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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 35 / No. 14: AAAI-21 Technical Tracks 14

Theoretical Analyses of Multi-Objective Evolutionary Algorithms on Multi-Modal Objectives

February 1, 2023

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Authors

Benjamin Doerr

Laboratoire d'Informatique (LIX), École Polytechnique, CNRS, Institut Polytechnique de Paris, Palaiseau, France


Weijie Zheng

Guangdong Provincial Key Laboratory of Brain-inspired Intelligent Computation, Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, China


DOI:

10.1609/aaai.v35i14.17459


Abstract:

Previous theory work on multi-objective evolutionary algorithms considers mostly easy problems that are composed of unimodal objectives. This paper takes a first step towards a deeper understanding of how evolutionary algorithms solve multi-modal multi-objective problems. We propose the OneJumpZeroJump problem, a bi-objective problem whose single objectives are isomorphic to the classic jump functions benchmark. We prove that the simple evolutionary multi-objective optimizer (SEMO) cannot compute the full Pareto front. In contrast, for all problem sizes n and all jump sizes k in [4..n/2-1], the global SEMO (GSEMO) covers the Pareto front in Θ((n-2k)n^k) iterations in expectation. To improve the performance, we combine the GSEMO with two approaches, a heavy-tailed mutation operator and a stagnation detection strategy, that showed advantages in single-objective multi-modal problems. Runtime improvements of asymptotic order at least k^Ω(k) are shown for both strategies. Our experiments verify the substantial runtime gains already for moderate problem sizes. Overall, these results show that the ideas recently developed for single-objective evolutionary algorithms can be effectively employed also in multi-objective optimization.

Topics: AAAI

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HOW TO CITE:

Benjamin Doerr||Weijie Zheng Theoretical Analyses of Multi-Objective Evolutionary Algorithms on Multi-Modal Objectives Proceedings of the AAAI Conference on Artificial Intelligence (2021) 12293-12301.

Benjamin Doerr||Weijie Zheng Theoretical Analyses of Multi-Objective Evolutionary Algorithms on Multi-Modal Objectives AAAI 2021, 12293-12301.

Benjamin Doerr||Weijie Zheng (2021). Theoretical Analyses of Multi-Objective Evolutionary Algorithms on Multi-Modal Objectives. Proceedings of the AAAI Conference on Artificial Intelligence, 12293-12301.

Benjamin Doerr||Weijie Zheng. Theoretical Analyses of Multi-Objective Evolutionary Algorithms on Multi-Modal Objectives. Proceedings of the AAAI Conference on Artificial Intelligence 2021 p.12293-12301.

Benjamin Doerr||Weijie Zheng. 2021. Theoretical Analyses of Multi-Objective Evolutionary Algorithms on Multi-Modal Objectives. "Proceedings of the AAAI Conference on Artificial Intelligence". 12293-12301.

Benjamin Doerr||Weijie Zheng. (2021) "Theoretical Analyses of Multi-Objective Evolutionary Algorithms on Multi-Modal Objectives", Proceedings of the AAAI Conference on Artificial Intelligence, p.12293-12301

Benjamin Doerr||Weijie Zheng, "Theoretical Analyses of Multi-Objective Evolutionary Algorithms on Multi-Modal Objectives", AAAI, p.12293-12301, 2021.

Benjamin Doerr||Weijie Zheng. "Theoretical Analyses of Multi-Objective Evolutionary Algorithms on Multi-Modal Objectives". Proceedings of the AAAI Conference on Artificial Intelligence, 2021, p.12293-12301.

Benjamin Doerr||Weijie Zheng. "Theoretical Analyses of Multi-Objective Evolutionary Algorithms on Multi-Modal Objectives". Proceedings of the AAAI Conference on Artificial Intelligence, (2021): 12293-12301.

Benjamin Doerr||Weijie Zheng. Theoretical Analyses of Multi-Objective Evolutionary Algorithms on Multi-Modal Objectives. AAAI[Internet]. 2021[cited 2023]; 12293-12301.


ISSN: 2374-3468


Published by AAAI Press, Palo Alto, California USA
Copyright 2022, Association for the Advancement of
Artificial Intelligence 1900 Embarcadero Road, Suite
101, Palo Alto, California 94303 All Rights Reserved

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