Runtime Analysis of Discrete Particle Swarm Optimization Applied to Shortest Paths Computation

Raß, Alexander; Schreiner, Jonas; Wanka, Rolf

doi:10.1007/978-3-030-16711-0_8

Cited by 3 publications

(5 citation statements)

References 16 publications

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“…Additionally, Raß et al (2019) is based on a preliminary version of the present paper. There the authors applied the ONEPSO to the single-source shortest path problem.…”

Section: Related Workmentioning

confidence: 99%

“…Theorem 4 (Raß et al 2019, Theorem 5/Theorem 7) The expected optimization time T(n), to solve the single-source shortest path problem with n nodes is bounded by…”

Section: Related Workmentioning

confidence: 99%

“…5. Nevertheless, an extensions allowing transitions inside a level X i is possible and has been considered already in the article (Raß et al 2019) which is based on an arXiv preprint of this article.…”

Section: Markov Model Of Onepsomentioning

confidence: 99%

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Exact Markov chain-based runtime analysis of a discrete particle swarm optimization algorithm on sorting and OneMax

et al. 2021

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Meta-heuristics are powerful tools for solving optimization problems whose structural properties are unknown or cannot be exploited algorithmically. We propose such a meta-heuristic for a large class of optimization problems over discrete domains based on the particle swarm optimization (PSO) paradigm. We provide a comprehensive formal analysis of the performance of this algorithm on certain “easy” reference problems in a black-box setting, namely the sorting problem and the problem OneMax. In our analysis we use a Markov model of the proposed algorithm to obtain upper and lower bounds on its expected optimization time. Our bounds are essentially tight with respect to the Markov model. We show that for a suitable choice of algorithm parameters the expected optimization time is comparable to that of known algorithms and, furthermore, for other parameter regimes, the algorithm behaves less greedy and more explorative, which can be desirable in practice in order to escape local optima. Our analysis provides a precise insight on the tradeoff between optimization time and exploration. To obtain our results we introduce the notion of indistinguishability of states of a Markov chain and provide bounds on the solution of a recurrence equation with non-constant coefficients by integration.

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“…Additionally, Raß et al (2019) is based on a preliminary version of the present paper. There the authors applied the ONEPSO to the single-source shortest path problem.…”

Section: Related Workmentioning

confidence: 99%

“…Theorem 4 (Raß et al 2019, Theorem 5/Theorem 7) The expected optimization time T(n), to solve the single-source shortest path problem with n nodes is bounded by…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Exact Markov chain-based runtime analysis of a discrete particle swarm optimization algorithm on sorting and OneMax

et al. 2021

Self Cite

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show abstract

“…Additionally, [RSW19] is based on a preliminary version of the present paper. There the authors applied the ONEPSO to the single-source shortest path problem.…”

Section: Related Workmentioning

confidence: 99%

“…This assumption holds for both problems we investigate in Section 5. Nevertheless, an extensions allowing transitions inside a level X i is possible and has been considered already in follow-up work [RSW19].…”

Section: Markov Model Of Onepsomentioning

confidence: 99%

Runtime Analysis of a Discrete Particle Swarm Optimization Algorithm on Sorting and OneMax

Mühlenthaler

Raß

Schmitt

et al. 2017

Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms

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Meta-heuristics are powerful tools for solving optimization problems whose structural properties are unknown or cannot be exploited algorithmically. We propose such a metaheuristic for a large class of optimization problems over discrete domains based on the particle swarm optimization (PSO) paradigm. We provide a comprehensive formal analysis of the performance of this algorithm on certain "easy" reference problems in a black-box setting, namely the sorting problem and the problem ONEMAX. In our analysis we use a Markov-model of the proposed algorithm to obtain upper and lower bounds on its expected optimization time. Our bounds are essentially tight with respect to the Markov-model. We show that for a suitable choice of algorithm parameters the expected optimization time is comparable to that of known algorithms and, furthermore, for other parameter regimes, the algorithm behaves less greedy and more explorative, which can be desirable in practice in order to escape local optima. Our analysis provides a precise insight on the tradeoff between optimization time and exploration. To obtain our results we introduce the notion of indistinguishability of states of a Markov chain and provide bounds on the solution of a recurrence equation with non-constant coefficients by integration.

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Runtime analysis of discrete particle swarm optimization algorithms: A survey

Mühlenthaler

Raß

2019

It - Information Technology

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A discrete particle swarm optimization (PSO) algorithm is a randomized search heuristic for discrete optimization problems. A fundamental question about randomized search heuristics is how long it takes, in expectation, until an optimal solution is found. We give an overview of recent developments related to this question for discrete PSO algorithms. In particular, we give a comparison of known upper and lower bounds of expected runtimes and briefly discuss the techniques used to obtain these bounds.

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Runtime Analysis of Discrete Particle Swarm Optimization Applied to Shortest Paths Computation

Cited by 3 publications

References 16 publications

Exact Markov chain-based runtime analysis of a discrete particle swarm optimization algorithm on sorting and OneMax

Exact Markov chain-based runtime analysis of a discrete particle swarm optimization algorithm on sorting and OneMax

Runtime Analysis of a Discrete Particle Swarm Optimization Algorithm on Sorting and OneMax

Runtime analysis of discrete particle swarm optimization algorithms: A survey

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