Multi$$^3$$: Optimizing Multimodal Single-Objective Continuous Problems in the Multi-objective Space by Means of Multiobjectivization

Aspar, Pelin; Kerschke, Pascal; Steinhoff, Vera; Trautmann, Heike; Grimme, Christian

doi:10.1007/978-3-030-72062-9_25

Cited by 4 publications

(2 citation statements)

References 18 publications

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“…Multiobjectivization of single-objective problems, i.e., adding well-suited additional (artificial) objectives and afterwards solving the MO (multimodal) problem, could potentially outperform state-of-the art SO optimizers. Initial experiments based on the MOGSA variant SOMOGSA already showed very promising results (Steinhoff et al, 2020;Aspar et al, 2021). Also, a hybridization with state-of-the art SO optimizers in order to overcome stochasticity induced by the initial search point should be a matter of future research.…”

Section: Discussionmentioning

confidence: 99%

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

Grimme

Kerschke

Aspar

et al. 2021

Computers & Operations Research

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Section: Discussionmentioning

confidence: 99%

“…We even noticed the potential to transfer knowledge gained on MO landscapes back to the SO case. As recently proposed in Steinhoff et al (2020), Aspar et al (2021), aspects of MOGSA may be utilized for local optimization in the SO domain. As schematically depicted in Fig.…”

Section: New Perspectives On Multimodality By Exploiting Localnessmentioning

confidence: 99%

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

Grimme

Kerschke

Aspar

et al. 2021

Computers & Operations Research

Self Cite

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To Boldly Show What No One Has Seen Before: A Dashboard for Visualizing Multi-objective Landscapes

Schäpermeier

Grimme

Kerschke

2021

Lecture Notes in Computer Science

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The objective that freed me: a multi-objective local search approach for continuous single-objective optimization

et al. 2022

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Single-objective continuous optimization can be challenging, especially when dealing with multimodal problems. This work sheds light on the effects that multi-objective optimization may have in the single-objective space. For this purpose, we examine the inner mechanisms of the recently developed sophisticated local search procedure SOMOGSA. This method solves multimodal single-objective continuous optimization problems based on first expanding the problem with an additional objective (e.g., a sphere function) to the bi-objective domain and subsequently exploiting local structures of the resulting landscapes. Our study particularly focuses on the sensitivity of this multiobjectivization approach w.r.t. (1) the parametrization of the artificial second objective, as well as (2) the position of the initial starting points in the search space. As SOMOGSA is a modular framework for encapsulating local search, we integrate Nelder–Mead local search as optimizer in the respective module and compare the performance of the resulting hybrid local search to its original single-objective counterpart. We show that the SOMOGSA framework can significantly boost local search by multiobjectivization. Hence, combined with more sophisticated local search and metaheuristics, this may help solve highly multimodal optimization problems in the future.

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Multi$$^3$$: Optimizing Multimodal Single-Objective Continuous Problems in the Multi-objective Space by Means of Multiobjectivization

Cited by 4 publications

References 18 publications

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

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

To Boldly Show What No One Has Seen Before: A Dashboard for Visualizing Multi-objective Landscapes

The objective that freed me: a multi-objective local search approach for continuous single-objective optimization

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