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

Huang, Zhengxin; Zhou, Yuejiao

doi:10.1609/aaai.v34i03.5615

Cited by 22 publications

(8 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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“…Hypermutation, and Immune Algorithms in particular, have been applied to solve various optimization problems, including multi-objective optimization problems [20,42,52]. In this article, we developed a novel hypermutation specific to test generation for RESTful APIs which faces many objectives (e.g., thousands of lines and code branches) to be optimized.…”

Section: Hypermutationmentioning

confidence: 99%

Adaptive Hypermutation for Search-Based System Test Generation: A Study on REST APIs with EvoMaster

Zhang

ArcuriAndrea

2021

ACM Trans. Softw. Eng. Methodol.

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REST web services are widely popular in industry, and search techniques have been successfully used to automatically generate system-level test cases for those systems. In this article, we propose a novel mutation operator which is designed specifically for test generation at system-level, with a particular focus on REST APIs. In REST API testing, and often in system testing in general, an individual can have a long and complex chromosome. Furthermore, there are two specific issues: (1) fitness evaluation in system testing is highly costly compared with the number of objectives (e.g., testing targets) to optimize for; and (2) a large part of the genotype might have no impact on the phenotype of the individuals (e.g., input data that has no impact on the execution flow in the tested program). Due to these issues, it might be not suitable to apply a typical low mutation rate like 1/ n (where n is the number of genes in an individual), which would lead to mutating only one gene on average. Therefore, in this article, we propose an adaptive weight-based hypermutation, which is aware of the different characteristics of the mutated genes. We developed adaptive strategies that enable the selection and mutation of genes adaptively based on their fitness impact and mutation history throughout the search. To assess our novel proposed mutation operator, we implemented it in the EvoMaster tool, integrated in the MIO algorithm, and further conducted an empirical study with three artificial REST APIs and four real-world REST APIs. Results show that our novel mutation operator demonstrates noticeable improvements over the default MIO. It provides a significant improvement in performance for six out of the seven case studies, where the relative improvement is up to +12.09% for target coverage, +12.69% for line coverage, and +32.51% for branch coverage.

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“…The classic benchmark LEADINGONES was used to construct the LOTZ (Laumanns, Thiele, and Zitzler 2004) and WLPTNO (Qian, Yu, and Zhou 2013) problems. These multi-objective benchmark problems are among the most intensively studied (Giel 2003;Doerr, Kodric, and Voigt 2013;Doerr, Gao, and Neumann 2016;Bian, Qian, and Tang 2018;Huang et al 2019;Huang and Zhou 2020;Osuna et al 2020). We note that these problems are unimodal in the sense that from each set of solutions P a set P witnessing the Pareto front can be computed by repeatedly selecting a solution from P , flipping a single bit in it, adding it to P , and removing dominated solutions from P .…”

Section: Introductionmentioning

confidence: 99%

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

Doerr

Zheng

2021

AAAI

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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.

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

Cited by 22 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)

Adaptive Hypermutation for Search-Based System Test Generation: A Study on REST APIs with EvoMaster

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

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