Multi3: Optimizing Multimodal Single-Objective Continuous Problems in the Multi-objective Space by Means of Multiobjectivization

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

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

Multi³: Optimizing Multimodal Single-Objective Continuous Problems in the Multi-objective Space by Means of Multiobjectivization

Pelin Aspar^*, Pascal Kerschke, Vera Steinhoff, Heike Trautmann, Christian Grimme

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

5 Citations (Scopus)

Abstract

In this work we examine the inner mechanisms of the recently developed sophisticated local search procedure SOMOGSA. This method solves multimodal single-objective continuous optimization problems by first expanding the problem with an additional objective (e.g., a sphere function) to the bi-objective space, and subsequently exploiting local structures and ridges of the resulting landscapes. Our study particularly focusses on the sensitivity of this multiobjectivization approach w.r.t. (i) the parametrization of the artificial second objective, as well as (ii) the position of the initial starting points in the search space. As SOMOGSA is a modular framework for encapsulating local search, we integrate Gradient and Nelder-Mead local search (as optimizers in the respective module) and compare the performance of the resulting hybrid local search to their original single-objective counterparts. We show that the SOMOGSA framework can significantly boost local search by multiobjectivization. Combined with more sophisticated local search and metaheuristics this may help in solving highly multimodal optimization problems in future.

Original language	English
Title of host publication	Evolutionary Multi-Criterion Optimization
Subtitle of host publication	11th International Conference, EMO 2021, Shenzhen, China, March 28–31, 2021, Proceedings
Editors	Hisao Ishibuchi, Qingfu Zhang, Ran Cheng, Ke Li, Hui Li, Handing Wang, Aimin Zhou
Place of Publication	Cham
Publisher	Springer
Pages	311-322
Number of pages	12
ISBN (Electronic)	978-3-030-72062-9
ISBN (Print)	978-3-030-72061-2
DOIs	https://doi.org/10.1007/978-3-030-72062-9_25
Publication status	Published - 2021
Externally published	Yes
Event	11th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2021 - Hampton by Hilton Hotel, Shenzhen, China Duration: 28 Mar 2021 → 31 Mar 2021 Conference number: 11 https://emo2021.org/

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	12654
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	11th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2021
Abbreviated title	EMO
Country/Territory	China
City	Shenzhen
Period	28/03/21 → 31/03/21
Internet address	https://emo2021.org/

Keywords

Local search
Multimodal optimization
Multiobjectivization
n/a OA procedure

Access to Document

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

Cite this

Aspar, P., Kerschke, P., Steinhoff, V., Trautmann, H., & Grimme, C. (2021). Multi³: Optimizing Multimodal Single-Objective Continuous Problems in the Multi-objective Space by Means of Multiobjectivization. In H. Ishibuchi, Q. Zhang, R. Cheng, K. Li, H. Li, H. Wang, & A. Zhou (Eds.), Evolutionary Multi-Criterion Optimization : 11th International Conference, EMO 2021, Shenzhen, China, March 28–31, 2021, Proceedings (pp. 311-322). (Lecture Notes in Computer Science; Vol. 12654). Springer. https://doi.org/10.1007/978-3-030-72062-9_25

Aspar, Pelin ; Kerschke, Pascal ; Steinhoff, Vera et al. / Multi³ : Optimizing Multimodal Single-Objective Continuous Problems in the Multi-objective Space by Means of Multiobjectivization. Evolutionary Multi-Criterion Optimization : 11th International Conference, EMO 2021, Shenzhen, China, March 28–31, 2021, Proceedings. editor / Hisao Ishibuchi ; Qingfu Zhang ; Ran Cheng ; Ke Li ; Hui Li ; Handing Wang ; Aimin Zhou. Cham : Springer, 2021. pp. 311-322 (Lecture Notes in Computer Science).

@inproceedings{16f9d1a83cc948ef809343bfdb80fda6,

title = "Multi3: Optimizing Multimodal Single-Objective Continuous Problems in the Multi-objective Space by Means of Multiobjectivization",

abstract = "In this work we examine the inner mechanisms of the recently developed sophisticated local search procedure SOMOGSA. This method solves multimodal single-objective continuous optimization problems by first expanding the problem with an additional objective (e.g., a sphere function) to the bi-objective space, and subsequently exploiting local structures and ridges of the resulting landscapes. Our study particularly focusses on the sensitivity of this multiobjectivization approach w.r.t. (i) the parametrization of the artificial second objective, as well as (ii) the position of the initial starting points in the search space. As SOMOGSA is a modular framework for encapsulating local search, we integrate Gradient and Nelder-Mead local search (as optimizers in the respective module) and compare the performance of the resulting hybrid local search to their original single-objective counterparts. We show that the SOMOGSA framework can significantly boost local search by multiobjectivization. Combined with more sophisticated local search and metaheuristics this may help in solving highly multimodal optimization problems in future.",

keywords = "Local search, Multimodal optimization, Multiobjectivization, n/a OA procedure",

author = "Pelin Aspar and Pascal Kerschke and Vera Steinhoff and Heike Trautmann and Christian Grimme",

note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.; 11th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2021, EMO ; Conference date: 28-03-2021 Through 31-03-2021",

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doi = "10.1007/978-3-030-72062-9_25",

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Aspar, P, Kerschke, P, Steinhoff, V, Trautmann, H & Grimme, C 2021, Multi³: Optimizing Multimodal Single-Objective Continuous Problems in the Multi-objective Space by Means of Multiobjectivization. in H Ishibuchi, Q Zhang, R Cheng, K Li, H Li, H Wang & A Zhou (eds), Evolutionary Multi-Criterion Optimization : 11th International Conference, EMO 2021, Shenzhen, China, March 28–31, 2021, Proceedings. Lecture Notes in Computer Science, vol. 12654, Springer, Cham, pp. 311-322, 11th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2021, Shenzhen, China, 28/03/21. https://doi.org/10.1007/978-3-030-72062-9_25

Multi³: Optimizing Multimodal Single-Objective Continuous Problems in the Multi-objective Space by Means of Multiobjectivization. / Aspar, Pelin; Kerschke, Pascal; Steinhoff, Vera et al.
Evolutionary Multi-Criterion Optimization : 11th International Conference, EMO 2021, Shenzhen, China, March 28–31, 2021, Proceedings. ed. / Hisao Ishibuchi; Qingfu Zhang; Ran Cheng; Ke Li; Hui Li; Handing Wang; Aimin Zhou. Cham: Springer, 2021. p. 311-322 (Lecture Notes in Computer Science; Vol. 12654).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - Grimme, Christian

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AB - In this work we examine the inner mechanisms of the recently developed sophisticated local search procedure SOMOGSA. This method solves multimodal single-objective continuous optimization problems by first expanding the problem with an additional objective (e.g., a sphere function) to the bi-objective space, and subsequently exploiting local structures and ridges of the resulting landscapes. Our study particularly focusses on the sensitivity of this multiobjectivization approach w.r.t. (i) the parametrization of the artificial second objective, as well as (ii) the position of the initial starting points in the search space. As SOMOGSA is a modular framework for encapsulating local search, we integrate Gradient and Nelder-Mead local search (as optimizers in the respective module) and compare the performance of the resulting hybrid local search to their original single-objective counterparts. We show that the SOMOGSA framework can significantly boost local search by multiobjectivization. Combined with more sophisticated local search and metaheuristics this may help in solving highly multimodal optimization problems in future.

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KW - Multimodal optimization

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Aspar P, Kerschke P, Steinhoff V, Trautmann H, Grimme C. Multi³: Optimizing Multimodal Single-Objective Continuous Problems in the Multi-objective Space by Means of Multiobjectivization. In Ishibuchi H, Zhang Q, Cheng R, Li K, Li H, Wang H, Zhou A, editors, Evolutionary Multi-Criterion Optimization : 11th International Conference, EMO 2021, Shenzhen, China, March 28–31, 2021, Proceedings. Cham: Springer. 2021. p. 311-322. (Lecture Notes in Computer Science). doi: 10.1007/978-3-030-72062-9_25