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Outline Introduction Historical Highlights Some Applications Little Known Approaches The Algorithms that the World Forgot Current State and Future Challenges Evolutionary Multi-Objective Optimization: Past, Present and Future Carlos A. Coello Coello [email protected] CINVESTAV-IPN Evolutionary Computation Group (EVOCINV) Computer Science Department Av. IPN No. 2508, Col. San Pedro Zacatenco exico, D.F. 07360, MEXICO Lisbon, Portugal, March 2019 Carlos A. Coello Coello EMOO: Past, Present and Future

Evolutionary Multi-Objective Optimization: Past, Present ......Evolutionary Algorithms Evolutionary algorithms seem particularly suitable to solve multiobjective optimization problems,

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Page 1: Evolutionary Multi-Objective Optimization: Past, Present ......Evolutionary Algorithms Evolutionary algorithms seem particularly suitable to solve multiobjective optimization problems,

OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Evolutionary Multi-Objective Optimization:Past, Present and Future

Carlos A. Coello Coello

[email protected]

Evolutionary Computation Group (EVOCINV)Computer Science Department

Av. IPN No. 2508, Col. San Pedro ZacatencoMexico, D.F. 07360, MEXICO

Lisbon, Portugal, March 2019

Carlos A. Coello Coello EMOO: Past, Present and Future

Page 2: Evolutionary Multi-Objective Optimization: Past, Present ......Evolutionary Algorithms Evolutionary algorithms seem particularly suitable to solve multiobjective optimization problems,

OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Outline of Topics

1 Introduction

2 Historical Highlights

3 Some Applications

4 Little Known Approaches

5 The Algorithms that the World Forgot

6 Current State and Future Challenges

Carlos A. Coello Coello EMOO: Past, Present and Future

Page 3: Evolutionary Multi-Objective Optimization: Past, Present ......Evolutionary Algorithms Evolutionary algorithms seem particularly suitable to solve multiobjective optimization problems,

OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Motivation

Most problems in nature have several (possibly conflicting)objectives to be satisfied (e.g., design a bridge for which wantto minimize its weight and cost while maximizing its safety).Many of these problems are frequently treated assingle-objective optimization problems by transforming all butone objective into constraints.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Formal Definition

Find the vector ~x∗ =[x∗

1 , x∗2 , . . . , x

∗n]T which will satisfy the m

inequality constraints:

gi(~x) ≤ 0 i = 1,2, . . . ,m (1)

the p equality constraints

hi(~x) = 0 i = 1,2, . . . ,p (2)

and will optimize the vector function

~f (~x) = [f1(~x), f2(~x), . . . , fk (~x)]T (3)

Carlos A. Coello Coello EMOO: Past, Present and Future

Page 5: Evolutionary Multi-Objective Optimization: Past, Present ......Evolutionary Algorithms Evolutionary algorithms seem particularly suitable to solve multiobjective optimization problems,

OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Notion of Optimality in MOPs

Having several objective functions, the notion of “optimum”changes, because in MOPs, we are really trying to find goodcompromises (or “trade-offs”) rather than a single solution as inglobal optimization. The notion of “optimum” that is mostcommonly adopted is that originally proposed by Francis YsidroEdgeworth in 1881.

Carlos A. Coello Coello EMOO: Past, Present and Future

Page 6: Evolutionary Multi-Objective Optimization: Past, Present ......Evolutionary Algorithms Evolutionary algorithms seem particularly suitable to solve multiobjective optimization problems,

OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Notion of Optimality in MOPs

This notion was later generalized by Vilfredo Pareto (in 1896).Although some authors call Edgeworth-Pareto optimum to thisnotion, we will use the most commonly accepted term: Paretooptimum.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Pareto Optimality

DefinitionWe say that a vector of decision variables ~x∗ ∈ F is Paretooptimal if there does not exist another ~x ∈ F such thatfi(~x) ≤ fi(~x∗) for all i = 1, . . . , k and fj(~x) < fj(~x∗) for at leastone j .

Carlos A. Coello Coello EMOO: Past, Present and Future

Page 8: Evolutionary Multi-Objective Optimization: Past, Present ......Evolutionary Algorithms Evolutionary algorithms seem particularly suitable to solve multiobjective optimization problems,

OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Pareto Optimality

Explanation of the Definition

In words, this definition says that ~x∗ is Pareto optimal if thereexists no feasible vector of decision variables ~x ∈ F whichwould decrease some criterion without causing a simultaneousincrease in at least one other criterion. Unfortunately, thisconcept almost always gives not a single solution, but rather aset of solutions called the Pareto optimal set. The vectors ~x∗

corresponding to the solutions included in the Pareto optimalset are called nondominated. The plot of the objective functionswhose nondominated vectors are in the Pareto optimal set iscalled the Pareto front.

Carlos A. Coello Coello EMOO: Past, Present and Future

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Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Mathematical Programming Techniques

Currently, there are over 30 mathematical programmingtechniques for multiobjective optimization. However, thesetechniques tend to generate elements of the Pareto optimal setone at a time. Additionally, most of them are very sensitive tothe shape of the Pareto front (e.g., they do not work when thePareto front is concave or when the front is disconnected).

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Evolutionary Algorithms

The idea of using techniques based on the emulation of themechanism of natural selection to solve problems can betraced as long back as the 1930s. However, it was not until the1960s that the three main techniques based on this notion weredeveloped: genetic algorithms [Holland, 1962], evolutionstrategies [Schwefel, 1965] and evolutionary programming[Fogel, 1966]. These approaches are now collectivelydenominated evolutionary algorithms.

Carlos A. Coello Coello EMOO: Past, Present and Future

Page 11: Evolutionary Multi-Objective Optimization: Past, Present ......Evolutionary Algorithms Evolutionary algorithms seem particularly suitable to solve multiobjective optimization problems,

OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Evolutionary Algorithms

Evolutionary algorithms seem particularly suitable to solvemultiobjective optimization problems, because they dealsimultaneously with a set of possible solutions (the so-calledpopulation). This allows us to find several members of thePareto optimal set in a single run of the algorithm, instead ofhaving to perform a series of separate runs as in the case ofthe traditional mathematical programming techniques.Additionally, evolutionary algorithms are less susceptible to theshape or continuity of the Pareto front (e.g., they can easilydeal with discontinuous or concave Pareto fronts), whereasthese two issues are a real concern for mathematicalprogramming techniques.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

The potential of evolutionary algorithms in multiobjectiveoptimization was hinted by Richard S. Rosenberg in his PhDthesis from 1967, which is entitled “Simulation of geneticpopulations with biochemical properties”.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

However, the first actual implementation of a multi-objectiveevolutionary algorithm (MOEA) was John David Schaffer’sVector Evaluated Genetic Algorithm (VEGA), which dates backto 1984. This was a naive multi-objective evolutionaryalgorithm, whose selection mechanism did not rely on Paretooptimality.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In the old days, two types of approaches were normallyadopted with evolutionary algorithms:

1. Aggregating functions: They basically transform amulti-objective optimization problem into a scalaroptimization problem. For example, a linear aggregatingfunction normally has the form: min

∑ki=1 wi fi(~x) where

wi ≥ 0 are the weighting coefficients representing therelative importance of the k objective functions of ourproblem.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In fact, linear aggregating approaches are the oldest mathematicalprogramming methods proposed to solve multi-objective optimizationproblems, since they can be derived from the (famous) Kuhn-Tuckerconditions for nondominated solutions. Linear aggregating functionsare considered “evil” by most EMO researchers because of theirlimitations (they cannot properly generate nonconvex portion of thePareto front). Note however, that nonlinear aggregating functionsdo not have this limitation.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

2. Lexicographic ordering: In this method, the user is askedto rank the objectives in order of importance. The optimumsolution is then obtained by minimizing the objectivefunctions, starting with the most important one andproceeding according to the assigned order of importanceof the objectives.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

David Goldberg’s seminal book on genetic algorithms (published in1989) introduced the notion of Pareto ranking: individuals in a MOEAmust be selected based on Pareto dominance, such that allnondominated individuals are considered equally good amongthemselves. He also pointed out the importance of maintainingdiversity as to allow the generation of several (different)nondominated solutions in a single run. Fitness sharing wasproposed for that sake.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

The basic expression adopted in fitness sharing is the following:

φ(dij) =

{1−

(dijσsh

)α, dij < σshare

0, otherwise(4)

where α = 1, dij indicates the distance between solutions i and j , andσshare is the niche radius (or sharing threshold). By using thisparameter, the fitness of the individual i is modified as:

fsi =fi∑M

j=1 φ(dij)(5)

where M is the number of individuals that are located in theneighborhood of the i-th individual.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

Several other approaches have been proposed to handlediversity:

ClusteringUse of entropyAdaptive gridsCrowdingPerformance indicatorsParallel coordinates

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

Since Goldberg’s early proposal, MOEAs consist of two basiccomponents:

A selection mechanism that normally (but not necessarily)incorporates Pareto optimality.A density estimator, which is responsible for maintainingdiversity, and therefore, keeping the MOEA fromconverging to a single solution.

Carlos A. Coello Coello EMOO: Past, Present and Future

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Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

Carlos M. Fonseca and Peter J. Fleming proposed theMultiobjective Optimization Genetic Algorithm (MOGA) in 1993.MOGA would remain as one of the most popular (and effective)multi-objective evolutionary algorithms during many years.MOGA uses a selection operator based on Pareto ranking andfitness sharing to maintain diversity.

Carlos A. Coello Coello EMOO: Past, Present and Future

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Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

Jeffrey Horn proposed the Niched Pareto Genetic Algorithm(NPGA) in 1994. The NPGA uses a tournament selectionbased on Pareto ranking and fitness sharing to maintaindiversity. However, not all the population needs to be ranked,since only a sample is used each time. The NPGA is fast andvery competitive.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

Kalyanmoy Deb proposed the Nondominated Sorting GeneticAlgorithm (NSGA) in 1994. The NSGA adopts a Pareto rankingselection based on layers of dominance and dummy fitnesses.Fitness sharing is adopted to maintain diversity. The NSGAwas slow and not very effective.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In 1998, Eckart Zitzler introduces the Strength ParetoEvolutionary Algorithm (SPEA) at a conference. The next year,this approach is published in the IEEE Transactions onEvolutionary Computation. SPEA uses an external archive toretain the nondominated solutions found during the search.This notion of elitism would soon become popular. A new waveof algorithms was about to arrive.

Carlos A. Coello Coello EMOO: Past, Present and Future

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Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In 1999, Joshua D. Knowles introduces the Pareto ArchiveEvolution Strategy (PAES). The next year, this approach ispublished in the Evolutionary Computation journal. PAES usesa (1+1) evolution strategy combined with a very clever externalarchive which is responsible of both storing nondominatedsolutions and distributing them in a uniform way (in objectivefunction space).

Carlos A. Coello Coello EMOO: Past, Present and Future

Page 26: Evolutionary Multi-Objective Optimization: Past, Present ......Evolutionary Algorithms Evolutionary algorithms seem particularly suitable to solve multiobjective optimization problems,

OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In 1999, Deb published in the Evolutionary Computation journala methodology to build multiobjective test problems that soonbecame very popular.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In 2000, Kalyanmoy Deb and his students introduced theNondominated Sorting Genetic Algorithm-II (NSGA-II). Twoyears later, this approach is published in the IEEE Transactionson Evolutionary Computation. The NSGA-II is very fast andeffective. It uses a crowded-comparison operator which takesinto consideration both the nondomination rank of an individualand its crowding distance. It also uses a plus selection (i.e.,parents and children are merged together and the bestindividuals from their union are selected). For more than 10years, NSGA-II was considered the reference approach withrespect to which other MOEAs had to be compared.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In 2001, Zitzler and his colleagues introduced SPEA2, whichhas 3 main differences with respect to its predecessor: (1) itincorporates a fine-grained fitness assignment strategy whichtakes into account for each individual the number of individualsthat dominate it and the number of individuals by which it isdominated; (2) it uses a nearest neighbor density estimationtechnique which guides the search more efficiently, and (3) ithas an enhanced archive truncation method that guaranteesthe preservation of boundary solutions.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In 2001, Coello Coello and Toscano-Pulido introduced the firstmicrogenetic algorithm for multi-objective optimization. ThemicroGA uses a population of only 4 individuals combined with3 forms of elitism. It is a very fast algorithm and highlycompetitive. Its main defect was its high number of parameters(eight).

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In 2002, Zitzler and his colleagues published a conferencepaper in which they indicated the limitations of many of theperformance measures (“metrics”) normally adopted to validatemulti-objective evolutionary algorithms in a quantitative way(many of them are not Pareto compliant). An extended versionof this paper was published in 2003 in the IEEE Transactions onEvolutionary Computation.

Carlos A. Coello Coello EMOO: Past, Present and Future

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Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In 2002, Deb and his colleagues introduce a new set of testfunctions that are scalable and that have true Pareto fronts thatcan be obtained analytically. This set is named DTLZ after thefirst letter of the last names of its creators.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In 2002, Laumanns and his colleagues introduced a relaxedform of Pareto dominance called ε-dominance as an archivingtechnique. ε-dominance allows to control the granularity of theapproximation of the Pareto front obtained. As a consequence,it is possible to accelerate convergence using this mechanism(if we are satisfied with a very coarse approximation of thePareto front).

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In 2003, Toscano Pulido and Coello Coello introduced themicrogenetic algorithm 2, which was the first attempt toproduce a parameterless MOEA. The µGA2 only requires oneparameter: the size of the external archive (i.e., how manynondominated solutions are required). The algorithm is evenable to stop by itself (by adopting a scheme to detectconvergence).

Carlos A. Coello Coello EMOO: Past, Present and Future

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Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In 2004, Zitzler introduces the Indicator-Based EvolutionaryAlgorithm (IBEA) in which he proposes to use a selectionmechanism based on a performance indicator. A few yearslater, many people would adopt this concept, using thehypervolume (the hypervolume of a set of solutions measuresthe size of the portion of objective space that is dominated bythose solutions collectively).

Carlos A. Coello Coello EMOO: Past, Present and Future

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Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

Many-Objective OptimizationIn 2005, research on many-objective optimization (problemshaving 4 or more objectives) flourishes. Proposals to deal withthese problems include: dimensionality reduction, relaxedforms of Pareto dominance and alternative ranking schemes.

This remains as a hot research topic in spite of the fact thatsome people have questioned if scalability in objective functionspace is really a source of difficulty.

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Historical HighlightsSome Applications

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Historical Highlights

In 2005, a new procedure to design test problems wasintroduced by Huband et al. This set is known as WFG(Walking-Fish Group) and is very popular today.

Carlos A. Coello Coello EMOO: Past, Present and Future

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Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In 2005, the first version of the S Metric Selection Evolutionary MultiobjectiveAlgorithm (SMS-EMOA) SMS-EMOA is published in a conference. Thejournal version of this algorithm was published in 2007. This MOEA is basedon the hypervolume performance measure. This initiated a new researchtrend, due to the limitations of Pareto dominance in the presence of a largenumber of objectives.

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Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In 2005, Joshua D. Knowles and Evan J. Hughes introducedparEGO, which is a MOEA that only performs 250 fitnessfunction evaluations. The approach, however, could only beused with problems of low dimensionality.

Carlos A. Coello Coello EMOO: Past, Present and Future

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Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In 2006, Zhang and Li proposed a MOEA based ondecomposition (MOEA/D). This approach decomposes amulti-objective optimization problem into a number of scalaroptimization subproblems and optimizes them simultaneously.

Carlos A. Coello Coello EMOO: Past, Present and Future

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Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Historical Highlights

In 2014, the NSGA-III is published in a two-parts paper thatappeared in the IEEE Transactions on EvolutionaryComputation. Its main aim is to deal with many-objectiveoptimization problems. The NSGA-III uses reference points andadopts a decomposition approach.

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Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Some Sample Applications

Chung et al. (2003,2004) used a variation of the micro-GAhybridized with a gradient method for the multi-objective designlow-boom supersonic business jets.

Carlos A. Coello Coello EMOO: Past, Present and Future

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Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Some Sample Applications

Benedetti et al. (2006) used the NSGA-II with k optimality todesign the tire-suspension system of a racing car. The problemhas 24 objectives, from which 18 are in conflict with each other.Some designs that outperformed the reference car design wereobtained.

Carlos A. Coello Coello EMOO: Past, Present and Future

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Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Some Sample Applications

Shimoyama (2006) adopted a multiobjective genetic algorithmcoupled to a robust design optimization approach called“design for six sigma”, to design a Mars exploratory airplane.

Carlos A. Coello Coello EMOO: Past, Present and Future

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Some Sample Applications

Rivas-Davalos and Irving (2005) adopted SPEA2 for powerdistribution system planning. Two objectives were minimized:economical cost and energy non-supplied.

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Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Little Known Multi-Objective Evolutionary Algorithms

There have been many multi-objective evolutionary algorithmsthat have been pretty much ignored:

The Nash Genetic Algorithm (Sefrioui, 1996).The Maximin Fitness Function (Balling, 2000).The Incrementing Multi-Objective Evolutionary Algorithm(IMOEA) (Tan et al., 2001).The Constraint Method-Based Evolutionary Algorithm(CMEA) for multi-objective optimization (Ranjithan et al.,2001).The Orthogonal Multi-Objective Evolutionary Algorithm(OMOEA) (Zeng et al., 2004).

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OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Number of papers published per year (early 2019)

Carlos A. Coello Coello EMOO: Past, Present and Future

Page 48: Evolutionary Multi-Objective Optimization: Past, Present ......Evolutionary Algorithms Evolutionary algorithms seem particularly suitable to solve multiobjective optimization problems,

OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Research representative of the current trends

New indicator-based MOEAs (based on hypervolume,IGD+, Deltap, R2, etc.).Use of surrogate and parallel methods to deal withcomputationally expensive objective functions.Methods to generate weights for dealing with inverted testproblems using decomposition-based MOEAs.New applications in a wide variety of domains (e.g.,software engineering, architecture, robotics, etc.)

Carlos A. Coello Coello EMOO: Past, Present and Future

Page 49: Evolutionary Multi-Objective Optimization: Past, Present ......Evolutionary Algorithms Evolutionary algorithms seem particularly suitable to solve multiobjective optimization problems,

OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Future Challenges

Schemes for dealing with large scale MOEAs (e.g., with10,000 decision variables)Efficient and effective hybridization schemes that combineMOEAs with mathematical programming techniques.New benchmarks that better represent the complexities ofreal-world problems.Challenging applications (e.g., preliminary design, in whichwe aim to find quickly good trade-offs rather than optimalsolutions).More theoretical work is needed (e.g., there is almost notheoretical work on parallel MOEAs).

Carlos A. Coello Coello EMOO: Past, Present and Future

Page 50: Evolutionary Multi-Objective Optimization: Past, Present ......Evolutionary Algorithms Evolutionary algorithms seem particularly suitable to solve multiobjective optimization problems,

OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

Some Criticism

A lot of “research by analogy” that lacks scientific valueand relevance now appears even in top journals.“New” research topics that are at the very leastquestionable (e.g., multimodal multi-objective optimization).Ironically, it is now more difficult to publish ideas that arereally new, since, for many reviewers, validationprocedures are now more important than the scientificcontributions of a paper.

Carlos A. Coello Coello EMOO: Past, Present and Future

Page 51: Evolutionary Multi-Objective Optimization: Past, Present ......Evolutionary Algorithms Evolutionary algorithms seem particularly suitable to solve multiobjective optimization problems,

OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

To know more about evolutionarymulti-objective optimization

Please visit the new webpage of the EMOO repository:

https://emoo.cs.cinvestav.mx/

Carlos A. Coello Coello EMOO: Past, Present and Future

Page 52: Evolutionary Multi-Objective Optimization: Past, Present ......Evolutionary Algorithms Evolutionary algorithms seem particularly suitable to solve multiobjective optimization problems,

OutlineIntroduction

Historical HighlightsSome Applications

Little Known ApproachesThe Algorithms that the World ForgotCurrent State and Future Challenges

To know more about evolutionarymulti-objective optimization

The EMOO repository currently contains:

Over 12,000 bibliographic references including 300 PhDtheses, 52 Masters theses, over 5770 journal papers andover 4380 conference papers.Contact information of 79 EMOO researchers.Public domain implementations of SPEA, NSGA, NSGA-II,the microGA, MOGA, ε-MOEA, MOPSO and PAES, amongothers.

Carlos A. Coello Coello EMOO: Past, Present and Future