Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints

Shi, Feng; Schirneck, Martin; Friedrich, Tobias; Kötzing, Timo; Neumann, Franz‐Josef

doi:10.1007/s00453-018-0451-4

Cited by 27 publications

(22 citation statements)

References 18 publications

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“…The analysis of the Multi-Objective ( +( , )) Genetic Algorithm (MO ( +( , )) GA) on general linear profit functions in the original article [4] had the same error as Theorem 9. In the following, we restate the corrected Subsection 5.2 as a whole for completeness.…”

Section: Theorem 9 the Reoptimization Time Of The Moea On Linear Funcmentioning

confidence: 96%

“…Proof The reasoning is similar to that of the proof of [4,Lemma 13]. To get an optimal solution y * with Hamming weight |x| 1 + 1 , it is necessary that the solution x ′ obtained in the mutation phase has x � j = 1 , where j is the index of a 0-bit with maximum weight in x.…”

Section: Lemma 16mentioning

confidence: 99%

“…In Theorem 9 of the original article [4], we claimed a bound of O(nD log D) for the expected reoptimization time of the Multi-Objective Evolutionary Algorithm (MOEA), where D = |B − B * | denotes the difference between the original constraint bound B and the new one B * . Its proof was based on the notion of candidate solutions x for which there is an optimum x * (assuming B ≤ B * ) such that x i = 1 implies x * i = 1 .…”

Section: The Multi-objective Evolutionary Algorithmmentioning

confidence: 99%

“…Besides, in the original proof of Theorem 12 in [4], regarding the MOEA with single bit flip operator (MOEA-S) on linear functions under dynamic uniform constraints, we used the fact that "[we] pessimistically assume that the optimum…”

Section: Theorem 9 the Reoptimization Time Of The Moea On Linear Funcmentioning

confidence: 99%

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Correction to: Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints

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Section: Theorem 9 the Reoptimization Time Of The Moea On Linear Funcmentioning

confidence: 96%

Section: Lemma 16mentioning

confidence: 99%

Section: The Multi-objective Evolutionary Algorithmmentioning

confidence: 99%

Section: Theorem 9 the Reoptimization Time Of The Moea On Linear Funcmentioning

confidence: 99%

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Correction to: Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints

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“…Studying the performances of evolutionary algorithms for dynamic models of combinatorial optimization problems is an emerging field in evolutionary computation [8,16,19,22,24,26]. Within the paper, we present the dynamic model of the Weighted Vertex Cover problem (WVC), which is simply named Dynamic Weighted Vertex Cover problem (DWVC).…”

Section: Introductionmentioning

confidence: 99%

Runtime Performances of Randomized Search Heuristics for the Dynamic Weighted Vertex Cover Problem

2020

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Randomized search heuristics such as evolutionary algorithms are frequently applied to dynamic combinatorial optimization problems. Within this paper, we present a dynamic model of the classic Weighted Vertex Cover problem and analyze the runtime performances of the well-studied algorithms Randomized Local Search and (1+1) EA adapted to it, to contribute to the theoretical understanding of evolutionary computing for problems with dynamic changes. In our investigations, we use an edge-based representation based on the dual form of the Linear Programming formulation for the problem and study the expected runtime that the adapted algorithms require to maintain a 2-approximate solution when the given weighted graph is modified by an edge-editing or weight-editing operation. Considering the weights on the vertices may be exponentially large with respect to the size of the graph, the step size adaption strategy is incorporated, with or without the 1/5-th rule that is employed to control the increasing/decreasing rate of the step size. Our results show that three of the four algorithms presented in the paper can recompute 2-approximate solutions for the studied dynamic changes in polynomial expected runtime, but the (1+1) EA with 1/5-th Rule requires pseudo-polynomial expected runtime.

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Analysis of Evolutionary Algorithms in Dynamic and Stochastic Environments

Neumann

Pourhassan

Roostapour

2019

Natural Computing Series

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Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints

Cited by 27 publications

References 18 publications

Correction to: Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints

Correction to: Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints

Runtime Performances of Randomized Search Heuristics for the Dynamic Weighted Vertex Cover Problem

Analysis of Evolutionary Algorithms in Dynamic and Stochastic Environments

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