Running Time Analysis of MOEA/D with Crossover on Discrete Optimization Problem

Huang, Zhengxin; Zhou, Yuejiao; Chen, Zefeng; He, Xiaowen

doi:10.1609/aaai.v33i01.33012296

Cited by 28 publications

(12 citation statements)

References 26 publications

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“…Like the SEMO and GSEMO, the (µ + 1) SIBEA also creates a single offspring per generation; different from the former, it works with a fixed population size µ. Recently, also decomposition-based multi-objective evolutionary algorithms were analyzed (MOEA/D) (Li et al 2016;Huang et al 2019;Huang and Zhou 2020), which decompose the multi-objective problem into several related single-objective problems and then solve each single-objective problem in a co-evolutionary manner. This direction is fundamentally different from the above works and our research.…”

Section: Introductionmentioning

confidence: 99%

A First Mathematical Runtime Analysis of the Non-dominated Sorting Genetic Algorithm II (NSGA-II)

Zheng

Liu

Doerr

2022

AAAI

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The non-dominated sorting genetic algorithm II (NSGA-II) is the most intensively used multi-objective evolutionary algorithm (MOEA) in real-world applications. However, in contrast to several simple MOEAs analyzed also via mathematical means, no such study exists for the NSGA-II so far. In this work, we show that mathematical runtime analyses are feasible also for the NSGA-II. As particular results, we prove that with a population size larger than the Pareto front size by a constant factor, the NSGA-II with two classic mutation operators and three different ways to select the parents satisfies the same asymptotic runtime guarantees as the SEMO and GSEMO algorithms on the basic OneMinMax and LOTZ benchmark functions. However, if the population size is only equal to the size of the Pareto front, then the NSGA-II cannot efficiently compute the full Pareto front (for an exponential number of iterations, the population will always miss a constant fraction of the Pareto front). Our experiments confirm the above findings.

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Section: Introductionmentioning

confidence: 99%

A First Mathematical Runtime Analysis of the Non-dominated Sorting Genetic Algorithm II (NSGA-II)

Zheng

Liu

Doerr

2022

AAAI

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“…EGD only uses the two components, i.e., population and mutation, of EAs. It would be interesting to incorporate crossover operators, a characterizing feature of EAs [Qian et al, 2013;Huang et al, 2019], into EGD, which may further improve the performance. EGD combines EAs with the basic GD algorithm.…”

Section: Discussionmentioning

confidence: 99%

Evolutionary Gradient Descent for Non-convex Optimization

Xue

Qian

et al. 2021

Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence

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Non-convex optimization is often involved in artificial intelligence tasks, which may have many saddle points, and is NP-hard to solve. Evolutionary algorithms (EAs) are general-purpose derivative-free optimization algorithms with a good ability to find the global optimum, which can be naturally applied to non-convex optimization. Their performance is, however, limited due to low efficiency. Gradient descent (GD) runs efficiently, but only converges to a first-order stationary point, which may be a saddle point and thus arbitrarily bad. Some recent efforts have been put into combining EAs and GD. However, previous works either utilized only a specific component of EAs, or just combined them heuristically without theoretical guarantee. In this paper, we propose an evolutionary GD (EGD) algorithm by combining typical components, i.e., population and mutation, of EAs with GD. We prove that EGD can converge to a second-order stationary point by escaping the saddle points, and is more efficient than previous algorithms. Empirical results on non-convex synthetic functions as well as reinforcement learning (RL) tasks also show its superiority.

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“…In this section, we present a runtime analysis of Algorithm 1 with CHM1 or CHM2 on COCZ, LPTNO, Dec-obj-MOP and Plateau-MOP. They have been widely used in theoretical analyses of MOEAs, e.g., (Laumanns, Thiele, and Zitzler 2004;Qian, Yu, and Zhou 2013;Li et al 2016;Bian, Qian, and Tang 2018;Huang et al 2019). Let |x| 1 denote the number of 1-bits in solution x.…”

Section: Analysis On Bi-objective Problemsmentioning

confidence: 99%

Runtime Analysis of Somatic Contiguous Hypermutation Operators in MOEA/D Framework

Huang

Zhou

2020

AAAI

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Somatic contiguous hypermutation (CHM) operators are important variation operators in artificial immune systems. The few existing theoretical studies are only concerned with understanding the optimization behavior of CHM operators on solving single-objective optimization problems. The MOEA/D framework is one of the most popular strategies for solving multi-objective optimization problems (MOPs). In this paper, we present a runtime analysis of using two CHM operators in MOEA/D framework for solving five benchmark MOPs, including four bi-objective and one many-objective problems. Our analyses show that the expected runtimes of CHM operators on the four bi-objective problems are better than or as good as that of the well-studied standard bit mutation operator. Moreover, using CHM operators in MOEA/D framework can improve the best known upper bound on the many-objective problem by a factor of n. This paper provides insight into understanding the optimization behavior of CHM operators in the well-known MOEA/D framework, and indicates that using the CHM operator in MOEA/D framework is a promising method for handling MOPs.

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Running Time Analysis of MOEA/D with Crossover on Discrete Optimization Problem

Cited by 28 publications

References 26 publications

A First Mathematical Runtime Analysis of the Non-dominated Sorting Genetic Algorithm II (NSGA-II)

A First Mathematical Runtime Analysis of the Non-dominated Sorting Genetic Algorithm II (NSGA-II)

Evolutionary Gradient Descent for Non-convex Optimization

Runtime Analysis of Somatic Contiguous Hypermutation Operators in MOEA/D Framework

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