IS-PAES: Multiobjective Optimization with Efficient Constraint Handling

Aguirre, Arturo Hernández; Rionda, Salvador Botello; Lizáarraga, Giovanni Lizáarraga; Coello, Carlos Coello

doi:10.1007/1-4020-2267-0_11

Cited by 6 publications

(4 citation statements)

References 8 publications

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“…In all cases MAP-Elites is several orders of magnitude worse than εDEag, except C1 in 10D where instead the configuration with crossover finds a better optimal value4. Once again, this conclusion is not surprising and is also in line with what was observed by Runarsson and Yao [22], who identified the reason for the sometimes poor results obtained by multi-objective approaches (such as [26,35,33,10]): in fact, when applied to constrained optimization, the Pareto ranking leads to a "bias-free" search that is not able to properly guide the search towards (and within) the feasible region. In other words, allowing the search to spend too many evaluations in the infeasible region makes it harder to find feasible solutions, but also to find feasible solutions with optimal values of the objective function.…”

Section: Numerical Resultssupporting

confidence: 81%

“…Despite these application needs, to date little research effort has been put on how to allow EAs to identify, rather than a single optimal solution, a diverse set of solutions characterized by different trade-offs of this kind. In this sense, the most notable exceptions that explicitly addressed this problem -although with contrasting results-have focused on multi-objective approaches, where the constraint violations were considered as additional objectives to be minimized [26,35,33,10,5], or surrogate methods [2].…”

Section: Introductionmentioning

confidence: 99%

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MAP-Elites for Constrained Optimization

Fioravanzo¹,

Iacca

2021

Constraint Handling in Metaheuristics and Applications

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Constrained optimization problems are often characterized by multiple constraints that, in the practice, must be satisfied with different tolerance levels. While some constraints are hard and as such must be satisfied with zero-tolerance, others may be soft, such that non-zero violations are acceptable. Here, we evaluate the applicability of MAP-Elites to "illuminate" constrained search spaces by mapping them into feature spaces where each feature corresponds to a different constraint. On the one hand, MAP-Elites implicitly preserves diversity, thus allowing a good exploration of the search space. On the other hand, it provides an effective visualization that facilitates a better understanding of how constraint violations correlate with the objective function. We demonstrate the feasibility of this approach on a large set of benchmark problems, in various dimensionalities, and with different algorithmic configurations. As expected, numerical results show that a basic version of MAP-Elites cannot compete on all problems (especially those with equality constraints) with state-of-the-art algorithms that use gradient information or advanced constraint handling techniques. Nevertheless, it has a higher potential at finding constraint violations vs. objectives trade-offs and providing new problem information. As such, it could be used in the future as an effective building-block for designing new constrained optimization algorithms.

show abstract

Section: Numerical Resultssupporting

confidence: 81%

Section: Introductionmentioning

confidence: 99%

MAP-Elites for Constrained Optimization

Fioravanzo¹,

Iacca

2021

Constraint Handling in Metaheuristics and Applications

View full text Add to dashboard Cite

show abstract

“…In all cases MAP-Elites is several orders of magnitude worse than εDEag, except C1 in 10D where instead the configuration with crossover finds a better optimal value 4 . Once again, this conclusion is not surprising and is also in line with what was observed by Runarsson and Yao [22], who identified the reason for the sometimes poor results obtained by multi-objective approaches (such as [11,25,32,34]): in fact, when applied to constrained optimization, the Pareto ranking leads to a "bias-free" search that is not able to properly guide the search towards (and within) the feasible region. In other words, allowing the search to spend too many evaluations in the infeasible region makes it harder to find feasible solutions, but also to find feasible solutions with optimal values of the objective function.…”

Section: Numerical Resultssupporting

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Evaluating MAP-Elites on constrained optimization problems

Fioravanzo

Iacca

2019

Proceedings of the Genetic and Evolutionary Computation Conference Companion

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Constrained optimization problems are often characterized by multiple constraints that, in the practice, must be satisfied with different tolerance levels. While some constraints are hard and as such must be satisfied with zero-tolerance, others may be soft, such that nonzero violations are acceptable. Here, we evaluate the applicability of MAP-Elites to "illuminate" constrained search spaces by mapping them into feature spaces where each feature corresponds to a different constraint. On the one hand, MAP-Elites implicitly preserves diversity, thus allowing a good exploration of the search space. On the other hand, it provides an effective visualization that facilitates a better understanding of how constraint violations correlate with the objective function. We demonstrate the feasibility of this approach on a large set of benchmark problems, in various dimensionalities, and with different algorithmic configurations. As expected, numerical results show that a basic version of MAP-Elites cannot compete on all problems (especially those with equality constraints) with state-of-the-art algorithms that use gradient information or advanced constraint handling techniques. Nevertheless, it has a higher potential at finding constraint violations vs. objectives tradeoffs and providing new problem information. As such, it could be used in the future as an effective building-block for designing new constrained optimization algorithms.

show abstract

Multi-objective Optimization

Coello¹

2018

Handbook of Heuristics

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IS-PAES: Multiobjective Optimization with Efficient Constraint Handling

Cited by 6 publications

References 8 publications

MAP-Elites for Constrained Optimization

MAP-Elites for Constrained Optimization

Evaluating MAP-Elites on constrained optimization problems

Multi-objective Optimization

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