Many-objective optimization using differential evolution with variable-wise mutation restriction

Denysiuk, Roman; Costa, Lino; Santo, I. A. C. P. Espírito

doi:10.1145/2463372.2463445

Cited by 33 publications

(17 citation statements)

References 33 publications

(33 reference statements)

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“…Denysiuk et al [5] mainly follow the standard way of showing ε-and hypervolume indicator values after a given budget of function evaluations and use performance profiles only briefly to show the distributions of the median values of both indicators. In another study, Denysiuk et al [6] also use performance profiles to study the median values of the IGD indicator. Also in those two papers, the performance profiles aggregate over problems with different search space and objective space dimensions.…”

Section: Related Benchmarking Studiesmentioning

confidence: 99%

“…The value tp,s is then defined as the time to reach the given target indicator quality of problem p for solver s and the data profile can be plotted as in the single-objective case. 6 We say solution x dominates solution y if ∀1 ≤ i ≤ k : fi(x) ≤ fi(y) and ∃1 ≤ i ≤ k : fi(x) < fi(y) and write x ≺ y. As such, multiobjective data profiles do not only allow to aggregate results over several test functions and target difficulties but also over different quality indicators.…”

Section: Transferring Single-objective Benchmarking Concepts To the Mmentioning

confidence: 99%

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Benchmarking Numerical Multiobjective Optimizers Revisited

Brockhoff

Tran

Hansen

2015

Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

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International audienceAlgorithm benchmarking plays a vital role in designing new optimization algorithms and in recommending efficient and robust algorithms for practical purposes. So far, two main approaches have been used to compare algorithms in the evolutionary multiobjective optimization (EMO) field: (i) displaying empirical attainment functions and (ii) reporting statistics on quality indicator values. Most of the time, EMO benchmarking studies compare algorithms for fixed and often arbitrary budgets of function evaluations although the algorithms are anytime optimizers. Instead, we propose to transfer and adapt standard benchmarking techniques from the single-objective optimization and classical derivative-free optimization community to the field of EMO. Reporting target-based runlengths allows to compare algorithms with varying numbers of function evaluations quantitatively. Displaying data profiles can aggregate performance information over different test functions, problem difficulties, and quality indicators. We apply this approach to compare three common algorithms on a new test function suite derived from the well-known single-objective BBOB functions. The focus thereby lies less on gaining insights into the algorithms but more on showcasing the concepts and on what can be gained over current benchmarking approaches

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Section: Related Benchmarking Studiesmentioning

confidence: 99%

Section: Transferring Single-objective Benchmarking Concepts To the Mmentioning

confidence: 99%

Benchmarking Numerical Multiobjective Optimizers Revisited

Brockhoff

Tran

Hansen

2015

Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

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“…It should be specially mentioned that a MOEA/D version [33] with DE operator won the CEC 2009 MOEA competition. Recently, a number of researchers [10,7,3] have started to investigate the performance of DE on MaOPs.…”

Section: Differential Evolutionmentioning

confidence: 99%

An Experimental Investigation of Variation Operators in Reference-Point Based Many-Objective Optimization

Yuan

Wang

2015

Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

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Reference-point based multi-objective evolutionary algorithms (MOEAs) have shown promising performance in manyobjective optimization. However, most of existing research within this area focused on improving the environmental selection procedure, and little work has been done on the effect of variation operators. In this paper, we conduct an experimental investigation of variation operators in a typical reference-point based MOEA, i.e., NSGA-III. First, we provide a new NSGA-III variant, i.e., NSGA-III-DE, which introduces differential evolution (DE) operator into NSGA-III, and we further examine the effect of two main control parameters in NSGA-III-DE. Second, we have an experimental analysis of the search behavior of NSGA-III-DE and NSGA-III. We observe that NSGA-III-DE is generally better at exploration whereas NSGA-III normally has advantages in exploitation. Third, based on this observation, we present two other NSGA-III variants, where DE operator and genetic operators are simply combined to reproduce solutions. Experimental results on several benchmark problems show that very encouraging performance can be achieved by three suggested new NSGA-III variants. Our work also indicates that the performance of NSGA-III is significantly bottlenecked by its variation operators, providing opportunities for the study of the other alternative ones.

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“…Defining the grid requires setting the number of devisions for each objective, with an inappropriate value leading to a poor performance. On the other hand, improving a diversity preserving mechanism can increase the scalability of MOEAs [8][9][10][11]. Also, the dominance relation can provide a high selection pressure, thereby producing a harmful impact on the search due to the loss of diversity [12].…”

Section: Introductionmentioning

confidence: 99%

Multiobjective evolutionary algorithm based on vector angle neighborhood

Denysiuk¹,

Gaspar‐Cunha²

2017

Swarm and Evolutionary Computation

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A B S T R A C TSelection is a major driving force behind evolution and is a key feature of multiobjective evolutionary algorithms. Selection aims at promoting the survival and reproduction of individuals that are most fitted to a given environment. In the presence of multiple objectives, major challenges faced by this operator come from the need to address both the population convergence and diversity, which are conflicting to a certain extent. This paper proposes a new selection scheme for evolutionary multiobjective optimization. Its distinctive feature is a similarity measure for estimating the population diversity, which is based on the angle between the objective vectors. The smaller the angle, the more similar individuals. The concept of similarity is exploited during the mating by defining the neighborhood and the replacement by determining the most crowded region where the worst individual is identified. The latter is performed on the basis of a convergence measure that plays a major role in guiding the population towards the Pareto optimal front. The proposed algorithm is intended to exploit strengths of decomposition-based approaches in promoting diversity among the population while reducing the user's burden of specifying weight vectors before the search. The proposed approach is validated by computational experiments with state-of-the-art algorithms on problems with different characteristics. The obtained results indicate a highly competitive performance of the proposed approach. Significant advantages are revealed when dealing with problems posing substantial difficulties in keeping diversity, including manyobjective problems. The relevance of the suggested similarity and convergence measures are shown. The validity of the approach is also demonstrated on engineering problems.

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Many-objective optimization using differential evolution with variable-wise mutation restriction

Cited by 33 publications

References 33 publications

Benchmarking Numerical Multiobjective Optimizers Revisited

Benchmarking Numerical Multiobjective Optimizers Revisited

An Experimental Investigation of Variation Operators in Reference-Point Based Many-Objective Optimization

Multiobjective evolutionary algorithm based on vector angle neighborhood

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