixed-integer program-ming and multi-objective optimization problems, and test theproposed framework on a case study based on the energy sys-tem design for commercial buildings such as a supermarket [4].We provide solutions to two cases; (a) optimal design basedon the single-objective economic behavior or the environmentalimpact (b) optimal design based on the multi-objective designcriteria, simultaneous optimization of economic and environ-mental behavior. We demonstrate that our framework enablesoptimization of expensive simulation-based models under mul-tiple competing objectives in a computationally efficient way.The results are presented in the form of Pareto-frontier, com-pare favorably to the model-based solution in [4].

[1] Boukouvala, F.; Misener, R.; Floudas, C. A. Eur. J. Oper.Res. 2015, 252, 701 – 727.

[2] Boukouvala, F.; Floudas, C. A. Optim. Lett. 2014, 1 – 19.[3] Misener, R.; Floudas, C. A. Journal of Global Optimiza-

tion 2014, 59, 503–526.[4] Liu, P.; Pistikopoulos, E. N.; Li, Z. Energy Policy 2010,

38, 4224–4231.

Multilevel Optimization for Resilient PlanningOf Interdependent Water and Energy Systems,Shanshan Hou, Neng Fan, University of Arizona. E-mail:shanshanh@email.arizona.edu.

Water is an important player for decisions in energy system. Itis used for many phases of energy production. Global waterwithdrawal for energy production in 2010 is around 15% ofthe world’s total water withdrawals. As more renewable energyresources, which are highly water-intensive, are planned to beintegrated, the percentage is expecting to grow. Also, energynetwork supply power for water distribution and extraction. TheUS consumes at least 521 million MWh a year for water-relatedoperations, and this is equivalent to 13% of total electricity con-sumption. These two infrastructure systems could be modeledas an interdependent network.

In this talk, we not only consider their operations and man-agement of both systems, but also the planning stage, whichcontains analysis of the possible failures to ensure the systemresiliency. Connecting the water and energy systems togetheras an interdependent network is different from the current state-of-the-art approach, which typically treats planning and oper-ations/management problems in a separate way. We build themultilevel optimization model to simulate the water and energyrelevant flows. In planning period, this model consists of thefacilities that could be built in water network and different gen-eration stations in energy network. In operation/managementperiod, it expresses the flow connection between water andenergy networks. Through applying multiple coefficients fordifferent energy generations, this optimization model includesdemands and flows of both water and energy.

In preliminary experiments, we tested the model in IEEE6-Bus and EPANet 1-Tank-1-Pump interdependent networkexample. In the IEEE 6-Bus network, it contains 3 solar gen-erators. It supplies power for tank, pump, and translating lines.On the other side, the generators need the water from tank andpump. We aim to simulating in 5-year planning period and mak-ing decisions for both water and energy network operations.And the objective is to save money for planning and manage-ment of the interdependent network, such as building new facil-ities, generating power and transporting water.

Understanding Electricity Consumption Pattern ofElectric Heaters, Ulaş Çakir, Olgun Aydin, Big DataResearch and Development Group, STM SavunmaTeknolojileri Mühendislik ve Ticaret A.Ş. E-mail:{ucakir,olgun.aydin}@stm.com.tr.The development of the consumer industry also linearly affectedthe amount of energy consumed in homes. It is not knownwhether the rate of increase of energy production can be reachedto the number and type of new generated devices. Furthermore,if the energy efficiency of the devices can not increase, it is nota science fiction for a near future to establish a power plant inevery house. We sought to approach the problem of optimiza-tion for improving the electricity consumption rates of homeappliances, which is the subject of many researches, with a dif-ferent perspective.

In this study, REFIT (Personalized Retrofit Decision SupportTools for UK Homes using Smart Home Technology) Electri-cal Load Measurements dataset was used. The dataset includeselectrical consumption in Watts for 20 households from theLoughborough area over the period 2013 - 2014 sampled at 8second intervals. Many different kinds of appliances had beenmonitored like fridge, freezer, washer dryer, washing machine,dishwasher, computer, television, electric heater, toaster, kettle,tumble dryer and so on.

Aims of this study are investigating electricity consump-tion of electric heaters Probability Distribution Function (PDF)among many complex distribution families and generatingupper and lower record values PDF to be able to calculate prob-ability of upper and lower record values exceeding some thresh-olds. For fitting distribution to electricity consumption of elec-tric heaters, started with calculating likelihood functions of thecandidate distributions. After that, parameters of the candidatedistributions were estimated. To find optimal parameters, maxi-mized the likelihood functions using Efficient Global Optimiza-tion (EGO) which is a Kriging Metamodeling technique basedoptimization method. Finally, PDF of upper and lower recordvalues were created by the aid of Record Values theory comesfrom Order Statistics.

Session T4-A: Discrete ProblemsThursday, 3:30-5:00, 1011BChair: Shaojie Tang

Profit Maximization with Multiple Products,Jing Yuan, Weili Wu, Zhao Zhang, Shaojie Tang, Ding-Zhu Du∗, University of Texas at Dallas, USA. E-mail:∗dzdu@utdallas.edu.

In profit maximization, a nonmotone submodular function withpossible negative value is considered to be maximized. Withmultiple products, a knapsack constraint would be introduced.Therefore, this work is on nonmonotone submodular maximiza-tion with knapsack constraint and with possible negative value.In general, this problem has no good approximation solution.However, for special case studied in this paper, the situation isdifferent.

Approximation Algorithms for the Group FacilityLocation Problems, Sai Jia, Dachuan Xua∗, DongmeiZhangb, aBeijing University of Technology, P.R. China,bShandong Jianzhu University, P.R. China. E-mail:∗xudc@bjut.edu.cn.

This work introduces a group facility location problem. Inthis problem, clients are divided into several groups and eachgroup’s clients must be served by the same facility. We for-mulate this problem as a set cover type integer linear pro-gram. Using primal-dual technique, we present a (2r + 1)-approximation algorithm, where r is a ratio of group’s cardi-nality between the second large one and the smallest one. Fur-thermore, we study the soft-capacitied group facility locationproblem and offer a 2(2r + 1)-approximation algorithm.

A Local Search Approximation Algorithm for theSum of Squares Facility Location Problem, DongmeiZhanga, Dachuan Xub∗, Peng Zhangc, Zhenning Zhangb,aShandong Jianzhu University, P.R. China, bBeijing Uni-versity of Technology, P.R. China, cShandong University,P.R. China. E-mail: ∗xudc@bjut.edu.cn.

In this paper, we study the sum of squares facility location prob-lem (SOS-FLP) which is an important variant of k-means clus-tering. In the SOS-FLP, we are given a client set C ⊂ Rp and auniform center opening cost f > 0. The goal is to open a finitecenter subset F ⊂ Rp and to connect each client to the closestopen center such that the total cost including center opening costand the sum of squares of distances is minimized. The SOS-FLP is introduced firstly by Bandyapadhyay and Varadarajan(2016) which offer a PTAS for the fixed dimension case. Usinglocal search technique, we offer a first constant approximationalgorithm for the SOS-FLP with general dimension. By explor-ing the structures of local and optimal solutions, we claim thatthe approximation ratio is 7.7721.

Robust Multi-Phase Covering Problem, Ou Sun,Neng Fan, University of Arizona, USA. E-mail:suno,nfan@email.arizona.edu.

Many sensor placement problems, such as deployment of sen-sors in water distribution network for monitoring and contam-ination detection, and installation of phasor measurement units(PMUs) in power systems to collect information for control, canbe converted to covering problems. Because of high expensesof sensors, in practice the minimum number of sensors is usu-ally placed in multiple periods, to reduce the financial burden,and also to maintain certain levels of observability. The fullfunction of sensors will be achieved after the deployment ofall required sensors. This paper first presents a brief introduc-tion of covering problems and set cover problem, and then for-mulates the multi-phase sensor placement problem by mixedinteger programming approaches for covering problems. Con-sidering the potential loss of connections between sensors, thedeterministic model will be extended to study probabilistic cov-ering problems for robust multi-phase covering problems. AsPMUs are becoming widely used in power systems to determinethe health of the system, this paper uses PMU placement prob-lem and multistage PMU placement problem as a special case,considering the zero-injection-bus property in power systems,to validate the proposed models and algorithms, and numericalexperiments will also be performed.

Session T4-B: Continuous ProblemsThursday, 3:30-5:00, PDRChair: Pham Duy Khanh

Necessary and Sufficient Conditions for QualitativeProperties of Infinite Dimensional Linear Program-ming, Pham Duy Khanha, Tran Hong Mob, Tran ThiTu Trinhc, aUniversidad de Chile, Chile, bTien GiangUniversity, Vietnam, cHo Chi Minh City University ofPedagogy, Vietnam. E-mail: apdkhanh@dim.uchile.cl,bmohongtran@yahoo.com.vn, ctutrinhkt94@gmail.com.

Necessary and sufficient conditions for qualitative propertiesof infinite dimensional linear programming such as solvability,duality, and complementary slackness conditions are studied inthis paper. As illustrations for the results, we investigate theparametric version of Gale’s example.

Finding the Global Infimum of an ArbitraryLebesgue Measurable Function, Michael Naaman,Senior Economist, Christensen Associates. E-mail:mtnaaman@LRCA.com.

In this paper, a framework is developed to find the global infi-mum of an arbitrary Lebesgue measurable function. We gen-eralize local minimizers to what we call local infimizers. Theset of local infimizers of a measurable function will coincideexactly with the set of local minimizers of its lower envelope,F , which is lower semicontinuous.

If one can approximate the optimization problem, F , withan epi-convergent sequence of functions, Fn, then the solutionof the approximate optimization problem may converge to thesolution of the original problem. However, this is only helpfulif the epi-convergent sequence of functions is sufficiently wellbehaved.

For instance, the sum of epi-convergent functions may notbe epi-convergent. To address some of these shortcomings, wewill require that for every point, (x,F(x)), in the graph of thetarget function, there exists a sequence of points, (xn,Fn(xn)),in the graph of Fn converging to (x,F(x)), furthermore, thespeed of convergence is uniformly bounded for every point inthe domain, which we are calling big convergence.

Big convergence gets around the summation problembecause one can easily embed the sequences in a higherdimensional space which preserves big convergence and epi-convergence.

Next, we prove that for any lower semicontinuous function,there exists a sequence of epi-convergent analytic functions thatalso converge bigly. The strategy is to approximate a lowersemicontinuous function with a sequence of simple functionsin the standard fashion. Since {x|F > c} is open, then theWhitney covering lemma can be used to approximate the openset with a finite number of well behaved Whitney cubes result-ing in a sequence of step functions converging pointwise. Theindicator functions making up the step function can be approx-imated with analytic mollifier-like functions.

The power series of the analytic sequence can be used toconstruct a polynomial that also satisfies the desired proper-ties. Furthermore, the sequence of global minimums convergesto the global infimum of F . Some examples of this smooth-ing technique are given for the topologist’s sine curve, Dirichlet

function and traveling salesman problem. A potential optimiza-tion algorithm is also discussed, which allows the set of globalinfimizers to be estimated.

Critical Multipliers in Variational Systemsvia Second-Order Generalized Differentiation,Boris Mordukhovicha, Ebrahim Sarabib∗, aWayneState University, bMiami University, USA. E-mail:∗sarabim@miamioh.edu.

In this talk we introduce the notions of critical and noncriti-cal multipliers for variational systems and extend to a generalframework the corresponding notions by Izmailov and Solodovdeveloped for classical Karush-Kuhn-Tucker (KKT) systems.It has been well recognized that critical multipliers are largelyresponsible for slow convergence of major primal-dual algo-rithms of optimization. Concentrating on a polyhedral subd-ifferential case and employing recent results of second-ordersubdifferential theory, we obtain complete characterizations ofcritical and noncritical multipliers via the problem data. It isshown that noncriticality is equivalent to a certain calmnessproperty of a perturbed variational system and that critical mul-tipliers can be ruled out by full stability of local minimizersin problems of composite optimization. For the latter classwe present the equivalence between noncriticality of multipli-ers and robust isolated calmness of the associated solution mapand then derive explicit characterizations of these notions viaappropriate second-order sufficient conditions.

Geometric Conditions of Reduction of Exhausters,Majid Abbasov, Saint Petersburg State University, Rus-sia. E-mail: abbasov.majid@gmail.com.

Exhausters are recently appeared concept in nondifferentiableoptimization, proposed by V.F. Demyanov. Despite the novelty,they showed themselves as an effective tool for study of nons-mooth functions. Optimality conditions were described in termsof these objects. This paved the way to construct new algo-rithms for optimization of nonsmooth functions. Exhausters arefamilies of convex compact sets that allow to represent a princi-pal part of the increment of the studied function in the form ofminimax or maximin of linear functions. These families are notuniquely defined. The smaller the family, the less are compu-tational costs when using algorithms. So an important problemof reducing exhausters appears. First this problem was stud-ied by V.A. Roshchina, who introduced definitions of minimalexhausters as well as the necessary and sufficient conditions forthe minimality. She also provided a technique of reduction ofthe family, based upon these conditions. In this work other con-ditions and procedures of reduction that has more transparentgeometric meaning are proposed. These new conditions can beimplemented easier in some real problems.

A Numerical Method for Solving Differential Inclu-sions with Fixed Right End, Alexander Fominyh, SaintPetersburg State University, Russia. E-mail: alexfom-ster@mail.ru.

The report explores differential inclusions with the given set-valued convex mapping. The final interval [0, T ] is considered,

where T > 0 is a given moment of time. It is required to finda solution of the differential inclusion, which satisfies the ini-tial condition x(0) = x0 and the final state x(T ) = xT , herex0, xT ∈ Rn are given vectors. With the help of support func-tions the original problem is reduced to minimization of a func-tional in the space of partially differentiable functions in theinterval [0, T ]. In case of continuous differentiability of a sup-port function of the set-valued mapping in phase variables thisfunctional is Gateaux differentiable. So we find the Gateauxgradient of this functional and obtain necessary and sufficientconditions for a minimum. On the basis of these conditions thenumerical method for solving the original problem is described.Numerical examples illustrate the method realization.

Session F1: Carathéodory PrizeFriday, 9:00-10:00, 1011CChair: Yaroslav Sergeyev

Some Recent Advances in Greedy Randomized Adap-tive Search Procedures, Mauricio Resende, Ama-zon.com, USA. E-mail: resendem@amazon.com.

The Greedy Randomized Adaptive Search Procedure, orGRASP, was introduced as a metaheuristic for combinatorialoptimization in a 1995 paper in the Journal of Global Optimiza-tion. Since then, GRASP has been widely applied to solve prac-tical combinatorial optimization problems in a wide range offields. In this talk we address some recent developments thathelp us understand how GRASP works.

Global Optimization as Rational Decision Makingunder Uncertainty, Antanas Žilinskas, Vilnius Univer-sity, Lithuania. E-mail: antanas.zilinskas@mii.vu.lt.

A review is presented on global optimization methods basedon the principles of rational decision making under uncertainty.The considered methods are aimed at expensive black boxobjective functions. Optimization problems of that type arequite frequent in practical applications where objective func-tions are available as long running computer programs, and theirproperties are difficult to elicit. Uncertainty in the propertiesand expensiveness of objective function complicate the solu-tion of the optimization problem. To substantiate a reasonablemethod for such problems we propose to appeal to the theoryof rational decision making under uncertainty. The followingthemes are discussed in the talk:

1. The selection of a statistical model of objective func-tions; the suitability of several stochastic functions fora model is discussed, possible generalizations are sup-posed.

2. The postulates of a rational search strategy are formu-lated, and the corresponding algorithms are described.

3. New ideas of definition of search strategy via multicrite-ria decision making are discussed.

4. The implementation of algorithms.

5. Generalization of the mentioned above ideas and resultsto the problems of multi-objective optimization.

6. Visualization of Pareto optimal solutions/decisions.

Carathéodory Prize

The Constantin Carathéodory Prize of the InternationalSociety of Global Optimization is awarded biannually toan individual (or a group) for fundamental contributionsto theory, algorithms, and applications of global opti-mization. The prize is awarded for outstanding work thatreflects contributions that have stood the test of time. Thecriteria include scientific excellence, innovation, signifi-cance, depth, and impact. The prize carries a cash awardof US $2,000 and a certificate.

Recepients2011 Hoang Tuy2013 Panos M. Pardalos2015 Christodoulos A. Floudas, Ignacio E. Grossmann,

and Nikolaos Sahinidis2017 Mauricio Resende and Antanas Žilinskas

Session F2-A: Problems with Special StructureFriday, 10:30-12:00, 1011BChair: Ruey-Lin Sheu

Highlight on Recent Progress for the TrustRegion Subproblem and Its Variants, Yong Hsiaa∗,Ruey-Lin Sheub†, aBeihang University, Beijing, P. R.China, bNational Cheng-Kung University, Taiwan. E-mail: ∗dearyxia@gmail.com, †rsheu@mail.ncku.edu.tw.

The talk aims to highlight important feature and results of thetrust region subproblem and its variants. The trust region sub-problem minimizes globally a possibly nonconvex quadraticfunction over the unit ball, whereas the generalization we dis-cuss and review here is either to replace the unit ball with ageneral quadratic function; or to add additional linear inequal-ity constraints to it, but not both. It is not until very recent thatpeople completely understood the aforementioned variants ofthe trust region subproblem, so the results are relatively new andnot known to many audiences in the society. As many resultsare scattered in some highly technical papers and many wereindeed contributed by the same authors of this talk, we feel thatit is necessary to address the core concepts and highlight theconnections in between the technicality of different extensions.We shall focus on the polynomial solvability of the problemseither by exploring the strong duality through a tight SDP relax-ation; or by some dimensional conditions; or by an inductionscheme which reduces recursively the extensions to the basictrust region subproblem.

Kuhn-Tucker Invexity of Non-convex Optimisa-tion Problems with Two Degrees of Freedom,Ksenia Bestuzheva, Hassan Hijazi, The AustralianNational University, Data61-CSIRO, Canberra 2601,Australia. E-mail: Ksenija.Bestuzheva@data61.csiro.au.

We study conditions under which every Karush-Kuhn-Tucker(KKT) point of a non-convex optimisation problem is a globaloptimiser. This property is known as KT invexity. Non-convexoptimisation problems are generally NP-hard, but KT invexityallows finding globally optimal solutions using interior pointmethods. In this work, we focus on problems with two degreesof freedom and a convex objective function. We provide suffi-cient conditions under which a problem is KT invex. This resultis used to prove KT invexity of the Optimal Power Flow prob-lem on a one-line electrical network with two generators andrealistic parameter values.

Dimension Decomposition Algorithm for 1-ConvexBox-constrained Minimization, Damien Gerard,Quentin Louveaux, University of Liège, Belgium. E-mail:damien.gerard@ulg.ac.be.

A 1-convex function is a function f : Rn → R such that any fix-ing of (n− 1) variables produces a convex function. In generala 1-convex function is not convex. For smooth functions, the1-convexity property would come down to having the functionHessian diagonal nonnegative. We aim at finding the globalminimum of 1-convex box-constrained functions. We prove

how the 1-convex property and a dimension decomposition canbe used to quickly derive upper and lower bounds on the func-tion over subsets of the feasible set. An exact tailor-made solveris developed and several major aspects of its implementation arediscussed. We also present new heuristics to further improvethe solver efficiency. Numerous instances are benchmarked andthe solver performance is compared to that of other well-knownglobal optimization software.

On Upper Bounding of 0-1 Multilinear Functionfor Boolean Logical Pattern Generation, Kedong Yan,Hong Seo Ryoo∗, Korea University, Seoul, The Republicof Korea. E-mail: ∗hsryoo@korea.ac.kr.

Logical Analysis of Data (LAD) is a combinatorialoptimization-based machine learning method. A key stage ofLAD is pattern generation, where useful knowledge in a train-ing dataset of two types of, say, + and − data under analysis isdiscovered. We showed that LAD pattern generation can be castas a 0-1 multilinear program (MP) with a single 0-1 multilinearconstraint [1]:

(PG) : maxx∈{0,1}2n

f (x) :=∑

i∈S+

∏j∈Ji

(1− x j)

subject tog(x) :=

∑i∈S−

∏j∈Ji

(1− x j) ≤ 0

The unconstrained maximization of f (without g) is straight-forward, thus the main difficulty of globally maximizing (PG)arises primarily from the presence of g and the interactionbetween f and g. Our previous study dealt with the task of lin-earizing g. Namely, we employed a graph theoretic analysis ofdata to discover sufficient conditions among neighboring dataand also neighboring groups of data for ‘compactly linearizing’g in terms of a small number of stronger valid inequalities, ascompared to what is obtained via 0− 1 linearization techniquesfrom the literature [2].

Extending this line of research, we analyze neighborhoodproperties among + and − data on a graph to develop a con-cave overestimation scheme for f based on its analysis in con-junction with g. To the best of our knowledge, this is the firsttime that a set of monomials in the objective function and con-straint(s) are analyzed together for obtaining a tighter relaxationof 0−1 MP. We present a set of sufficient conditions for obtain-ing a compact linearization of (PG) and numerically demon-strate their utility on benchmark datasets, in comparison withthe existing methods from the literature.

[1] Kedong Yan, Hong Seo Ryoo: 0-1 multilinear program-ming as a unifying theory for LAD pattern generation.Discrete Applied Mathematics 218, 21–39 (2017).

[2] Kedong Yan, Hong Seo Ryoo: Strong valid inequalitiesfor Boolean logical pattern generation. Journal of GlobalOptimization (under review)

Session F2-B: Data AnalysisFriday, 10:30-12:00, PDRChair: Melis Onel

Opportunities for Global Optimization in Big DataAnalytics, Melis Onel, Yannis A. Guzman, ChrisKieslich, Christodoulos A. Floudas , Efstratios N. Pis-tikopoulos, Texas A&M University, USA. E-mail:melis@tamu.edu.

Advancements in technology has enabled the rapid increase inthe ability to collect enormous amounts of data – “Big Data” –in real time leading to improvements in diagnostics and deci-sion making in various chemical processes [1]. Today, extract-ing valuable insights from Big Data is essential in developingsmart manufacturing methods in process systems engineering,sustaining safe operation in industrial processes and enhancingpersonalized healthcare [2].

In this talk, we will present and discuss optimization-basedframeworks in big data analytics that develop models for data-driven, real-time decision making. Central to the discussion isthe high-dimensional nonlinear feature selection problem whereopportunities for global optimization arise. Feature selection(a.k.a dimensionality reduction) is crucial to encapsulate highlynonlinear and interconnected nature of the data inputs which inturn improves model accuracy and robustness. We will presentoptimization model formulations in Support Vector Machinesetting that cast the high-dimensional feature selection prob-lem into implicit nonlinear feature space, resulting in minimum-maximum mixed-integer nonlinear optimization problems [3].Computational studies show that new algorithms outperformexisting state-of-the-art methods in the machine learning liter-ature and show great promise for accurate, real-time decisionmaking from Big Data in chemical process operations.

[1] Beck, David AC, et al. “Data science: Accelerating inno-vation and discovery in chemical engineering.” AIChEJournal 62.5 (2016): 1402-1416.

[2] Qin, S. Joe. “Process data analytics in the era of big data.”AIChE Journal 60.9 (2014): 3092-3100.

[3] Guzman, YA, et. al. “A global optimization framework forfeature selection with Support Vector Machines.” Submit-ted.

Hybrid Clustering based on Text and (Hyper-)Graphusing Nonnegative Matrix Factorization, Rundong Du,Barry Drake, Haesun Park, Georgia Institute of Technol-ogy, USA. E-mail: rdu@gatech.edu.

We present a method for clustering hybrid data that containsboth text contents and (hyper-)graph structure. The methodis based on constrained low rank approximation and the mainidea is to jointly optimize the Nonnegative Matrix Factoriza-tion (NMF) objective for text clustering and the SymmetricNMF (SymNMF) objective for graph clustering. We propose aneffective algorithm for the joint objective function, based on theblock coordinate descend (BCD) method. The proposed methodis formulated for the situation where the text contents are asso-ciated with graph nodes. The method can also be applied witha natural conversion of the problem when a hypergraph is usedinstead or the text contents are associated with (hyper-)graphedges.

Experiments show that the hybrid method outperforms eachof its components alone (NMF and SymNMF) in clusteringquality and has potential applications to citation recommen-dations of papers and patents, organization hierarchy detec-tion and team/department detection. The method proposed inthis paper can also be applied to general data expressed withboth feature space vectors and pairwise similarities and can beextended to the case with multiple feature spaces or multiplesimilarity measures.

Automatic Text Summarization with Multi-objectiveOptimization (ATS-MOO), Chihoon Jung, RituparnaDatta, Aviv Segev, KAIST, South Korea. E-mail: chi-hoon.jung@kaist.ac.kr.

Multi-document summarization aims to solve information over-load problem by providing condensed summary from a givenset of documents on a topic. In this work, we propose anovel multi-objective optimization approach for generic multi-document summarization. The proposed method is based ontwo conflicting objective functions, namely, coverage and diver-sity. The generated summary aims to maximize the content cov-erage of the original documents, while maximizing the diver-sity between sentences within the summary. We apply k-meansclustering to the original document set and use cluster centroidsto extract topics for the coverage computation. We sum thecosine similarity of each pair of sentences in the summary toestimate diversity. The similarity is estimated based on theVector Space Model (VSM) representation of the text snippetswith TF-IDF (term frequency - inverse document frequency)term weighting scheme. The advantage of our method comesfrom using a global optimization technique, so that the problemis considered in a global perspective as compared to a greedyapproach that may get stuck on the local optimum. The noveltyof the proposed method is in the ability to generate multiplePareto optimal solutions of candidate summaries on which wecan develop a parameter optimization technique to get the mosteffective summary compared to the human generated summary.We evaluate the proposed method with the Document Under-standing Conference (DUC) open benchmark dataset widelyused in automatic text summarization evaluation. The resultsare compared with the human generated gold standard summaryusing the Recall-Oriented Understudy for Gisting Evaluation(ROUGE) metric. The preliminary experiment on DUC2002dataset shows that the proposed method successfully generateseffective summaries and shows better performance compared tothe existing methods.

This work was supported by the ICT RD program ofMSIP/IITP. [2016-0-00563,Research on Adaptive MachineLearning Technology Development for Intelligent AutonomousDigital Companion]

Multi-Objective Optimization and KnowledgeExtraction of Plate-Fin Heat Sink Using Evolution-ary Algorithms Rituparna Datta, Shree Ram Pandey,Aviv Segev, KAIST. E-mail: rdatta@kaist.ac.kr.

The efficient performance and durability of electronic devicessignificantly depend on their cooling mechanism. Heat sinks arewidely used for the purpose of cooling electronic devices. Thepresent work deals with the multi-objective optimization of twodifferent configurations of plate-fin heat sinks. Two importantcriteria that have impact on the performance of plate-fin heat

sinks are the entropy generation rate and the cost. In the presentstudy these criteria are considered as the objective functions foroptimization which are found to be conflicting in nature. If onlyminimum entropy generation rate is considered, it would giveproper heat dissipation but the design may be cost inefficient.On the other hand, simultaneous minimization of cost alongwith minimum entropy generation rate will ensure more flexibledesign options. To have a balanced design, two aforesaid con-tradictory objective functions, i.e. minimum entropy genera-tion rate and minimum cost, are considered in the present work.A multi-objective evolutionary algorithm (MOEA) is used tosolve the above mentioned non-linear problem under differentdesigns and geometric restrictions. The non-dominated solu-tions from multi-objective optimization are further analyzedto extract knowledge that may represent relationships betweenthe objective functions and the design variables. The knowl-edge can be utilized by thermal engineering experts and systemdesigners to choose an appropriate heat sink design for specificapplications.

This work was supported by the ICT RD program ofMSIP/IITP. [2016-0-00563,Research on Adaptive MachineLearning Technology Development for Intelligent AutonomousDigital Companion]

Session F3-A: Global Optimization in NetworksFriday, 1:30-3:00, 1011BChair: Baski Balasundaram

The Maximum Quasi-clique Problem, Baski Balasun-daram, Zhuqi Miao, Oklahoma State University. E-mail:baski@okstate.edu.

A γ-quasi-clique in a simple undirected graph refers to a sub-set of vertices that induce a subgraph with edge density at leastγ ∈ [0, 1], i.e. the induced subgraph contains at least γ timesthe number of maximum possible edges. If γ = 1, this defini-tion corresponds to a classical clique. If γ < 1, it relaxes therequirement of all possible edges in the clique definition. Quasi-clique model has been used to detect dense clusters in graph-based data mining, especially in large-scale, error-prone datasets in which clique model can be overly restrictive. The max-imum γ-quasi-clique problem, which seeks a γ-quasi-clique ofmaximum cardinality from a given graph, can be formulated asa mathematical program with a linear objective function and asingle quadratic constraint in binary variables. This talk willdiscuss a Lagrangian dual of the formulation, and introducesan upper bounding technique based on it. The tightness of thistechnique in comparison to mixed-integer programming refor-mulations (or more precisely, their linear programming relax-ations), and its effectiveness in a branch-and-bound algorithmwill also be discussed.

Parallel Russian Doll Search for Computing Max-imum Vertex Weight Hereditary Structures inGraphs, Eugene Lykhovyd, Sergiy Butenko, TexasA&M University, College Station, TX, USA. E-mail:{lykhovyd,butenko}@tamu.edu.

A graph property is hereditary on induced subgraphs if it holdsfor all vertex-induced subgraphs of a graph satisfying this prop-erty. Given a fixed nontrivial, hereditary graph property and avertex-weighted graph, we consider the problem of finding themaximum weight subset of vertices inducing a subgraph sat-isfying this property. One of the effective approaches for solv-ing this problem is the so-called Russian Doll Search algorithm.This method is an example of a combinatorial brand-and-boundframework, so the natural question about parallelism arises. Weinvestigate possible modification to achieve speed-ups usingparallel computing. Sample results of numerical experimentsfor several hereditary properties on classical benchmark graphsare included.

A Nonconvex Quadratic Optimization Approachto the Maximum Edge Weight Clique Problem,Seyedmohammadhossein Hosseiniana, Dalila B.M.M.Fontesb, Sergiy Butenkoa, aTexas A&M University, Col-lege Station, TX, USA, bUniversidade do Porto, Porto,Portugal. E-mail: a{hosseinian,butenko}@tamu.edu,bfontes@fep.up.pt.

The maximum edge weight clique (MEWC) problem, definedon a simple, edge-weighted graph, is to find a subset of verticesinducing a complete subgraph with the maximum total sum of

edge weights. We propose a quadratic optimization formulationfor the MEWC problem and study characteristics of this formu-lation in terms of local and global optimality. We establish thecorrespondence between the local maxima of the proposed for-mulation and maximal cliques of the underlying graph, imply-ing that the characteristic vector of a maximum edge weightclique in the graph is a global optimizer the continuous prob-lem. A heuristic based on the proposed formulation is also pre-sented, and its quality is tested through numerical experimentson DIMACS benchmarks.

Error- and attack-resilient clusters in networks withdecision-dependent uncertainties, Hossein Dashti,Pavlo A. Krokhmal, University of Arizona, USA. E-mail:{hdashti,krokhmal}@email.arizona.edu.

Network robustness issues are crucial in a variety of applica-tion areas, such as energy, defense, communications, and so on.Unpredictable failures of network components (nodes and/oredges) can be caused by a variety of factors, including man-made and natural disruptions, which may significantly affector inhibit networks functionality. In many situations, one ofthe key robustness requirements is that every pair of nodes areconnected, with the number of intermediate links between thembeing as small as possible. Additionally, if nodes in a cluster areconnected by several different paths, such a cluster will be morerobust with respect to potential network component disruptions.In this work, we study the problem of identifying error- andattack-resilient clusters in graphs, particularly power grids. Itis assumed that the cluster represents a R-robust 2-club, whichby definition is a subgraph with at least R node/edge disjointpaths connecting each pair of nodes, where each path consistsof at most 2 edges. Uncertain information manifests itself inthe form of stochastic number of errors/attacks that could hap-pen in different nodes. If one can reinforce the network com-ponents against future threats, the goal is to determine optimalreinforcements that would yield a cluster with minimum risk ofdisruptions.

Session F3-B: Derivative-free OptimizationFriday, 1:30-3:00, PDRChair: Thomas R. Bewley

Problem Complexity Theory and Optimal Algo-rithm for Zero-Order Global Optimization,Serge L. Shishkin∗, Alan Finn, United TechnologiesResearch Center, East Hartford, CT, USA. E-mail:∗shishks@utrc.utc.com.

Theory of complexity of convex optimization problems andoptimality of methods is under active research since 70’s. Rig-orous analyses of complexity bounds allowed to prove opti-mality for modern methods of Convex Programming. Nothingof the scale happened though in the field of Global Optimiza-tion (GO). It was noted early on that the general class of GOproblems is NP-hard, thus the algorithm best performing on theworst problem is the direct search. With this trivial fact, thediscussion on optimality of GO methods virtually died. Also,theoretical comparison of different GO methods was impossi-ble and researches had to resort to numerical simulations forassessment of their methods.

In this paper, an approach is proposed to more discriminat-ing assessment of GO problem complexity. A function, called“Complexity Measure”, is defined on the class of GO prob-lems, and that class is split on subclasses accordingly to itsvalue. Then the complexity of each subclass is estimated andexpressed as linear function of Complexity Measure of that sub-class. That also allows to estimate optimality of different GOmethods.

Branch-and-Bound (BnB) methods is one of the most pop-ular GO paradigms and the one of very few that has rigor-ous guarantees of finding the solution. Most popular by far isthe version based on Cartesian lattice Zn (“Cubic” BnB). Thisapproach is simple since operation of replacing cubic elementby its sub-cubes is trivial. Unfortunately, it is far from optimaldue to two factors: first, each splitting of the cube creates 2n

new cubes which is great number even for reasonably small n;second, Cartesian lattice itself is not as good for covering assome other lattices, in particular, the lattice A∗. Deficiencies ofthe Cartesian grid led many researchers to attempts to use otherlattices; however difficulty of refinement of covering elementforced them to leave strict BnB scheme and construct methodsbased on function approximation based on adaptive grid.

That brings us to the second object of this paper: to developestimation methodology for the efficiency of different versionof BnB method and present a method that has as good estimatesas possible. We consider very general layout of BnB, in partic-ular, we do not at first specify the lattice on which BnB con-struction is based. For that “abstract” BnB, upper estimate isproven on necessary number of function evaluations (so-calledlaboriousness) for all problem subclasses defined earlier. Thatestimate depends linearly on subclass complexity. For conven-tional “Cubic” BnB lower estimate is also derived. Then, newBnB method is constructed based on the lattice A∗n that offersbetter characteristics as a base of covering than the Cartesianlattice. The upper laboriousness estimates for this new meth-ods are very good; it is enough to say that they are smallerthan lower estimates for “Cubic” BnB by asymptotical factorof O ((4/3)n). Nevertheless, these upper estimates are very con-servative still; in the typical case when object function has justfew areas of high variation, the laboriousness of the methodson problem subclass tends (asymptotically) to the complexity

of that subclass which is the absolute low bound. This is whywe call the method optimal.

The results presented in the paper lay out rigorous founda-tion for theory of problem complexity and algorithm optimalityfor Global Optimization.

Acknowledgement: This work was supported in part by theDefense Advanced Research Projects Agency within MSEEprogram under Contract No. FA8650-11-1-7150.

Optimization of IMEXRK Time Integration Schemesvia Delaunay-based Derivative-free Global Optimiza-tion, Thomas R. Bewleya, Shahrouz Alimohammadia,Daniele Cavaglieria, Pooriya Beyhaghib, aUCSD,bASML. E-mail: bewley@eng.ucsd.edu.

This work introduces and applies a powerful new vari-ant, dubbed ∆-DOGS(ΩZ), of our lab’s Delaunay-basedDerivative-free Optimization via Global Surrogates familyof algorithms [1] to the practical problem of identifying anew, low-storage, high-accuracy, Implicit/Explicit Runge-Kutta(IMEXRK) time integration scheme for high performance com-puting (HPC) applications, like the simulation of turbulence.The optimization scheme developed and used in this work,which is provably globally convergent under the appropri-ate assumptions, combines the essential ideas of (a) our ∆-DOGS(Ω) algorithm [2], which is designed to efficiently opti-mize a nonconvex objective function f (x) within a nonconvexfeasible domain Ω described by a number of constraint func-tions c`(x), with (b) our Ω-DOGS(Z) algorithm [3], which aimsto reduce the number of function evaluations on the bound-ary of the feasible domain that would otherwise be called forvia the restriction that all function evaluations lie on a Carte-sian grid, which is subsequently refined as the iterations pro-ceed, over the rectangular search domain Ls considered. Theidentification of the optimal parameters of IMEXRK schemesinvolves (1) a complicated set of nonlinear constraints, whichare imposed in order to achieve the desired order of accuracyin addition to a handful of important stability properties, whichleads to a highly nonconvex, disconnected feasible domain, and(2) a highly nonconvex objective function, which represents acompromise between a few different measures characterizingthe leading-order error and potential stability shortcomings ofthe resulting scheme. This structure makes the computation ofnew IMEXRK schemes a challenging and well-suited practi-cal test problem for global optimization algorithms to solve.In this work, the new optimization algorithm developed, ∆-DOGS(ΩZ), introduces the notion of “support points”, whichare points defined and used to eliminate constraint and objec-tive function evaluations on the boundary of the search domain,where these functions are sometimes ill-behaved, while restrict-ing all datapoints to like on a Cartesian grid that is successivelyrefined as convergence is approached. For validation, the con-vergence of ∆-DOGS(ΩZ) and ∆-DOGS(Ω) are compared on achallenging problem of optimizing a low-storage IMEXRK for-mulation. Results indicate a notably accelerated convergencerate using ∆-DOGS(ΩZ). In the end, a low-storage third-orderaccurate IMEXRK algorithm for the time integration of stiffODEs was identified which exhibited remarkably good stabilityand accuracy properties as compared with existing IMEXRKschemes.

[1] P. Beyhaghi et al (2016) Delaunay-based Derivative-freeOptimization via Global Surrogates, Part I: Linear Con-

straints, JOGO, 66 (3), p. 331-382, and Part II: ConvexConstraints, JOGO 66 (3), p. 383-415.

[2] S. Alimohammadi et al (submitted) Delaunay-basedDerivative-free Optimization via Global Surrogates PartIII: Nonconvex Constraints, JOGO, submitted.

[3] P. Beyhaghi and T. Bewley (submitted) Implementationof Cartesian grids to accelerate Delaunay-based Optimiza-tion with bound constraints. JOGO, submitted.

Implementation of Dense Lattices to AccelerateDelaunay-based Optimization with Linear Con-straints, Pooriya Beyhaghia, Shahrouz Alimohammadib,Thomas R. Bewleyb, aASML, bUCSD. E-mail: bew-ley@eng.ucsd.edu.

Delaunay-based Derivative-free Optimization via GlobalSurrogates (∆-DOGS) is a family of algorithms designed forlow-dimensional optimization problems in which the objec-tive function is both nonsmooth and expensive to evaluate [1].During the optimization process, ∆-DOGS models the objec-tive function with a (computationally inexpensive) interpolat-ing “surrogate”, and represents the uncertainty of this surro-gate using as synthetic piecewise-quadratic model built on theframework of a Delaunay triangulation of the available data-points. Unfortunately, the behavior of this artificially-generateduncertainty function is sometimes found to be somewhat irreg-ular near the feasible domain boundaries. In the case of sim-ple bound constraints on the feasible domain, this irregular-ity was mitigated [2] by considering both a “discrete searchfunction” (over existing datapoints) and a “continuous searchfunction” (over the entire feasible domain), while restrictingthe datapoints to lie on a Cartesian grid (which coincides withthe corners of the feasible domain) that is successively refinedas convergence is approached; this quantization strategy effec-tively prevents datapoints from clustering near the boundary ofthe feasible domain in this case. The present work considersthe more difficult case with linear constraints on the feasibledomain, for which the generalization of the above approachis not straightforward. Rather than using a Cartesian grid,the proposed approach, dubbed ∆-DOGS(Λ), quantizes to adense n-dimensional lattice [3] (which is, again, successivelyrefined as convergence is approached) defined over the interiorof the n-dimensional feasible domain. Points near the (n − 1)-dimensional boundaries of the feasible domain are quantizedto (n − 1)-dimensional lattices defined over these boundaries;points near the (n − 2)-dimensional “edges” of the feasibledomain are quantized to (n − 2)-dimensional lattices definedover these edges, etc. A carefully-controlled “gap” is required(and, used) between each of these families of quantization lat-tices in order to assure convergence. For validation, the newoptimization algorithm developed in this work is compared withprevious schemes developed in this family on a range of stan-dard optimization problems with linear constraints.

[1] P. Beyhaghi et al (2016) Delaunay-based Derivative-freeOptimization via Global Surrogates, Part I: Linear Con-straints, JOGO, 66 (3), p. 331-382, and Part II: ConvexCon- straints, JOGO 66 (3), p. 383-415.

[2] P. Beyhaghi and T. Bewley (submitted) Implementationof Cartesian grids to accelerate Delaunay-based Optimiza-tion with bound constraints. JOGO, submitted.

[3] P. Belitz and T. Bewley (2013) New horizons in sphere-packing theory, part II: lattice-based derivative-free opti-mization via global surrogates. JOGO 56, 61-91.

Delaunay-based Optimization with Rescaling andDimension Reduction Leveraging Multivariate Adap-tive Polyharmonic Splines, Shahrouz Alimohammadia,Pooriya Beyhaghib, and Thomas R. Bewleya, aUCSD,bASML. E-mail: bewley@eng.ucsd.edu.

Delaunay-based Derivative-free Optimization via GlobalSurrogates (∆-DOGS) is a family of algorithms designed forlow-dimensional (n . 10) optimization problems in whichthe objective function is both nonsmooth and expensive toevaluate [1]. We have recently introduced [2] a new inter-polation method, dubbed multivariate adaptive polyharmonicsplines (MAPS), which modifies the venerable polyharmonicspline method in a manner particularly well suited for appli-cations to such surrogate-based optimization strategies; duringthe interpolation process, MAPS rescales the parameters con-sidered according to their significance in the optimization prob-lem, based on the data available at that iteration. In the presentwork, the rescaling of the parameters inherent to the MAPSinterpolation method is integrated with the ∆-DOGS optimiza-tion algorithm itself. The rescaling of parameter space per-formed by MAPS facilitates the identification and removal ofthe less significant parameters in the optimization problem dur-ing many iterations of the optimization algorithm. This signifi-cantly accelerates convergence, and enables the consideration ofsomewhat higher dimensional problems in this setting. For val-idation, the new optimization algorithm developed in this workis applied to a practical hydrofoil shape optimization problemwith seven adjustable parameters, as considered previously byour group; numerical results show a notable acceleration in con-vergence as compared with existing schemes.

[1] P. Beyhaghi et al (2016) Delaunay-based Derivative-freeOptimization via Global Surrogates, Part I: Linear Con-straints, JOGO, 66 (3), p. 331-382, and Part II: ConvexConstraints, JOGO 66 (3), p. 383-415.

[2] S Alimohammadi et al (2017) Delaunay-based opti-mization in CFD leveraging multivariate adaptive poly-harmonic splines (MAPS). Proceedings of the 58thAIAA/ASCE/AHS/ASC Structures, Structural Dynamics,and Materials Conference, p. 129.

Session F4-A: Algorithmic/Computational AspectsFriday, 3:30-5:00, 1011BChair: Lewis Ntaimo

Irreducible Infeasible Subsystem (IIS) Decomposi-tion for Probabilistically Constrained Stochastic Pro-gramming, Lewis Ntaimoa, Julian A. Gallego-Arrublab,Bernardo K. Pagnoncellic, Gianpiero CanessacTexasA&M University, College Station, TX, USA, bA.T. Kear-ney, Inc., Chicago, Illinois, USA, cUniversidad AdolfoIbanez, Santiago, Chile. E-mail: antaimo@tamu.edu.

Probabilistically constrained stochastic programs (PC-SPs) dealwith problems involving constraints that do not have to holdwith certainty. This class of stochastic programs has manyapplications in science and engineering but is still very chal-lenging to solve. Furthermore, linear programming (LP) pro-vides very weak bounds on the optimal value. In this talk,we introduce a new decomposition approach using irreducibleinfeasible subsystem (IIS) inequalities to strengthen the LP-relaxation of PC-SPs. We first establish the theoretical resultsfor determining IIS inequalities for the continuous case, andthen extend the results to the binary case and give example illus-trations. Next, we devise an IIS branch-and-cut algorithm forPC-SP and report on preliminary computational results.

A Cutting Plane Method for Risk-constrained Travel-ing Salesman Problem with Continuously DistributedRandom Arc Costs, Qipeng Phil Zheng, University ofCentral Florida, USA. E-mail: Qipeng.Zheng@ucf.edu.

This paper considers the risk-constrained stochastic travelingsalesman problem with random arc costs which is continuouslydistributed. In the