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hand and therefore performs optimisation. Engineering designoptimisation (EDO) is not new. This process is often manual, time

paper. It is recognised that the design is dependent on themanufacturing processes to be used and thewhole life cycle issues.This paper considers the manufacturability and life cycle issues as

CIRP Annals - Manufacturing Technology 57 (2008) 697715

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s.econsuming and involves a step by step approach to identify theright combination of the product and associated process para-meters for the best solution. Often the manual approach does notallow a thorough exploration of the solution space to nd theoptimumdesign, resulting in sub-optimal designs.With increasingglobal competition, it is necessary to design products that are ableto satisfy human needs in the most effective manner. This keynotepaper identies recent approaches to automating the manualoptimisation process and the challenges this brings for theengineering community.

In real life, identication of the optimum design of an industrialproblem is often not possible because of the size of the problemand lack of knowledge. In this situation, design optimisation isessentially seen as design improvement. This paper uses designoptimisation as the goal for any design improvement task.

The terms optimise, optimisation, optimal, optimum areoften used in a very loose sensewithout necessarily referring to theuse of specic optimisation techniques. In this paper, onlyoptimisation as relating tomechanical design problems or discreteproducts is considered. It obviously excludes optimisationproblems in thermouid processes, manufacturing processes aswell as process manufacturing areas [1,2]. However, the optimisa-tion of shapes such as turbines or tools in interaction with thethermouids or manufacturing processes are considered as well as

constraints or one of the objectives for the design optimisation.Multi-disciplinary [6,7] and civil engineering structural optimisa-tions [8] are not covered in this keynote paper in order to limit thescope.

1.1. Basics

Performing EDO often requires knowledge about the stage ofdesign, design variables and their minimum and maximum limits(independent variables), constraints, measurement of the designperformance (dependent variables), design parameters andrelationships between the independent and dependent variables(i.e. a design evaluation model). The design variables aredependent on the level of product denition available at thedifferent stages of the design optimisation. The design stages canvary from conceptual or preliminary design, and from congura-tion to detailed design.

Design variables are expressed in either quantitative orqualitative terms. In many design optimisation problems, it iseasy to measure the design variables, such as length, weight andtemperature. They are referred to as quantitative design variables.But in real life design problems, variables such as aesthetics andmanufacturability are difcult to measure and they are referred toas qualitative variables [9]. The nature of the model developmentwill vary depending on the types of the variables. In order to reducethe possible choices for a design, each variable is given aminimumand maximum value, called the bounds of the variable. Somedesign parameters remain constant for a given design problem.

* Corresponding author.

E-mail address: r.roy@craneld.ac.uk (R. Roy).

0007-8506/$ see front matter 2008 CIRP.doi:10.1016/j.cirp.2008.09.007Recent advances in engineering design o

Rajkumar Roy (2)a,*, Srichand Hinduja (1)b, RobertaDecision Engineering Centre, Department of Manufacturing, Craneld University, Crab School of Mechanical, Aerospace and Civil Engineering, University of Manchester, MacDepartment of Materials and Production Engineering, University of Naples Federico II

1. Introduction

Every time a product is created or designed to satisfy humanneeds, the creator tries to achieve the best solution for the task in

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the constraints arising from these interfaces such as manufactur-ability. It should be noted that optimisation of the organisation/management of the design process [35] is not included in the

optimisation which is the process of identifying the right combination of

ne manually, time consuming and involves a step by step approach. This

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R. Roy et al. / CIRP Annals - Manufacturing Technology 57 (2008) 697715698function of the design variables and can be of two types: non-equality and equality type. For example, the temperature on aturbine blade has to be less than the melting point of thematerial, i.e. T(x) < Tmax or the cost of a design must be less thanor equal to a budgeted amount, i.e. C(x) Cmax, where x is thevector of design variables: (x1, x2, . . ., xi)

T. In case of mechanicaldesign a dimensional constraint [10] introduces tolerance on thedimension and becomes an in-equality constraint asLmax tolerance L(x) Lmax + tolerance, where L stands forthe length of a component. On the other hand, equalityconstraints are those that must be satised, examples includephysics-based constraints, such as F = ma. Satisfying constraintsis a challenge for any optimisation task, especially if it is anequality constraint [11]. It is advisable to convert an equalityconstraint to a suitable in-equality constraint where possible.

Development of the design evaluation model (or objectivefunction or tness function) is dependent on the nature of thevariables and constraints. The model assumes that certain aspectsof the design remain constant, and they are called designparameters. The design parameters are often used to reduce thetotal number of design choices (or design space). The model canalso be either quantitative or qualitative in nature. Quantitativemodels can be either simulation based, analytical or empirical,whereas the qualitative models are generally knowledge-based.Considering the above three aspects, the optimisation problem canbe mathematically represented as

optimiseminimize or maximizeF jx; p; j 1;2; . . . ; J (1)

with variable bounds as ximin xi ximax; where i = 1, . . ., n, p is a

vector of design parameters, and subject to constraints:

gkx0 and hmx 0 (2)

where k = 1, 2, . . ., K and m = K + 1, . . ., M.Fj(x, p) are the objective functions for the design problem.

Minimisation of a function F(x, p) is equivalent to maximisation ofF(x, p). It should be noted that the multiple objective functionsrepresent different measures of performance for the same design,such as weight, cost and quality [12].

This paper starts with classication of EDO problems. Then themajor mathematical challenges faced in design optimisation arehighlighted with a special focus on mechanical and real life designproblems. EDO approaches are then grouped and mapped againstthe types of optimisation problems in Section 4. Section 5 presentsan analysis of trends in different optimisation techniques in thelast 10 years. This section identies the most popular andpromising techniques for design optimisation based on theliterature. Section 6 is about current practice in industry. Thenext three sections discuss in detail the three major approachesand present a critical analysis of the research with examples.Sections 10 and 11 discuss the future challenges and potentialtechniques to address large-scale design optimisation.

2. Classication of engineering design optimisation problems

A classication of the EDO problem is necessary to select theright approach for a given problem. An enhanced version of theclassication proposed in an earlier publication [13] for EDOproblems is presented in Table 1. The classication is developedbased on ve basic schemes and two view points. The basicschemes are: design variables, constraints, objective functions,problem domains and the environment for the design. The twoviewpoints are design evaluation effort and the degrees of freedomof the design problem. The ve major classication schemes andtheir categories as discussed below:

Design variables play a major role in EDO. The number of designvariables, their natures, permissible values and mutual depen-or

A constraint on a design, on the other hand, denes physicalfunctional limits of a design. The constraint is dened as aclassies the EDO problems as uni-modal or multi-modalbased on the number of optimal solutions that the problem has.Multi-modal problems can also be categorised as sensitive androbust. The former has mostly very sensitive optima, whereasthe latter has at least one robust optimum. The nature of thesearch space can also be classied as linear and nonlinearbased on the nature of underlying equations in the objectivefunction.

Based on this criterion, EDO problems can also be classied asntinuous, discontinuous depending on whether the equationsvolved in the problem have any discontinuities and not-denedutside the feasible space when the objective function cannot bealuated if any constraint is violated. A function is said to beparable if it can be decomposed into functions that involveroups of variables rather than just a single variable. Inseparabilityanifests itself as cross-product terms, and makes the effect of aariable on the function dependent on the values of other variablesthe function.number of constraints, constraint development and evaluationtime are factors that signicantly affect the optimisation process[16,17].Objective functions are used to evaluate a design solution withinthe optimisation context. The number of objective functions,their nature and whether they are separable determines thecomplexity of the optimisation task. In real life most of theoptimisation problems are multi-objective. Multi-objectiveoptimisation becomes more complex with more than about 10objectives for a problem [18]. Quantitative objective functionscan be further classied as simulation based (e.g. FEA, CFD)[19], analytical (e.g. mathematical models created from rstprinciples and with domain knowledge) [20] and empirical[21]. Qualitative objective functions involve issues likemanufacturability and aesthetics [14]. One of the majorchallenges in EDO is to deal with computationally expensiveobjective functions. Typically, simulation-based models take along time to evaluate. The nature of a search space alsodencies can affect the overall complexity of the optimisationtask. Most of real life or industrial design optimisation problemsare likely to be multi-dimensional [14]. The complexity isdened as the level of effort required to formulate theoptimisation problem and identify the optimum solution(s). Instatic or parameter optimisation problems, the design variablesare independent of each other whereas in trajectory or dynamicoptimisation problems, the design variables are all continuousfunctions of some other variable(s). Another perspective of thisclassication is provided by other researchers [15], based ontime-dependence of optimisation problems. Depending on thevalues permitted for design variables, EDO problems can becategorised as integer-valued, real-valued and mixed-integer(that involve both integer and real variables). Variable depen-dence occurs when the variables are functions of each other. It isoften observed that there are variable dependencies among reallife design problems. This has an effect of constraining the searchspace [13].

Existence of constraints in an EDO problem affects the optimisa-tion approach to be used. The constraints can be linear ornonlinear in nature. A mixed-integer programming (MIP)problem is one where some of the design variables areconstrained to have only integer values at the optimal solution.Constraint programming denes higher-level constraints thatapply to integer variables. The most common and useful higher-level constraint is the all-different constraint, which applies to aset of variables, say x1, x2, x3, x4 and x5. This constraint assumesthat the variables can have only a nite number of possiblevalues (say 1 through 7), and species that the variables must beall different at the optimal solution. One of the possible values forthe optimimum could be (7, 6, 4, 3, 2). The travelling salesmanproblem is an example of constraint programming. The last twotypes of constraints make optimisation much more difcult. The

TaCl

R. Roy et al. / CIRP Annals - Manufacturing Technology 57 (2008) 697715 699

ble 1assication of EDO problems.Problem domain brings different physics considerationwithin theoptimisation. Multiple domains require a multi-disciplinaryapproach to the optimisation [6,22]. Establishing interdepen-dence between the domains for real life design problems andoptimising them simultaneously, such as aircraft design, requiressignicant effort andmakes the optimisationmore complex thansingle domain optimisation.The optimisation environment involves considerations likeuncertainties in the design, level of knowledge available aboutthe design solutions, importance of designer involvement andnally the nature of the environment. Lately there has beensignicant interest in design optimisation with uncertainties[23]. The uncertainties can be associatedwith the design variabledenition as well as in the model development [24]. Knowledgeabout the design environment is often lacking for real lifeproblems [14]. Not knowing about the design space and locationof the optimum makes the optimisation task more challenging.Some design tasks require designer involvement to improve theircondence and also to involve them in qualitative designevaluation; this is called interactive optimisation [25]. The

involvement increases the degrees of freedom of the optimisa-tion due to non-uniform behaviour of human experts and alsoinvolves signicant effort from the expert designer. And nallythe nature of the environment could be static or dynamic. Thedynamic nature of the environment will impact the designvariables as well as the design evaluation. If it is dynamic, theoptimisation will require more effort and involve more degreesof freedom than a static environment.

The design evaluation effort viewpoint is related to thecomputational effort required to develop and evaluate a designmodel due to the nature of the design variables, constraints,objective functions, problem domains and the environment.

complex. This section identies the major mathematical chal-lenges that are relevant for EDO, especially for real life problems.

3.1. Global and robust optimisation

Mathematical optimisation aims to determine the globally bestsolution for a problem for a given objective. In engineering design,it is often not possible to even identify if a global optimum isreached during the optimisation process. In the design context,feasible solutions against multiple nonlinear constraints that aresignicantly better than the current solutions are often acceptableconsidering the computational resources required. Global optimi-sation becomes very time consuming with a large number ofdesign variables (typically much more than 30), equality con-straints and noisy objective functions (using simulation models).

R. Roy et al. / CIRP Annals - Manufacturing Technology 57 (2008) 697715700Whereas, degrees of freedom of an EDO problem includes thenumber and number of types of design variables, constraints,objective functions, problem domains and environmental factorslike uncertainty, designer condence required and dynamicbehaviour involved in a design.

Table 1 presents two categories of design evaluation effort:inexpensive and expensive, and another two categories for thedegrees of freedom: small and large. Based on these two viewpoints, an EDO problem can be classied as a small-scale, expertdependent, algorithm dependent and large-scale problem (Fig. 1).Examples of a small-scale problem are connecting plate design[26], turbine blade cooling system design [20] and automotivemagnetorheological brake design [27]. Examples of expertdependent design optimisation includes fast axis feed drive design[28], microend drill design [29], product and assembly design for abre reinforced plastic track wheel [30], parallel kinematicmechanisms design for ve-axis milling operations [31], machinetool spindle design [32], bearing design for ultrasonic machines[33], power transmission system design [34], sintered productshape optimisation [35], use of rapid prototyping for faster productoptimisation [36], product redesign using value oriented life cyclecosting [37], cutting tool design [3840] and mould design [41].Examples of algorithm dependent design optimisation includereliability-based cantilever beam and a simplied car crashworthi-ness based design [42] and multi-disciplinary aircraft conceptsizing problem with uncertainty [43]. In real life, sometimes wewant to optimise a system (rather than just a component) withinteraction. Technological constraints are used to re-evaluate thelimit boundaries and to formulate a large-scale design optimisa-tion problem [an early example in 44]. There is a lack of research inlarge-scale design optimisation area. Most of the componentdesign optimisations do not address design of an assembly or useof computationally expensive but more realistic simulation-baseddesign evaluations (i.e. no further approximation using surrogatemodels). The problem of size in design optimisation is alsodiscussed by other researchers [45]. Multi-objective and multi-disciplinary design of blended wing body unmanned aerial vehicle(UAV) presents a large-scale design optimisation application [46].

3. Mathematical challenges in design optimisation

Mixed nature of design variables, nonlinearity of the objectivefunctions and constraints make a design optimisation more

Fig. 1. Classication of EDO problems.EDO also applies local optimisation using gradient information andHessian matrices (second derivatives) in the local region. In caseswhere simulation approaches, such as nite element analysis (FEA)are employed, even local optimisation becomes difcult because oflack of knowledge about the design space based on the models[47]. The gradient-based approach is often not suitable for real lifedesign optimisation as the models in such real life problems areoften non-differentiable. Due to the presence of uncertainty, in reallife optimisation, it is often required to determine less sensitivesolutions as robust designs (Fig. 2). Robust solutions are areas inthe search space where signicant changes in design variablesproduce only insignicant changes in the performance of thedesign [24]. The challenge is to identify robust regions in the designspace.

3.2. Multi-modal and multi-objective optimisation

Some designs involve multiple good solutions, such as antennadesign [48] and turbine blade design [14].

This type of optimisation is called multi-modal optimisation(Fig. 3). The challenge is to identify as many optima as possible toprovide a choice of good solutions to the designer. The taskbecomes more difcult with an increase in the number of designvariables. Real life engineering designs often have more than oneconicting objective functions thus requiring a multi-objectiveoptimisation approach.

The optimisation identies several solutions that are goodconsidering the objective functions, they are called Paretosolutions. Fig. 4 shows a Pareto front dening the solutions for atwo objective (F1 and F2) problem. The multi-objective optimisa-tion becomes more difcult with increasing number of objectivesand it has been shown in [18] that existing multi-objectiveoptimisation algorithms do not perform well with more than veobjectives.

3.3. Dealing with design variable interactions

Many real-life design optimisation problems also involveinteraction among decision variables. Ideally, the optimum design

Fig. 2. An illustration of global and local optima and robust solutions.

R. Roy et al. / CIRP Annals - Manufacturing Technology 57 (2008) 697715 701could be obtained by varying the design variables of a givenproblem in a random fashion independent of each other. This is notpossible formany applications, such as turbine blade design. In thistype of design, if the value of a given variable changes, the values ofothers should be changed in a unique way to get the requiredresults. There are two types of interactions among the design

Fig. 3. An illustration of multi-modal design optimisation problem.

Fig. 4. Pareto front identied using multi-objective optimisation.variables: inseparable function interaction and variable depen-dence [13]. In this section inseparable function interaction isdiscussed as it is more relevant for EDO problems and it is difcultto handle. Inseparable interaction occurs when the effect that avariable has on the objective function(s) depends on the values ofother variables in the function (Fig. 5). For example, in Fig. 5(a) thenature of the effect of A on y does not change due to variation in thevalue of B, but in Fig. 5(b) it does (the slope of the line is changed).The impact of the interaction becomes more signicant withmultiple objectives.

Traditional techniques such asweighted sumapproach and goalprogramming suffer from serious limitations in dealing with thecomplexities introduced by inseparable function interaction [13].The interaction also poses a signicant challenge to GA-basedoptimisation approaches by making it more difcult for it to buildthe building blocks used in a GA. Furthermore, in its presence, amulti-objective optimisation problem cannot be decomposed intosimpler parts. Furthermore, even if a set of optimal solutions are

Fig. 5. An example of inseparable function interaction. (a) No interaction and (b)inseparable function interaction.the design variables and the parameters can introduce uncertaintyin the design making the objective function Fj (x, p) uncertain. Theuncertain objective function can be represented using the mean(m) and standard deviation (s) (robust design optimisation withnormal distribution):

optimise R mFx; p;sFx; p (4)Or optimise a noisy objective function:

optimise Rx; p Fx; p e (5)where e N(m, s), e.g. normal distribution.

In case of noise in x and F:

optimise Rx; p Fx e1; p e2 (6)If the utility function optimisation approach is used, the

objective function can be represented as

maxU Z

uFpFdF . . . (7)

To achieve the feasibility of constraints under uncertainty, ageneral probabilistic feasibility formulation can be expressed asfollows:

P gkx; p0 Pok;k (8)

where k = 1, . . ., L, number of constraints and Pok,k is the desiredprobability for satisfying constraint k. Parkinson et al. [54] havebasdesesign [50], utility function optimisation [51,52] and reliability-ed design optimisation [53]. (Eq. (1)) shows formulation of aign optimisation problemwithout uncertainty. In practice, bothThedncertainties in design could come frommanufacturing variations.re are several approaches to deal with uncertainty: robustvaruobtained, it is difcult to maintain them since any change in onevariable must be accompanied by related changes in others [12].There is a lack of research in developing effective designoptimisation algorithms for inseparable interactions.

Generalised regression genetic algorithm (GRGA) is developedto deal with mixed-integer (i.e. with integer and real variables)multi-objective design optimisation problems with inseparablefunction optimisation [13]. The GRGAworkswith the relationshipsamong design objective functions. It is observed that in case of amulti-objective design optimisation, any continuous part of aPareto front will represent a relationship between the objectives.Consider a two-objective optimisation problem having f1 and f2 asthe two objective functions. For any continuous portion of thePareto front, there exists a function F involving f1 and f2. Supposethe problem has two decision variables x1 and x2 that dene thefunctions f1 and f2, i.e., f1 and f2 can be expressed as f1(x1, x2) andf2(x1, x2), leading to F1:

F f 1; f 2 0;F f 1x1; x2; f 2x1; x2 0) F1x1; x2 0:

(3)

The above equations show existence of relationship(s) amongthe variables of the solutions belonging to any continuous portionof the Pareto front. GRGA aims to explore this relationship usingnonlinear multi-variable regression analysis [49]. It uses therelationship thus obtained to

perform periodic and nal re-distribution of solutions for aidingtheir spread;

use history of change of regression coefcients for guiding thesearch towards the Pareto front;

use rate of change of regression coefcients as the terminationcondition of the algorithm.

3.4. Dealing with uncertainty

Real life design often involves uncertainties with the designiables, constraints and objective functions. For example,

require any additional skill, it may take less time to select a betterdesign, and it gives incremental improvement. On the other hand,the major challenges are in the form of dependency on a fewexperts who could evaluate the designs and nd truly novel andsignicantly better designs. Fig. 8 shows how different optimisa-tion approaches are used to address different classes of designoptimisation problems. It is observed that algorithm-dependentand large-scale optimisation classes require signicant research indeveloping optimisation approaches.

A design of experiment (DOE) is a structured, organizedmethodfor determining the relationship between factors (Xs) affecting adesign and the performance of that design (Y) (e.g. maximumstress, weight or cost).

Once the contributions of the factors (i.e. design variables) onthe performance are identied, the information is used to identifyan ideal set of design variable values that is expected to yield thebest result. The DOE approach to design optimisation can reducethe design time, and can often nd better performing designs that

R. Roy et al. / CIRP Annals - Manufacturing Technology 57 (2008) 697715702simplied (Eq. (8)) to reduce the computation time as (assumingnormal distribution for the constraints):

mgk Iksgk0 (9)where Ik =F

1Pok,k and F1() is the inverse function of the

cumulative density function (CDF) of a standard normal distribu-tion. Locating the optimum design solution is not trivial within anuncertain environment. Jin et al. [52] have demonstrated that ameta-modelling approach using Kriging could be used effectivelyto locate a solution close to the optimum without muchcomputational cost. However, this technique depends on theaccuracy of the meta-model.

Reliability-based design optimisation works on the basis of aconcept of reliable design space (RDS), within which any designsatises the reliability requirements [42]. Designing a vehicle withoptimum crashworthiness requires the reliability-based approach.This type of optimisation problem can be represented as

minimise R0 x1;mx2 ;mp (10)

Such that; probgkx1; x2; pi0irx1k ; x1Lower x1

x1Upper; mx2 Lower mx2 mx2 Upper

where R0 is the reliability-based objective function, x1 is the vectorof deterministic design variables, and x2 and p are the vectors ofrandomdesign variables and design parameters.mx2 andmp are themean vectors of x2 and p. gk() is the kth constraint, and there are Lnumber of constraints. prob() is the probability function whichdenotes the probability of satisfying the kth constraint. The symbolrx1k

denotes the design reliability (or desired reliability/prob-ability) of satisfying the kth constraint. Often this optimisation isconsidered as an iterative numerical analysis process searching themost probable point (MPP) [55]. This is a time consuming processand several researchers have tried to reduce the computationalcosts by improving the reliability analysis method [5658]. Thelatest of these efforts [59] has demonstrated an improved approachby (1) analytically converting the feasible design space to thereliable design space, and (2) performing a deterministicoptimisation constrained by the reliable design space. The majorchallenge for these techniques is to address constraint functions ofdeep valleys.

3.5. Computationally expensive objective functions and surrogate

models

Design optimisation is limited by the computational cost of thedesign evaluation. Use of simulation techniques such as FEA,computational uid dynamics (CFD) and dynamic simulation ofmechanisms are very expensive. The simulations also bringunwanted noise in the evaluation [47]. Any optimisation approachthat requires several evaluations of the design is not suitable fordesign optimisation. A common approach to address the noise andcomputational cost issues is to use the simulation as numericalexperiments (instead of physical experiments), perform a numberof the experiments based on a design of experiment approach andthen develop an approximate model based on the simulationresults. Curve tting and other data modelling techniques are usedfor creating this surrogate models or meta-models [60]. A detailedreview of meta-modelling techniques has presented three majorstrategies for the modelling: sequential, adaptive and directsampling [61]. This review has identied that the meta-modellingapproach becomes less attractivewith an increase in the number ofdesign variables.

3.6. Dealing with qualitative design space

Design optimisation is often performed with quantitativeinformation. This information is based on a principle of numericalreckoning and is the ability to express the behaviour of aphenomenon in numbers using numerical models. There areaspects of a physical system that are less understood andambiguous or cannot be modelled using a numerical framework;these are termed as qualitative [60]. The qualitative nature ofdesign variables, objective function and constraints can contributein incorporating human knowledge either through a knowledge-based system framework [60] or through direct interaction [25]. Aknowledge-based approach based on fuzzy logic to deal with thequalitative design space introduces signicant discontinuities asshown in Fig. 6 for hot rolled rod shape optimisation. Optimisationwithin a highly discontinuous space is difcult. If the quantitativeand qualitative information is treated together within oneoptimisation framework, granularity of the qualitative informationshould also match the measurement scale of the quantitativeinformation, and that is not trivial. Another major challenge is toavoid any individual bias and user inconsistency.

4. An overview of engineering design optimisation approaches

Engineering designs are still optimised mostly through amanual iterative process where the designer compares a fewdesigns based on a small number of criteria (such as maximumstress and weight) and then selects the best design. It is such acommon procedure that it is not often published. Fig. 7 shows anoverview of EDO approaches based on publications over the last 10years. The designs are initially checked against any constraintssuch asmaximumcost, and only feasible designs are considered foroptimisation. This manual process is often limited to selectingdesigns which are recognised by the designers, and it fails toidentify any unknown but potentially signicantly better designs.This category of design optimisation is termed here as expert-based optimisation. This expert-based optimisation approachoften uses expert judgement (knowledge based) or simulationtechniques such as FEA or CFD analysis for the design optimisation.The major advantage of this approach is that designers do not

Fig. 6. The discontinuous nature of search space for rod shape design, where theroundness is a qualitative objective function and load quantitative [60]. R-1 stands

for Region 1.

of

R. Roy et al. / CIRP Annals - Manufacturing Technology 57 (2008) 697715 703are outside the comfort zone of designers. The approach providesa structure to the optimisation, but it can still be a very manualprocess. The approach works fairly well with design variables thatare independent from each other. In real life situation that is oftennot the case [14,62,63].

Use of algorithms for design optimisation is gaining popularity.This helps to partially automate the optimisation process andallows a better search for the best design. The algorithmicapproach to EDO can be mostly categorised for ve reasons:dealing with increasing complexity, real life design requirements,increasing designer condence, hybrid and other. Roy et al. [64]identied the above criteria as part of the major challenges in

Fig. 7. An overviewadoption of algorithmic design optimisation in industry. Thecomplexity of design optimisation varies from highly constrainedoptimisation, multi-disciplinary, multi-objective and multi-modaloptimisation. Multi-disciplinary design optimisation aims to nd aglobally best solution considering more than one discipline, saystructure, weight and aerodynamics [65]. For example, Wang et al.[66] presents multi-disciplinary optimisation of helicopter airintake scoop design involving couplings among deicing, aero-dynamic, and engine performance. Fig. 9 shows increasingpopularity and demand for multi-disciplinary optimisation com-pared to other design optimisation approaches. This analysis isbased on searches in Engineering Village database during 19972006. Multi-objective design optimisation is also gaining popu-larity since the last 5 years.

Fig. 8. Engineering design approaches vs. different classes of the optimisationproblem.Real life engineering design requires designs that are robust,reliable and can operate with inherent uncertainties associatedwith engineering systems. This is a growing area of research in thelast 10 years (Fig. 9). Reliability-based design optimisation looksfor optimal solutions considering probabilistic constraints [42].This optimisation approach is popular in structural designoptimisation as well. Another real life design requirement is toobtain robust optimum that is not sensitive to design tolerances,production parameter drifts during operation, and model sensi-tivities. Robust optimisation approaches [50] search for solutionsthat are in robust regions within a design space and locate theoptimum among the robust solutions. Ciof et al. [67] present a

EDO approaches.robust design approach formagnets and identies optimumdesignthat is not sensitive to design and manufacturing tolerances.Design optimisation within uncertain environment is a similarconcept to robust and reliability-based optimisation. In thiscategory approaches to quantify uncertainty and then performoptimisation is grouped together. Agarwal et al. [43] havedemonstrated the use of evidence theory to quantify epistemicuncertainty in a multi-disciplinary design problem. Increasingdesigner condence on the algorithmic design optimisation is akey challenge to increase adoption of the approach in industry.Currently, two main approaches are used to address this issue: byinvolving the designers during the optimisation process and bycapturing their knowledge as qualitative objective functions forthe design. Designers often complain about the simplicity of theapproximate models used in algorithmic design optimisation. It isoften not possible to analytically or numerically model everyimportant aspect of a design mainly due to the level of effortrequired.

To address this need, several researchers [6870] havepresented an interactive design optimisation approach wheredesigners can qualitatively judge designs and give a rating. Designsare optimised based on this qualitative tness function and otherquantitative functions together. Oduguwa et al. [60] havedeveloped a knowledge-based model of the qualitative aspectsof steelmaking roll design by involving designers and design teamleaders. The model is then used together with other quantitativetness measures for a multi-objective optimisation.

The other two categories represent hybrid approaches toalgorithmic optimisation and approximate model based and single

nte

R. Roy et al. / CIRP Annals - Manufacturing Technology 57 (2008) 697715704objective optimisations. Rao and Shyju [71] present a hybridmeta-heuristic algorithm for combinatorial optimisation of laminatecomposite cylindrical skirt which combines the good features ofpopular guided local search algorithms like simulated annealingand tabu search. Qazi and Linshu [72] present a neural networkbased data driven approach to identify optimum conceptual designof spacecraft. Single objective approaches are still used, althoughmulti-objective optimisation is more close to reality and arebecoming popular. Deb [12] gives a good overview of singleobjective design optimisation approaches. The next section of thispaper identies major optimisation techniques used in each of theoptimisation approaches. Fig. 10 shows an overall growth in designoptimisation publications and a comparison with the optimisationused for mechanical parts. It is observed that adoption ofoptimisation approaches in mechanical part design is slower thanthe overall growth in all sectors together. Due to complexitiesmechanical part design optimisation often uses expert basediterative process.

5. Trends in design optimisation techniques

There are several optimisation techniques that are used indesign optimisation: human knowledge-based engineering tointelligent (adaptive) algorithms. Teti and Kumara [73] extensivelyinvestigated the state-of-the-art, technological challenges anddevelopment trends in applications of intelligent computingmethods in production engineering and gave particular attentionto the solution of design problems and issues in the manufacturing

Fig. 9. EDO approaches preseenvironment. Fig. 11 presents a list of several of these optimisationtechniques against relevant algorithmic design optimisation

Fig. 10. Growth of design optimisation publication and a comparison with theoptimisation for mechanical parts.approaches. The list attempts to identify all major approachesused in design optimisation including a few very recent techniquesthat are gaining popularity. The purpose of the diagram is topresent the whole spectrum of design optimisation and help inbringing different approaches together to solve real life designoptimisation problems.

Based on the Engineering Village database (Inspec andCompendex), it is observed that the top three design optimisationalgorithms used in the last 10 years (19972006) are: GeneticAlgorithms (693 publications), Linear and Quadratic programming(142 publications) and Simulated Annealing (98 publications).There are 58,982 publications on genetic algorithms over the last10 years (19972006) based on the Engineering Village databasesearch, whereas only 693 of them are related to designoptimisation. Please note, the results are limited to the qualityof the database. EDO needs to exploit more of the growingalgorithmic optimisation techniques.

It is worth noting that while genetic algorithms is the mostpopular technique for design optimisation, swarm intelligence [74]has become popular in the last 5 years and show potential forfurther use in design optimisation.

6. Engineering design optimisation in practice

Recently a survey was conducted involving ve UK-basedcompanies from aerospace, automotive and steelmaking industry(total nine engineers) to investigate issues related to EDO inindustry. The surveywas based on a semi-structured questionnaire

d in literature (19972006).uthEcofr

seevonom

AinpD5McopEleMm4d in face to face interviews and in email response. Results fromsurvey were also enhanced through discussions during thelutionary Computing in Practice sessions in the GECCO 2007ference (http://www.sigevo.org/gecco-2007/). Major remarksthe survey are reported below (Fig. 12).

ll the organisations had a design development process (at leastformally) and optimisation of the design took place within therocess using mostly expert-based optimisation approach.esign optimisation was time consuming and needed at least0% of design life cycle.ost did not use GA for the design optimisation (this is inntrast to the number of publications where GA is the mostopular).xisting expert-based optimisation approaches were relativelyss time consuming than GA.ajority admitted that they did not have a process to developodels for design evaluation.0% surveyed followed sequential process like:FEA and Computer Aided Engineering followed by classicalDOE and regression analysis.

R. Roy et al. / CIRP Annals - Manufacturing Technology 57 (2008) 697715 705

TTinTo

TfoLathhe main criterion to optimise a design was cost.he majority measured design efciency manually by compar-g:performance against target;output with cost;man-hours spent with other sister centers; orwith previous practice.he survey shows the majority of the companies try to achieveptimised design:as a balance between cost, quality and time but the designmaynot be the best;40% generally support continuous improvement as a way toimprove the design.here is a signicant gap in getting test result feedback on timer the design optimisation.st minute change in design specication puts a lot of strain one resources and therefore inhibits the optimisation.

Fig. 11. Major techniques used in relevant alg

Fig. 12. Industrial survey observation.

locofo

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oriLack of integrated software tools to support the optimisationprocess.Internationally (through discussions at GECCO) there is anincreasing recognition of algorithmic optimisation for engineer-ing design. GAs are known to designers as a potential technique.There are issues related to the recognition of IntellectualProperty rights for designs developed using evolutionarycomputing technique (stochastic method) such as GAs.Major inhibitors to the use of an algorithmic approach for designoptimisation are:work load and priorities, cost and constraints inoperating especially within global organisations. Global organi-sations often like to decide the design process and tools to beused centrally, which could stie local interests in using analgorithmic approach for optimisation.

Developing novel designs using GAs may fail to describe agical product development process involving stakeholders. Thisuld be difcult when applying for patents or intellectual rightsr a design.

. Expert based design optimisation

Design optimisation of real life problems is often done byesigners using their experience. This process is often iterative,me consuming and is limited by the knowledge of the designer.hlmann and Schauer [29] have used FEA and empirical loadalysis to optimise the shape of microend mills (see Fig. 13).

osatti et al. [31] have presented an approach to optimise parallelinematicmechanisms based on kineto-static optimisation criteriathe only criteria. Zirn et al. [28] have optimised fast axis feed

thmic design optimisation approaches.

R. Roy et al. / CIRP Annals - Manufacturing Technology 57 (2008) 697715706drives using an analytical approach through nonlinear stabilityanalysis. The optimisation is based on experimental results whichare limited in numbers, and therefore does not fully explore thedesign space. A similar approach is adopted by Lange et al. [30]where they used FEA simulations and lightweight prototyping forevaluating a selected set of designs. Other similar researches arereported by Heisel and Klotz [33]. A trial and error approach todevelop advanced materials for net shape sintering of gradedlaminated powder compact is also presented by Mori and Osakada[35]. FFAwas used to evaluate the designedmaterials. Lutters et al.and Vaneker et al. [75,76] developed a what-if analysis baseddecision support system for design optimisation. The approachreduces workload of expert designers and provides better insightabout the design space.

But this approach is still limited by the amount of search onecan perform to nd the best solution. Another expert basedapproach to optimise design is based on inexpensive and rapidprototype development. For example, Krause et al. [36] havepresented a methodology to link CAD and rapid prototyping keyareas in a design to support the product development process. It is

Fig. 13. Conventional and optimised microend mills [29].argued that for effective use of rapid prototyping in optimisation, itshould be fully integrated as part of the product development. Janzet al. [37] have developed an approach to optimise designsmanually based on value-oriented life cycle cost analysis. Theapproach considers life cycle cost as the only objective, in realitythere are several objectives, such as environmental impact.

The other approach to expert based design optimisation is touse a computer based system that uses knowledge elicited fromexperts and can automate the design. knowledge-based systems(KBSs) (also called expert systems) are computer programsembodying knowledge about a narrow domain for solving and/or searching for the optimal solution to problems related to thatdomain [77]. More information on the technology of KBSs can befound in most standard KBS textbooks [78].

Kimura et al. [79] have developed an expert system for injectionmoulding tool design. This is resource intensive during the expertsystem development and is dependent on the participation of thedesigners. The approach is more suitable for variant type designs.Yang et al. [80] have described an intelligent design system byintegrating an expert system, FEA and a CAD system for forging tooldesign. The integrated approach has reduced the design optimisa-tion time through automated link, but the nal selection is stilldriven by the designers. Ismail et al. [81] used an expert systemshell called kappa for press tool design optimisation. Thisapproach is also suitable for variant type design. Teti et al.[82,83] have applied intelligent computing approaches to thedesign of multi-step cold forging tools for the fabrication of multi-diameter shafts with different congurations and diverse workmaterials. Initially, a rule-based expert system was developed forthe generation of cold forging working sequences and identica-tion of the corresponding tool design. Then, supervised learningneural network techniques were applied to assess the producttechnological feasibility and associate the correct forming toolgeometries to be employed.

8. Design of experiment-based design optimisation

It is often difcult to mathematically establish a relationshipbetween product performances and its design variables. Design ofexperiment (DOE) is a technique to empirically understand theimpacts of design variables on the design performance andtherefore aid in identifying optimum variable values [14]. Thisexperimental method of optimisation is based on a fractionalfactorial experiment which allows an experiment to be conductedwith only a fraction of all the possible experimental combinationsof design variable or design factor values. Standard orthogonalarrays are used to design the experiments. The orthogonal arraydenes the values of the parameters for each experiment.Frequently, two orthogonal arrays are used, i.e. design and noisefactormatrices. A potential weakness of the approach is that it maylead to a large number of experiments. To overcome this problem,some researchers [8487] have proposed the use of a combinedarray where control and noise factors are combined in a singlearray. Each factor is divided into levels, typically 25. Experimentsare designed as a combination of the factor levels. Signal to noiseratio is used as a metric to summarise the contribution of eachfactor level and the amount of variability observed duringmultipleexperiments. A mean signal to noise ratio value is calculated foreach design factor level. This data is statistically analysed usinganalysis of variation (ANOVA) techniques. To maximise the designperformance andminimise the noise, factor levels with the highestimpact are selected as the optimum design variable values. DOEhas two types of use in design optimisation, one is directoptimisation and the other is a supporting role, where DOE isoften used to dene the data points for surrogate modeldevelopment.

8.1. Direct optimisation using DOE

Rout and Mittal [88] have applied the DOE technique tooptimise design variables for a rather complex planar robotmanipulator. The researchers introduced a normally distributednoise and used simulation-based experiments instead of physicaltrials. Selecting the right levels for each design factor andidentifying the real noise involved are the major challenges inusing DOE. It is also observed that this technique is more suitablefor designs with a smaller number of variables (around 10).Evangelaras et al. [89] have presented a DOEwith combinedmatrixto reduce the number of experiments required. Yu and Jin [90] haveused DOE to optimise microelectronic packages in two stages: rstto identify the most important design variables, and then a fullfactorial DOE was carried out to study the key factors and theirinteractions.

8.2. Supporting modelling and optimisation

DOE is also used to dene the data points to develop surrogatemodels in case of expensive objective functions. Oduguwa et al.[60] have demonstrated the use of the orthogonal matrix for datapoint selection for response surface modelling of FEA results for asteel rolling system design. Hou et al. [91] have presented anapproach to use DOE with D-optimal criteria technique toconstruct response surface for the objective of specic energyabsorption and the constraint of maximum peak load, respectivelyto perform crashworthiness based design. The research uses an

of variables. It is also observed that parameter optimisation often

Fig. 15. Experimental results (assuming two objectives) (units:Wcr in kg/s, Twg in K)[14].

R. Roy et al. / CIRP Annals - Manufacturing Technology 57 (2008) 697715 707iterative linear process to approximate the real nonlinearity in theproblem. Shuaeib et al. [92] have designed a motorcycle helmetliner material with expensive FEA simulation and DOE to under-stand the effect of different factors on the helmet design. Similarresearch is reported by other researchers [9395]. Yeniay et al. [96]have utilised a dual response surface approach to quantifyvariability in critical performance characteristics during theconceptual design phase of a launch vehicle. In this example bothmean and variability is minimised simultaneously. There are otherdesign applications where a trade-off between the mean perfor-mance and variability is required.

9. Genetic algorithms for design optimisation

Genetic algorithms are stochastic search and optimisationalgorithms that mimic Darwins theory of biological evolution. Theidea behind a GA is to use this power of evolution to solveoptimisation problems. The father of the Genetic Algorithm is JohnHolland who invented it in the early 1970s. As seen in Section 5,GAs are currently the most popular design optimisation algo-rithms; the popularity has grown rapidly in the last 10 years. GAworks on the composition of genetic traits called chromosomes, inwhich successive operations through crossover or mutation giverise to better performing off-springs (population) due to successiverenement of these hereditary traits. GA works with a populationof design solutions (rather than single solutions as is the case withmany traditional optimisation algorithms) and tries to nd the bestsolution. A design solution, composed of the design variables, isrepresented as a single chromosome. This chromosome can beeither binary or real valued. The GA starts with a randompopulation of the chromosomes. The chromosomes are evaluatedusing an objective or tness function. GA is not dependent ongradient-based model for the design evaluation, and this is anadvantage in using the GA. The chromosomes are manipulated byGA parameters such as crossover and mutation. Crossovercombines characteristics of two parent chromosomes to producetwo children chromosomes and mutation brings a sudden changein the chromosome. GA is based on passing hereditary traits fromgood designs to the next generation through a selection processsimilar to natural selection. A good description of GA is presentedin [12]. GA is more popular for multi-objective design optimisationthan classical optimisation algorithms [12]. This section providesan overview of GAs to solve mechanical EDO problems. GAs aremostly used for design parameter (or size) optimisation, shapeoptimisation or topology optimisation. Nassef and ElMaraghy [97]have also used GA for type and magnitude optimisation ofgeometric tolerances. The methodology can be computationallyexpensive, although the authors offer some ideas to reduce thecost.

9.1. Genetic algorithms for parameter optimisation

Design parameter optimisation problems include automotivechassis design, turbine blade cooling system design, vehiclesuspension design, wing planform design, bearing design, micro-uidics, microactuator design, multibody rail vehicle design, speedreducer design, composite leaf spring and composite drive shaftdesign. Most of these applications are multi-objective in naturewith less than ve objectives [98]. It is also observed that some ofthe applications have dealt with more than 10 design variables butwhen it comes to constraints, it is observed that the number ofconstraints is typically less than 5. Most of the applications involvemixed type variables. There are applications that are only tested ontest functions, 12 out of 30 parameter optimisation problems areabout real life applications. One of the challenges in the parameteror size optimisation problem is to deal with design variableinteraction, as mentioned in Section 3.3. Roy et al. [20] havepresented a turbine blade cooling system optimisation problemwith inseparable design variable interaction. Roy [14] presentsdevelopment of an analytical model (that is the objective functionfor the design) to calculate coolantmass ow for radial passage andmetal temperature gas side (Fig. 14) based on twelve designvariables. The problem also has 15 constraints including the designvariable bounds. The model follows an iterative process tocalculate the tness values. This design problem is nonlinearand has bias in the design space. The tness function is implicit andmulti-layered. Hence, the determination of tness values requiresan iterative procedure in which the effect that a variable has on theobjective functions depends on the values of other variable in thefunction. This shows a high degree of inseparable functioninteraction [20]. Full details of the model are presented in [14].For any continuous portion of a Pareto front, there is a uniquerelationship involving objective functions. This relationship isdifcult to obtain analytically, and even if it is found, it has limitedusefulness since mapping from function space to variable space isvery complex. However, the existence of a relationship amongtness functions of Pareto solutions necessarily implies thatcorresponding relationship(s) exist among the decision variablesof these solutions [13]. An advanced GA called generalisedregression GA (GRGA) is used to explore this relationship withinthe turbine blade design optimisation. It is observed that GRGA hasconverged to the global Pareto front as shown in Fig. 15 and againstan exhaustive search (10,000 random points). The application hasestablished that GRGA successfully handles complex inseparablefunction interaction to identify a range of optimum feasibledesigns fromwhich one could nally be chosen based on designerspreferences.

One of the major problems in parameter optimisation applica-tions is the computational costs of the tness functions. One of thecommonways to deal with this is to use surrogatemodels based ona small number of simulation results. The major challenge is todevelop acceptable surrogate models in the case of larger numbers

Fig. 14. Design of a turbine blade cooling system [14].

design evaluation cost by using distributed parallel computingenvironment.

Nash equilibrium is the solution of a non-cooperative strategyof multi-objective optimisation rst introduced by Nash in 1951[123]. For a multi-objective optimisation with N objectives, a Nashgame consists ofN players, each in charge of one objective and abletomodify their sub-set of variables. GA implements this concept bydividing the population of design solutions into a number of sub-populations, each sub-population focusing on one design objectivekeeping other objectives xed. This approach helps to implement aparallel GA with reduced interaction time between the sub-populations. When no sub-population can further improve hisobjective function, the system has reached a state of equilibriumnamed Nash equilibrium. Although this approach has demon-strated a signicant speeding up as compared to sequential GA, itcould be further improved by better synchronisation requirementbetween sub populations.

It is observed that shape optimisation with a larger number ofdesign variables requires numerical simulation to evaluate thedesigns, thus making it often computationally expensive. Use ofapproximation methods such as surrogate model-based designevaluation (to reduce computational cost) is often not suitable dueto the large number of design variables. Galantucci et al. [119] havepresented a novel application of GA and neural networks for shaperegistration problem. Registration, dened as the process ofmatching geometric entities, is performed when multiple scanneddata sets must be aligned or when an existing model must match

R. Roy et al. / CIRP Annals - Manufacturing Technology 57 (2008) 697715708uses hybrid genetic algorithms where the algorithm is used toidentify good solutions and then a local search tries to nd theoptimum solution. A trend in the literature is the growingapplication of parameter optimisation for multi-objective designproblems [99104]. Multi-objective optimisation mostly dealswith a small number of objectives (less than 5). Kurpati et al.describes an improved constraint handling for speed reducerdesign and a design of a eet of ships with more than veconstraints [105]. The improvement is made in the tnessassignment stage of a multi-objective GA and are all based upona Constraint-First-Objective-Next model. Most of the otherpapers investigated had less than ve constraints. Similarly,majority of the application papers address design optimisationwith less than 10 design variables [106109]. It is observed thatdesign problems with more than 10 design variables are oftenexpensive to evaluate. One approach to deal with such problem is tousemeta-models instead of simulation-basedmodels for the designevaluation [100,101,110]. Duvigneau and Visonneau [111] haveused neural networks to create an inexpensive model of the design,similar to a meta-model. The model development would requiremore example design solutions than fractional factorial designs, likekriging. In terms of types of GAs used, hybrid algorithms are morepopular. Mian et al. [112] have presented a kriging assisted multi-objective genetic algorithmwhere the kriging-basedmeta-model isused to evaluate some designs. If the kriging-based evaluationchanges the non-dominated solutions within a GA generation, thenthosedesigns are evaluatedusing simulation. This approach reducesthe overall number of evaluations required and is suitable forcomputationally expensive design.

The other type of hybrid GA is developed by integrating localsearch techniques at the end of the GA [110]. Depince et al. [109]present an innovative mix of GA with a collaborative optimisationalgorithm. This hybrid GA is suitable for multi-level designproblems. Luo and Dai [113] have presented a hybrid GA thatincorporates previous knowledge about the design, called GeneExpression and Handling Genetic Algorithm (GEHGA). The inclu-sion of engineering design experiences and knowledge signi-cantly improves the algorithms quality of the initial populationand provides the capability of generating better genetic elementsfor the consequent generations. Another important problem forsize optimisation is hierarchical design, such as machine tooldesign. Yoshimura and Izui [114] have presented a hierarchicalchromosome structure that can deal with multilevel designproblems. For a complex multilevel design, such as rod rollingsystem design a very long chromosome could occur.

9.2. Genetic algorithms for shape optimisation

Shape optimisation is characterised by a larger number ofvariables and expensive evaluation. Application of shape optimi-sation includes compressor blade prole design [99], haptic devicedesign [115], pole shape of the synchronous generators [116],nozzle shape optimisation [117], parallel mechanism design [118]and automatic registration of free form surfaces [119]. Similar tothe previous paragraph, hybrid type GA is also popular in shapedesign problems. Deterministic local search is integrated with GAin [111]. Shape optimisation also often involves relatively largernumber of design variables, thus increasing their degree offreedom [99,115,116,120]. There are several attempts to dealwith computationally expensive shape design optimisationproblems. The expensive optimisation is performed either byparallel implementation of the GAwith game theory [117,121,122]or by more efcient GAs that require less expensive designevaluation [99,112]. Wang et al. [121] have presented ahierarchical GA where at the beginning they use very coarseand approximate models of design as objective functions and afterthe searchmatures they usemore precise models. This reduces thecomputational cost signicantly but at the same time achieves theaccuracy required for the nal design solutions. Then theyimplemented game theory tools with the GA to address thedigitized point clouds. This process is crucial in several applica-tions such as reverse engineering, CAD-based inspection andcomputer vision. Articial neural networks technique is used forpatternmatching, whereas GA is used tominimize error deviationsbetween the geometric entities. The formulation of the optimisa-tion problem using GA encodingwas performed by subdividing thepopulation into six sub-populations, one for each parameter to beoptimised, i.e. the translation components and Eulers angles.Fig. 16a and b show the results achieved by using a GA-basedoptimisation.

The other major challenge in shape optimisation is to deal withthe qualitative nature of objective functions [25,124129]. Thereare twomajor approaches in using GA for qualitative optimisation.One approach is to develop a fuzzy expert system to capture thequalitative nature of the objective function [60,127] and the other

Fig. 16. (a) A plastic element of the rear part of a motorcycle chassis [119]. (b) Finalalignment of the point clouds using the GA for the plastic part shown above [119].

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R. Roy et al. / CIRP Annals - Manufacturing Technology 57 (2008) 697715 709proposal has to be available that represents the structure of thedesign solution. Topology optimisation is widely used in structuraloptimisation applications, e.g. truss design [130132], and theseresearches are not covered in this paper. Week et al. [133]identied the potential of topology optimisation in productdevelopment and argued that the target should be the integrationof topology and shape optimisation in a CAD-System in order toproduce a tool which supports the complete design process.Mackerle [134] presents a recent review on topology optimisation.Chapman et al. [135] presents a cantilever beam topologyoptimisation using GAs. They identify that the optimisation ofteninvolves a large number of variables and involve computationalexpensive design evaluations (e.g. using FEA). In order to reducethe computational time, Kim and Weck [136] have proposed avariable length chromosome GA for progressive renement intopology optimisation. The chromosome length is increased by anincrease in the resolution of the existing design variables or by theaddition of new design variables during encoding. Bharti et al.[137] have used amulti-objective GA to optimally place cables andstruts in a bay or a section of an aircraft wing. Sid et al. [138] havedeveloped a novel topology representation using Bezier curveswith varying thicknessmaterial in a nite elementmodel. This newtechnique avoids the formation of disconnected elements andcheckerboard patterns in optimal topology design. They usemodied crossover and mutation GA operators to deal with thenew representation. Lu and Wang have shown how topologyoptimisation could identify totally new designs [139]. They applyGAs for developing designs of slider air bearings that meet thestrict performance demands of current hard disk drives. Thetopology-optimised design can be better than the one obtainedafter shape optimisation from an initial design. Although GA hassignicant potential for topology optimisation, scalability becomesa major weakness, especially because of computationally expen-sive design evaluation. There is a lack of GAs application for real lifeand large-scale topology optimisation problems. In future gridcomputing based approach for multi-objective GAs implementa-tion could address this issue [140].

10. Future challenges in algorithmic engineering designoptimisation

Considering the growth in publications using the algorithmicapproach for EDO, this approach has the best potential to improve adesign. Fig. 10 shows lack of popularity of algorithmic approach formechanical systems design optimisation compared to non-mechanical systems. This section identies the major challengesof algorithmic approaches for real life optimisation and thencomments on the possible reasons for lack of interest in themechanical systems design community. The major challenges are

Real life features: The features of real-life optimisation problems,especially the presence of interaction among decision variables,lack of prior problem knowledge and qualitative issues, createchallenges for optimisation algorithms. The lack of robustoptimisers that can effectively deal with these features preventstheir successful application in industry. This is particularly truefor those industries that deal with a wide range of complexdesigns.

Model development: All optimisation algorithms work onmathematical models of real-life designs. It was observed thatteractive GA [25]. The major limitation of these approaches isat not more than three to four objective functions can bedressed. With an increasing number of objective functions, theesign space becomes more discontinuous, making it difcult fore designers to interact effectively due to obvious human fatigue.

.3. Genetic algorithms for topology optimisation

Before using a size or shape optimisation, an initial designin

to involve designers directly within the search using anmetric reasoning such as feature technology/recognition to bemore integrated into the analysis algorithms and the optimisa-tion procedure to achieve what has been termed feature-basedoptimisation [145]. When these are addressed, several advan-tages will make optimisation techniques more attractive toengineers in industry who are not experts in optimisationtechniques. For example, most loading and boundary conditionscan be automatically extracted from feature-based CADmodel ofa product. Also, it would be easier to automatically generateintuitive visualisation which has been identied by Hernandezet al. [146] as a key need in order for engineers in industry to bebetween feature-based parametric CAD models and optimisa-tion/analysis models that ensure automatic bidirectional con-versions do not exist at present. Several researchers haveidentied this deciency [143,144]. Nosner [143] noted that afterthe shape or topology optimisation stage, the design engineerstill has to interact with the results to ensure that features areintegrated into the CAD model in an appropriate way.Researchers [143,145] have noticed that the lack of featureinformation prevents the application of meaningful engineeringconstraints. Addressing these needs requires high level geo- Infunctions (e.g. fuzzy expert system-based model) increasesexponentially with the increase in number of variables. Develop-ingaqualitativeobjective function that representsabroad rangeofphysical phenomena from a different perspective at a level whichallows useful and veriable inference to be drawn can also becomputationally expensive and non-trivial [60].tegration with CAD and simulation: The bidirectional interfacecosts. In linewith this there is increasing interest to solve real lifelarge-scale design optimisation problems. Recently, use of gridand distributed computing is beginning to address this issue forlarge-scale optimisation problems [141,142]. This is discussed inmore detail in Section 12.Qualitative design space: Another major challenge would be toextend the algorithmic optimisation approaches to deal withlarger scale qualitative design spaces. It would be ideal to handlequantitative and qualitative information together within oneframework. Design evaluation time using qualitative objectiveaimprovement process. This process gradually evolves in thecompany, and hence its people resist the implementation of anynew optimisation system and the associated organisationalchanges. Further, the costs associated with creation, installationand maintenance of optimisation algorithms discourage theiruse in industry.Computational expense of design evaluation: One approach to dealwith computationally expensive design evaluation models is todevelop surrogate models to replace the expensive designmodels. Increasingly there is demand to work with moreccurate models and nd ways to deal with the computational Dsince designers prefer maintaining full control on the designimprovement process, they have little faith in themodels that areprovided to them. This makes them skeptical about the resultsobtained from the optimisation algorithms. This situation isfurther worsened by the fact that there is a lack of modeldevelopment skills among designers in industry. There is also alack of commercial tools required for carrying out the task ofmodel development. It is also observed in some cases thatdesigners lack knowledge about how legacy models may work;often they nd it difcult to understand existing models.Designer condence: Another inhibitor to the use of optimisa-tion algorithms in industry is the important role of designersskills and experience in the design improvement process. Thismakes the optimisation task very difcult tomodel and encode inalgorithmic form. The lack of designers knowledge in using thesealgorithms also presents a further obstacle to their use inindustry. This could be addressed by involving designers in thesearch process either to provide their past knowledge as startingpoint of the optimisation for objective function development [9]or through an interactive optimisation process [25].esign improvement process: Each company has its own design

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R. Roy et al. / CIRP Annals - Manufacturing Technology 57 (2008) 697715710deterministic thinking. It is necessary to introduce optimisationconcepts, techniques and model building approaches within theundergraduate course curriculum.

The following are some potential reasonswhy designers are stillot using the algorithmic approach in the design of mechanicalstems as effectively as others:

Complexity from scalability: Scalability is a major challenge formechanical systems design optimisation. Large-scale designoptimisation requires approaches to deal with the complexity.Lack of understanding of the behaviour of complex mechanicalsystems: There is a lack of understanding about the interactionoptimisation algorithm(s). The automatic upgrade mechanismsalready present in most software that allows the update throughthe Internet may be helpful also. But the upgrade needs to gobeyond the black box method and be transparent as well asupgrading the unied taxonomy. However, please note thatthere is no single best optimisation algorithm for all problems,this is called no free lunch theorem [149].Dynamic optimisation: Recently there is interest in designoptimisation within a dynamic environment. One example isto optimise rotor-bearing systems with dynamic constraints[150]. Maalawi [151] presents a wind turbine design optimisa-tion with dynamic loading conditions from wind speeds andyawning motions of the turbine. One approach to consider adynamic environment is presented in the contribution of Changand Joo [152] using dynamic simulation of mechanisms. Theseresearches are still developing and signicant amount ofresearch would be required to extend the results to complexmulti-objective design optimisations. In the case of a dynamicmulti-objective optimisation the designers could obtain a set ofPareto optimal design solutions that change with time. The nextchallenge is to develop an optimisation approach that is robustagainst the changing environment and supports designers toselect the design solution.Education: Designers also lack knowledge of optimisationconcepts and an overview of approaches. stochastic optimisa-tion, like genetic algorithms, is contradictory to conventionalnot getting bogged down with all the mathematics andcomputational algorithm details of every new development?Even in commercial integrated optimisation tools/environmentsuch as VisualDOC or Altair OptiStruct, the user is still required toselect the optimisation technique to be used to solve a problem.Egorov et al. [148] have made some contributions in thisdirection by proposing an evolutionary self-organising algorithmwhich adaptively selects algorithm(s) suitable for each particularproblem. The technique is capable of handlingmultiple objectivefunctions and constraints which may be non-differentiable,stochastic, with multiple optima, and mixed variables and usersare not required to have any knowledge of nonlinear program-ming or optimisation procedures. However, the user is stillrequired to set up the equations dening the physics of theproblem. The use of a unied taxonomy of problems and solutiontechniques may also help this problem of selecting the bestminformation backbone or infrastructure [147] that is exible tosupport changes in geometry, meshes etc and able to dynami-cally link with FEA or optimisation and CAD systems throughdata exchange of native parametric CAD formats. In the long-term, it would require an extendible integrated informationinfrastructure for CAD/FEA/Optimisation based on internationalinteroperability standards such as STEP (ISO 10303).

Selecting an appropriate optimisation algorithm: Since there areseveral optimisation algorithms, how can the user select the bestethod without missing out on the most effective technique butfeinapplication of geometric modelling and reasoning will allowanalysis (e.g. FEA), optimisation algorithms and parametricature-based CAD systems to be transparently and intuitivelytegrated. In the short term, this may mean an integratedcomfortable with the use of optimisation techniques. TheThe process of design search and optimisation involvesodelling and analysis of engineering problems to yield techni-lly and economically improved designs. CFD is involved in thisrocess when it comes to design optimisation of automotive androspace products. Detailed analysis of the properties of theseroducts using CFD is usually computationally and data intensive.between mechanical components and their behaviours. Thismakes model development very challenging. Numerical simula-tion, virtual testing, qualitative model development can addressthis problem with additional computational and developmentcosts.

Inherent uncertainty in performance of mechanical systems:Uncertainty is another major challenge for mechanical systemsdesign optimisation. There is a signicant level of interest in thisarea of optimisation research. Robust design, design withuncertainty and reliability-based design optimisations areaddressing the issue and all of them have problem withscalability (large-scale problem).

11. Future approaches to engineering design optimisation

It is observed form the analysis presented above there are threemajor areas of improvement when it comes to use of computing toaddress engineering design optimisation: improve efciency andspeed of optimisation and use human knowledge effectivelywherenecessary. The two following sections will discuss role of Grid anddistributed computing to speed up the optimisation and involvemultiple experts in the design process; and emergent computingtechniques for better efciency and speed in the optimisation.

11.1. Engineering design optimisation using grid and distributed

computing

Large-scale EDO of complex mechanical systems such asaerodynamic wing design and gas turbines involve complexprocesses with multiple iterative steps that require huge data andcomputational resources to obtain satisfactory optimum solutions[153,154]. The use of control theory and parallel distributedcomputing has proved to greatly improve the speed of aero-dynamic shape optimisation of supersonic aircraft design [155].Though parallelising and distributing different computationaltasks to different processors in distributed computing architectureimproves speed of design optimisation, the need for multi-disciplinary experts to collaborate and share data and knowledgeusing heterogeneous platforms (software and hardware) is a bigchallenge. Grid computing is distributed computing taken to thenext evolutionary level. The goal is to create a large and powerfulself-managing virtual computing system out of a large collection ofconnected heterogeneous computers sharing various combina-tions of resources. Grid computing provides the middleware formulti-disciplinary experts to analyse and optimise designs fromdifferent geographical locations [141]. This section presents theadvantages of using high performance computing (HPC) and gridcomputing for the optimisation.

Design optimisation involves workow of steps with depen-dencies. These workow dependencies can be difcult toaccomplish within the time constrain of most projects becauseof the number of analysis tools involve in analysing meshgeneration and sending solutions to the next step. An automatedand integrated workow process can be implemented within agrid-enabled environment [156,157]. Practical design optimisationof laminated composite structures leads to high dimensional,multi-modal and non-differentiable optimisation problems whichare difcult to solve [142]. This problem is further complicated asthere is no unique laminate conguration which can give anoptimum solution for all design criteria simultaneously. Usingdistributed parallel computing and grid computing can overcomethis problem as each node will perform computations for eachcriteria. These are a kind of divide and conquer optimisationprocesses [158].

R. Roy et al. / CIRP Annals - Manufacturing Technology 57 (2008) 697715 711Grid tools like Geodise (grid-enabled optimisation design searchfor engineers) incorporates distributed data, computational andanalysis tools as services for engineers to access and use efciently[159]. Sasaki et al. [160] have demonstrated application of a hybridgenetic algorithmic formulti-objective optimisation of single stagerotor/stator blades for a multistage compressor to improveaerodynamic performance in terms of efciency, blockage andloss, while satisfying four aerodynamic constraints to maintain theow similar to a baseline geometry.

Current limitations in parallel distributed and grid computingin the area of design optimisation are non-inclusion of companyculture in grid platforms, lack of tangible denition of what qualityof service means to different users and lack of economic modelsthat implement service-oriented architectures based on demandand supply chain strategies as obtained in conventional globalmarket. Another limitation is the lack of security guarantee thatsome sensitive data such as cost model which is part of designoptimisation may be accessed by competitors. Future trends in theresearch aim to tackle the limitations mentioned. Gridbus is aproject that aims at providing an economic model for service-oriented distributed and grid computing applications. Workowmanagementmodels that tackle design optimisation dependenciesare part of future research trend. Building robust securitymeasuresinto the Grid Security Infrastructures so that only the provider hasaccess to sensitive data is the trend in grid security. All thesefeatures of a large-scale design optimisation can be addressedusing a service-oriented grid computing.

11.2. Emergent computing techniques

Swarm Intelligence was identied as a promising newoptimisation technique in Section 5. It is an attempt to developalgorithms inspired by the collective behaviour of social insectsand other animal societies. There are two major categories ofalgorithmic optimisation swarm intelligence approaches: antcolony optimisation algorithms and particle swarm optimisationalgorithms. Dorigo and Blum [161] have provided a comprehensivesurvey of theoretical foundation of ant colony optimisation. Thealgorithms constitute mostly algorithms for discrete optimisationthat took inspiration from the observation of the foraging behaviorof ant colonies [73]. These algorithms have more potential toaddress qualitative search spaces in design optimisation. Recentlyant colony optimisation research is extended to continuous designspaces as well [162] using a hybrid approach with chaoticsequences. On the other hand particle swarm intelligence isinspired by human social behaviour [163]. Particle swarmoptimisation algorithms are applied to several parameter andlayout optimisation problems, such as recongurablemachine tooldesign [164], design of composite structures [165], layout ofsatellite modules [166], induction motor design [167] and ceramictile manufacturing [168]. The optimisation is also becomingpopular for multi-objective optimisation [169173] and fordynamic environments optimisation [174]. A recent trend is tointegrate features of swarm intelligence with other optimisationtechniques for more efciency [175178].

Simulated annealing is another popular optimisation techniqueas identied in Section 5. The technique is a global optimisationprocedure which is inspired by the physical process of annealing[179,180]. Suman and Kumar have presented a survey of simulatedannealing application for single and multi-objective optimisations[181]. The technique is used for both parameter [167,182183] andshape optimisations [184186].

Other recent approaches with potential for application indesign optimisation are continuous estimation of distributionalgorithm for continuous single and multi-objective designproblems [187189], and differential evolution technique forconstrained design optimisation [17,107,190,191]. Zhou and Sunhave presented a survey of estimation of distribution algorithms[192]. Emergent synthesis approach is used to solve complexsynthesis problem inmanufacturing [193195]. Distributed designfor a complex product like aircraft has similar synthesis challenge(at least it is a case II problem). Design is becoming more complexwith new product-service system-based business models [196]. Inthis new business model, companies sell functionality rather thanthe product itself, and in some industry it is a long-term provision[197]. Design of product-service systems includes co-design ofphysical (e.g. product) and non-physical solutions (e.g. life longservice and support). Emergent synthesis has signicant potentialto contribute to product-service system design.

Quantum computing is a new computing paradigm withsignicant promise. The basic principle of quantum computationis that the quantum properties (Qubits) can be used to representand structure design related information, and that quantummechanisms can be devised and built to perform operations withthis information. Quantum computing provides a faster and moreefcient computing framework [74,198]. The recent trend inoptimisation includes a hybrid approach to use quantumcomputing for combinatorial, and non-convex optimisationproblems. It is observed that the optimisation performance hasimproved by integrating quantum computing with geneticalgorithms [199,200] or swarm intelligence [201,202]. Quantumcomputing based optimisation techniqueswould have a signicantpotential for large-scale design optimisation problems.

12. Summary and concluding remarks

EDO has evolved with time from a totally manual process tocomputer-based approaches. This paper proposes a classicationof the optimisation problems based on two view points: designevaluation effort and degrees of freedom. These view points arerelevant for mechanical engineering problems and show themajorissues in the optimisation. Mathematical challenges in designoptimisation identify current state of the optimisation. The studythen supports classifying the EDO approaches as expert-based,DOE-based and algorithmic. It is observed that current approachesare unable to address large-scale problems. The number ofpublications recorded in one of the commercial databases is usedas a criterion to judge the relative popularity of differentapproaches and optimisation techniques. It is observed that thegenetic algorithm is the most popular algorithmic technique foroptimisation. However, the algorithmic approach for designoptimisation (e.g. GA) is not very popular within the small numberof industries surveyed. Although algorithmic approaches areincreasingly used to solve mechanical component design optimi-sation problems, but some of themare never published as papers inorder to protect the intellectual property. The study identies themajor inhibitors in the industry acceptance of the optimisationapproach. An overview of expert-based and DOE-based optimisa-tion and application of GAs have identied the current state of theresearch. Lack of knowledge and a systematic model developmentprocess inhibits designers to adopt the algorithmic approach.

It is observed that scalability is the biggest challenge.Algorithmic optimisation is becoming popular for EDO based onthe number of papers published, but it is still not widely used inindustry. GAs are the most popular algorithmic optimisationapproach. Large-scale optimisation will require more research intopology design, computational power and efcient optimisationalgorithms. Grid computing provides an opportunity to improvethe speed of EDO and involve multiple experts. Emergentcomputing techniques such as swarm intelligence and quantumcomputing improve efciency and speed of the optimisation.Future success of EDO is in application of expert knowledge withexisting and emergent algorithmic and computing approaches tolarge-scale designs, supported by education on optimisation.

Acknowledgements

Authors are grateful to Professors F.L. Krause, Moshe Shpitalni,Tetsuo Tomiyama, G. Seliger, Stephen Lu, Peihua Gu, Neil Dufe,Joost R. Duou, John Corbett, K. Ueda, S. Tichkiewitch, L. Monostori

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