On Test Functions for Evolutionary Multi-objective Optimization

Okabe, Tatsuya; Jin, Yaochu; Olhofer, Markus; Sendhoff, Bernhard

doi:10.1007/978-3-540-30217-9_80

Cited by 85 publications

(49 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There have been several attempts to define test suites and toolkits for testing multi-objective evolutionary algorithms (MOEAs) [1], [2], [3], [4], [5]. However, existing multiobjective test problems do not test a wide range of characteristics and problem features, and are often designed in a hard-wired manner.…”

Section: Introductionmentioning

confidence: 99%

Use of the WFG Toolkit and PISA for Comparison of MOEAs

Bradstreet

Barone

While

et al. 2007

2007 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making

View full text Add to dashboard Cite

Abstract-Understanding the behaviour of different optimisation algorithms is important in order to apply the best algorithm to a particular problem. The WFG toolkit was designed to aid this task for multi-objective evolutionary algorithms (MOEAs), offering an easily modifiable framework that allows practitioners the ability to test different features by "plugging" in different forms of transformations. In doing so, the WFG toolkit provides a set of problems that exhibit a variety of different characteristics.This paper presents a comparison between two state of the art MOEAs (NSGA-II and SPEA2) that exemplifies the unique capabilities of the WFG toolkit. By altering the control parameters or even the transformations that compose the WFG problems, we are able to explore the different types of problems where SPEA2 and NSGA-II each excel. Our results show that the performance of the two algorithms differ not only on the dimensionality of the problem, but also by properties such as the shape and size of the underlying Pareto surface. As such, the tunability of the WFG toolkit is key in allowing the easy exploration of these different features.

show abstract

Section: Introductionmentioning

confidence: 99%

Use of the WFG Toolkit and PISA for Comparison of MOEAs

Bradstreet

Barone

While

et al. 2007

2007 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making

View full text Add to dashboard Cite

show abstract

“…This could be achieved using the Okabe framework for constructing multiobjective test problems [22].…”

Section: Resultsmentioning

confidence: 99%

Rotationally Invariant Crossover Operators in Evolutionary Multi-objective Optimization

Iorio

2006

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract.Multi-objective problems with parameter interactions can present difficulties to many optimization algorithms. We have investigated the behaviour of Simplex Crossover (SPX), Unimodal Normally Distributed Crossover (UNDX), Parent-centric Crossover (PCX), and Differential Evolution (DE), as possible alternatives to the Simulated Binary Crossover (SBX) operator within the NSGA-II (Non-dominated Sorting Genetic Algorithm II) on four rotated test problems exhibiting parameter interactions. The rotationally invariant crossover operators demonstrated improved performance in optimizing the problems, over a non-rotationally invariant crossover operator.

show abstract

“…Zhou et al [9] propose a specialized EA to implicitly handle and profit from regularities in the objective as well as in the decision space. Such regularities stem from the test functions proposed by Okabe et al [8] and can not be expected generally.…”

Section: Introductionmentioning

confidence: 93%

“…Some effort has been made in the development of test functions not only with regard to a nice behaving Pareto-front, but also with aspired properties in the decision space, cf. Okabe et al [8]. Zhou et al [9] propose a specialized EA to implicitly handle and profit from regularities in the objective as well as in the decision space.…”

Section: Introductionmentioning

confidence: 99%

Pareto Set and EMOA Behavior for Simple Multimodal Multiobjective Functions

Preuß

Naujoks

Rudolph

2006

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Recent research on evolutionary multiobjective optimization has mainly focused on Pareto-fronts. However, we state that proper behavior of the utilized algorithms in decision/search space is necessary for obtaining good results if multimodal objective functions are concerned. Therefore, it makes sense to observe the development of Pareto-sets as well. We do so on a simple, configurable problem, and detect interesting interactions between induced changes to the Pareto-set and the ability of three optimization algorithms to keep track of Pareto-fronts.

show abstract

On Test Functions for Evolutionary Multi-objective Optimization

Cited by 85 publications

References 19 publications

Use of the WFG Toolkit and PISA for Comparison of MOEAs

Use of the WFG Toolkit and PISA for Comparison of MOEAs

Rotationally Invariant Crossover Operators in Evolutionary Multi-objective Optimization

Pareto Set and EMOA Behavior for Simple Multimodal Multiobjective Functions

Contact Info

Product

Resources

About