The one-dimensional Ising model: Mutation versus recombination

Fischer, Simon; Wegener, Ingo

doi:10.1016/j.tcs.2005.04.002

Cited by 54 publications

(53 citation statements)

References 13 publications

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“…Crossover operators subsequently have been shown to be useful in more cases. These include Ising models [16,49], the TwoPaths instance class of the problem of computing unique input-output sequences [30], some instance classes of the vertex cover problem [39], and the all-pairs shortest path problem [10,9,11]. Meanwhile, on the contrary, Richter et al [44] produced the Ignoble Trail functions where a crossover operator was shown to be harmful.…”

Section: Related Workmentioning

confidence: 99%

An analysis on recombination in multi-objective evolutionary optimization

Qian

Zhou

2013

Artificial Intelligence

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Evolutionary algorithms (EAs) are increasingly popular approaches to multi-objective optimization.One of their significant advantages is that they can directly optimize the Pareto front by evolving a population of solutions, where the recombination (also called crossover) operators are usually employed to reproduce new and potentially better solutions by mixing up solutions in the population.Recombination in multi-objective evolutionary algorithms is, however, mostly applied heuristically.In this paper, we investigate how from a theoretical viewpoint a recombination operator will affect a multi-objective EA. First, we employ artificial benchmark problems: the Weighted LPTNO problem (a generalization of the well-studied LOTZ problem), and the well-studied COCZ problem, for studying the effect of recombination. Our analysis discloses that recombination may accelerate the filling of the Pareto front by recombining diverse solutions and thus help solve multi-objective optimization. Because of this, for these two problems, we find that a multi-objective EA with recombination enabled achieves a better expected running time than any known EAs with recombination disabled.We further examine the effect of recombination on solving the multi-objective minimum spanning tree problem, which is an NP-Hard problem. Following our finding on the artificial problems, our analysis shows that recombination also helps accelerate filling the Pareto front and thus helps find approximate solutions faster.

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Section: Related Workmentioning

confidence: 99%

An analysis on recombination in multi-objective evolutionary optimization

Qian

Zhou

2013

Artificial Intelligence

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“…This question has recently been answered positively for the all-pairs shortest path problem [4] and the Ising model [9,32].…”

Section: Preliminariesmentioning

confidence: 99%

Evolutionary Algorithms and Matroid Optimization Problems

Reichel

Skutella

2008

Algorithmica

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We analyze the performance of evolutionary algorithms on various matroid optimization problems that encompass a vast number of efficiently solvable as well as NP-hard combinatorial optimization problems (including many well-known examples such as minimum spanning tree and maximum bipartite matching). We obtain very promising bounds on the expected running time and quality of the computed solution. Our results establish a better theoretical understanding of why randomized search heuristics yield empirically good results for many real-world optimization problems.

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“…The first theoretical runtime analysis considering niching methods was presented by Fischer and Wegener [2] for a fitness function derived from a generalized Ising model on ring graphs. The authors compare the well-known (1+1) EA with a (2+2) GA with fitness sharing.…”

Section: Introductionmentioning

confidence: 99%

Theoretical analysis of diversity mechanisms for global exploration

Friedrich

Oliveto

Sudholt

et al. 2008

Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation

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Maintaining diversity is important for the performance of evolutionary algorithms. Diversity mechanisms can enhance global exploration of the search space and enable crossover to find dissimilar individuals for recombination. We focus on the global exploration capabilities of mutation-based algorithms. Using a simple bimodal test function and rigorous runtime analyses, we compare well-known diversity mechanisms like deterministic crowding, fitness sharing, and others with a plain algorithm without diversification. We show that diversification is necessary for global exploration, but not all mechanisms succeed in finding both optima efficiently.

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The one-dimensional Ising model: Mutation versus recombination

Cited by 54 publications

References 13 publications

An analysis on recombination in multi-objective evolutionary optimization

An analysis on recombination in multi-objective evolutionary optimization

Evolutionary Algorithms and Matroid Optimization Problems

Theoretical analysis of diversity mechanisms for global exploration

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