Stratos Pistikopoulos - Reflections

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Professor Christodoulos A. Floudas

• Research inspiration & impact on my career

• Texas A&M Energy Institute – the big “move”

• Personal reflections

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Optimization under uncertainty (Two-stage stochastic programming)

ResearchInspiration#1

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ResearchInspiration#2Bi-level programming

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Process synthesis under uncertaintyResearchInspiration#3

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§ Onekeyapproach– Assumelineardecisionrules:

§ Setyasanaffinefunctionoftheuncertainty– simplifiestheproblem.§ CanbesolvedasStaticRobustOptimization

( ) { }

T T

( , )min max min

. . ,

, :

U

s tÎWÎ

+

³ Î

W = Î ³ - -

x y x uu

x

y

c x b y

Ax d x S

x u y S Wy h Tx Mu

x: “here-and-now” decisionsy: “wait-and-see” decisionsu: uncertainty

= +y q Qu

ResearchInspiration#1:Adjustable Robust Optimization

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ResearchInspiration#1:Adjustable Robust Optimization§ Generalizeddecisionrulesthroughmulti-parametricprogramming:

§ Solvethelowerlevelproblemmulti-parametrically consideringu andxasparameters

§ Arrivetoasetof(exact)affinedecisionrulesvalidforthewholefeasiblespaceofuand“here-and-now”decisionsx.

𝑦 =

𝑄$𝑢 + 𝑃$𝑥 + 𝑞$𝑖𝑓𝐺$𝑢 + 𝐻$𝑥 ≤ ℎ$𝑄1𝑢 + 𝑃1𝑥 + 𝑞1𝑖𝑓𝐺1𝑢 + 𝐻1𝑥 ≤ ℎ1

⋮𝑄3𝑢 + 𝑃3𝑥 + 𝑞3𝑖𝑓𝐺3𝑢 + 𝐻3𝑥 ≤ ℎ3

x: “here-and-now” decisionsy: “wait-and-see” decisionsu: uncertainty

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ResearchInspiration#1:Adjustable Robust Optimization§ Generalizeddecisionrulesthroughmulti-parametricprogramming:

§ Canbeextendedtoproblemswith:n Variables: Mixed-Integer forboth“here-and-now”and“wait-and-see”decisions.n Objective:

¨UpperLevel: Non-Linear¨ LowerLevel: Quadratic

n Constraints:¨UpperLevel: Non-Linear¨ LowerLevel: Linear

𝑦 =

𝑄$𝑢 + 𝑃$𝑥 + 𝑞$𝑖𝑓𝐺$𝑢 + 𝐻$𝑥 ≤ ℎ$𝑄1𝑢 + 𝑃1𝑥 + 𝑞1𝑖𝑓𝐺1𝑢 + 𝐻1𝑥 ≤ ℎ1

⋮𝑄3𝑢 + 𝑃3𝑥 + 𝑞3𝑖𝑓𝐺3𝑢 + 𝐻3𝑥 ≤ ℎ3

x: “here-and-now” decisionsy: “wait-and-see” decisionsu: uncertainty

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§ NP-hardeveninthebi-levellinearcase(withoutintegervariablesatanylevel)Ø NeedforGlobaloptimization

§ SolutionmethodusingKKT:

KKT

y

x

Visweswaran V, Floudas CA, Ierapetritou MG, Pistikopoulos EN (1996) A Decomposition-Based Global Optimization Approach for Solving Bilevel Linear and Quadratic Programs, State of the Art in Global Optimization: Computational Methods and Applications, Springer US, Boston, MA, 139-162

ResearchInspiration#2:Bi-level programming - Challenges

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ResearchInspiration#2:Bi-level programming – by multi-parametric programming§ Globaloptimizationalgorithmfortheexactsolutionoftwoclassesofbi-levelprogrammingproblems:

1. Bi-levelmixed-integerlinearprogrammingproblems(B-MILP)2. Bi-levelmixed-integerquadraticprogrammingproblems(B-MIQP)

containingbothintegerandcontinuousvariablesatbothoptimizationlevels.§ Mainidea:

Thefeasiblesetofthelowerlevelproblemismulti-parametricintermsofthedecisionvariablesoftheupperlevelproblem.

§ ComputationalImplementation- B-POP§ AMATLABtoolboxforbi-levelprogramming§ AnextensiontoouralreadydevelopedPOPtoolboxFeatures:

n Bi-levelprogrammingsolversforB-MILP andB-MIQP problemsn Abi-levelproblemgeneratorn Abi-levelproblemlibrary

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Recast as a mp-MIQP Solve the mp-MIQP using POP®

Substitute mp solution in the upper level

Solve single-level MIQP

CR Objective1 z1

2 z2

… …k zk

Compare and choose optimum

Parameters:

B-MIQP 1 2

34

5

Bi-levelMixed-Integerprogramming– Thealgorithm

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ResearchInspiration#3:Generalized Modular Representation Framework

Mass/HeatExchanger

Pure HeatExchanger

SplitterMixer

• Building block: Multi-functional mass/heat exchange module& Pure heat exchanger module

• Process alternatives: Mass and heat exchange possibilitiesNo pre-postulation!

• Optimal flowsheet: Conventional unit & Innovative designPotential for intensified designs!

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ResearchInspiration#3:Generalized Modular Representation Framework § Representation of process units with GMF

Reactive distillation

Two-phase reactor

Jacketed homogeneous reactor

Connected reactor- distillation Columns

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Professor Christodoulos A. Floudas

• Research inspiration & impact on my career

• Texas A&M Energy Institute – the big “move”

• Personal reflections

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TexasA&MEnergyInstitute– thebig“move”

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Texas A&M Energy Institute PillarsTransform the

Energy Research Landscape

Educate the Next Generation of

Leaders in Energy

Establish a Vibrant External Partnerships

Program in Energy

TexasA&MEnergyInstitute– thebig“move”

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Multi-Scale Energy Systems

Engineering

Materials, Catalysis and Separation for

Energy

Energy Economics, Law,

Policy and Societal Impact

Fossil & Non-Fossil Based

Technologies for Energy

Texas A&M Energy Institute – Research programTexasA&MEnergyInstitute– thebig“move”

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Systems-WideThinkingandStructure§ Aholisticandinter-disciplinaryapproachtoresearchandeducationinenergy

§ Crossingdisciplinesandsectors§ Connectingthe“dots”withintheentireenergylandscape

§ Seekingthetransformationsthatarefoundalongtheseamsofstereotypicalacademicandindustrialscopesandparadigms

TexasA&MEnergyInstitute– thebig“move”Texas A&M Energy Institute - Focus

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MasterofScienceinEnergy

Designedtointroducestudentsandprofessionalstothemultipleinterdisciplinaryfacetsofenergy:

CertificateinEnergy

10modulesoftheprofessional“MasterofScienceinEnergy”degreeprogrameitherinresidenceoron-line.

Energy TechnologiesEnergy Law

BusinessMulti-scale Energy Systems Engineering

Materials for EnergyEconomics and Finance

In-Person/Online

Thesis/Non-Thesis

Professionals

10 Months

Module-Based

TexasA&MEnergyInstitute– thebig“move”Texas A&M Energy Institute – Master program

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energy.tamu.edu

TexasA&MEnergyInstitute– thebig“move”Texas A&M Energy Institute

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1. Smart Manufacturing™ and the Clean Energy Smart Manufacturing Innovation Institute (CESMII)

2. RABIT institute: Rapid Advancement in Process Intensification Deployment

TexasA&MEnergyInstitute– thebig“move”Big Initiatives

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Professor Christodoulos A. Floudas

• Research inspiration & impact on my career

• Texas A&M Energy Institute – the big “move”

• Personal reflections

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PersonalReflectionsMilestones:

1. University years

2. Graduate school

3. Career

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Wedding - August 1994PersonalReflections

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Christening - August 1999PersonalReflections

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Milestones:

1. University years

2. Graduate school

3. Career

4. Family

5. Our summers

6. Texas A&M University

PersonalReflections

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Sargent Medal Awarded to Professor Floudas

http://energy.tamu.edu/sargent-medal-awarded-professor-christodoulos-floudas-institution-chemical-engineers-icheme/

Named after Roger Sargent, thefounding father of ProcessSystems Engineering, the medalwas launched to recognize amajor contribution to researchin the area of computer-aidedproduct and processengineering

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Aggie Muster, 2017 - Reflections display

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Aggie Muster, 2017 - Reflections displayProfessor Christodoulos Floudas is Gone

We can shed tears that he is gone,Or we can smile because he lived.

We can close our eyes and pray this is all a bad dream,Or we can open our eyes and appreciate all that he left.

We can feel empty because we can’t see his smile,Or we can be filled with resolve like he always was.

We can turn our back on tomorrow and relive yesterday,Or we can be inspired by him and live our lives to fulfillment.

We can remember him and dwell only on his death,Or we can cherish his memory and help make it live on.

We can close our mind, feel empty and fret about our loss,Or we can do what he would want:

Smile, and bring our passion for life’s many possibilities.

Tribute byTexas A&M Institute for Advanced Study

Stratos Pistikopoulos - Reflections