Peeking beyond peaks: Challenges and research potentials of continuous multimodal multi-objective optimization

Grimme, Christian; Kerschke, Pascal; Aspar, Pelin; Trautmann, Heike; Preuß, Mike; Deutz, André H.; Wang, Hao; Emmerich, Michael

doi:10.1016/j.cor.2021.105489

Cited by 17 publications

(5 citation statements)

References 109 publications

(145 reference statements)

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“…They all neglect diversity in decision space and thus may miss alternative global solutions of similar quality. Multi-modal MOPs have been tackled by integrating archiving, multiple populations, and niching techniques for preserving diverse solution sets in decision space [8]. Another stream of research exploit properties of landscape characteristics to move along local structures [9,10,14,19,23] and preserve locally efficient solutions [15].…”

Section: Methodsmentioning

confidence: 99%

“…These multi-modal MOPs impose specific challenges on algorithms due to their characteristics in terms of locally efficient sets, ridges and basin structures. Important is the distinction between multi-global and multi-local scenarios [8]: diverse solution sets in decision space map to the same images to the Pareto-front in objective space or, alternatively, the former might correspond to different local fronts in objective space. Of course, there might also be combinations of both.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the potential of automated algorithm configuration on multi-modal multi-objective optimization problems

Rook

Trautmann

Bossek

et al. 2022

Proceedings of the Genetic and Evolutionary Computation Conference Companion

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Hardness of Multi-Objective (MO) continuous optimization problems results from an interplay of various problem characteristics, e. g. the degree of multi-modality. We present a benchmark study of classical and diversity focused optimizers on multi-modal MO problems based on automated algorithm configuration. We show the large effect of the latter and investigate the trade-off between convergence in objective space and diversity in decision space. CCS CONCEPTS• Computing methodologies → Continuous space search.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the potential of automated algorithm configuration on multi-modal multi-objective optimization problems

Rook

Trautmann

Bossek

et al. 2022

Proceedings of the Genetic and Evolutionary Computation Conference Companion

Self Cite

View full text Add to dashboard Cite

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“…Ming et al [17] considered constraints in MMOPs and constructed a constrained MMOP test suite, CMMOP. Finally, Liang et al [18] proposed a constrained MMOP benchmark test suite, constrained multimodal multi-objective test function (CMMF), that contains constraints in addition to multimodal and multiple objectives.…”

Section: Existing Mmop Benchmarkmentioning

confidence: 99%

Hybrid Operator and Strengthened Diversity Improving for Multimodal Multi-Objective Optimization

Zhang,

Du,

Zhu

et al. 2024

Tsinghua Sci. Technol.

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Multimodal multi-objective optimization problems (MMOPs) contain multiple equivalent Pareto subsets (PSs) corresponding to a single Pareto front (PF), resulting in difficulty in maintaining promising diversities in both objective and decision spaces to find these PSs. Widely used to solve MMOPs, evolutionary algorithms mainly consist of evolutionary operators that generate new solutions and fitness evaluations of the solutions. To enhance performance in solving MMOPs, this paper proposes a multimodal multi-objective optimization evolutionary algorithm based on a hybrid operator and strengthened diversity improving. Specifically, a hybrid operator mechanism is devised to ensure the exploration of the decision space in the early stage and approximation to the optima in the latter stage. Moreover, an elitist-assisted differential evolution mechanism is designed for the early exploration stage. In addition, a new fitness function is proposed and used in environmental and mating selections to simultaneously evaluate diversities for PF and PSs. Experimental studies on 11 widely used benchmark instances from a test suite verify the superiority or at least competitiveness of the proposed methods compared to five state-of-the-art algorithms tailored for MMOPs.

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“…Here we consider MMOPs in the case of real-valued parameters, or continuous optimization. This field has recently gotten more traction, with reviews [31], proposed formal definitions [14] and new visualization techniques [30].…”

Section: Introductionmentioning

confidence: 99%

Obtaining Smoothly Navigable Approximation Sets in Bi-objective Multi-modal Optimization

Scholman

Bouter

Dickhoff

et al. 2022

Lecture Notes in Computer Science

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Even if a Multi-modal Multi-Objective Evolutionary Algorithm (MMOEA) is designed to find solutions well spread over all locally optimal approximation sets of a Multi-modal Multi-objective Optimization Problem (MMOP), there is a risk that the found set of solutions is not smoothly navigable because the solutions belong to various niches, reducing the insight for decision makers. To tackle this issue, a new MMOEAs is proposed: the Multi-Modal Bézier Evolutionary Algorithm (MM-BezEA), which produces approximation sets that cover individual niches and exhibit inherent decision-space smoothness as they are parameterized by Bézier curves. MM-BezEA combines the concepts behind the recently introduced BezEA and MO-HillVallEA to find all locally optimal approximation sets. When benchmarked against the MMOEAs MO Ring PSO SCD and MO-HillVallEA on MMOPs with linear Pareto sets, MM-BezEA was found to perform best in terms of best hypervolume.

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Peeking beyond peaks: Challenges and research potentials of continuous multimodal multi-objective optimization

Cited by 17 publications

References 109 publications

On the potential of automated algorithm configuration on multi-modal multi-objective optimization problems

On the potential of automated algorithm configuration on multi-modal multi-objective optimization problems

Hybrid Operator and Strengthened Diversity Improving for Multimodal Multi-Objective Optimization

Obtaining Smoothly Navigable Approximation Sets in Bi-objective Multi-modal Optimization

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