Evolutionary Algorithms and the Maximum Matching Problem

Giel, Oliver; Wegener, Ingo

doi:10.1007/3-540-36494-3_37

Cited by 151 publications

(168 citation statements)

References 14 publications

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“…Some examples are the partition problem [20] and the problems of finding maximum matchings [10], minimum spanning trees [16], and Euler tours [15,2,4,3] in graphs.…”

Section: Known Resultsmentioning

confidence: 99%

Refined runtime analysis of a basic ant colony optimization algorithm

Doerr

Johannsen

2007

2007 IEEE Congress on Evolutionary Computation

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Neumann and analyzed the runtime of the basic ant colony optimization (ACO) algorithm 1-Ant on pseudoboolean optimization problems. For the problem OneMax they showed how the runtime depends on the evaporation factor. In particular, they proved a phase transition from exponential to polynomial runtime. In this work, we simplify the view on this problem by an appropriate translation of the pheromone model. This results in a profound simplification of the pheromone update rule and, by that, a refinement of the results of Neumann and Witt. In particular, we show how the exponential runtime bound gradually changes to a polynomial bound inside the phase of transition.

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“…Some examples are the partition problem [20] and the problems of finding maximum matchings [10], minimum spanning trees [16], and Euler tours [15,2,4,3] in graphs.…”

Section: Known Resultsmentioning

confidence: 99%

Refined runtime analysis of a basic ant colony optimization algorithm

Doerr

Johannsen

2007

2007 IEEE Congress on Evolutionary Computation

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“…Even more important, it quickly became one of the most powerful tools for both proving upper and lower bounds on the expected optimization times of evolutionary algorithms. For example, see [HY04,GW03,GL06,HJKN08,NOW09,OW].…”

Section: Introductionmentioning

confidence: 99%

Multiplicative Drift Analysis

2012

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In this work, we introduce multiplicative drift analysis as a suitable way to analyze the runtime of randomized search heuristics such as evolutionary algorithms.We give a multiplicative version of the classical drift theorem. This allows easier analyses in those settings where the optimization progress is roughly proportional to the current distance to the optimum.To display the strength of this tool, we regard the classical problem how the (1+1) Evolutionary Algorithm optimizes an arbitrary linear pseudo-Boolean function. Here, we first give a relatively simple proof for the fact that any linear function is optimized in expected time O(n log n), where n is the length of the bit string. Afterwards, we show that in fact any such function is optimized in expected time at most (1 + o(1))1.39en ln(n), again using multiplicative drift analysis. We also prove a corresponding lower bound of (1 − o(1))en ln(n) which actually holds for all functions with a unique global optimum.We further demonstrate how our drift theorem immediately gives natural proofs (with better constants) for the best known runtime bounds for the (1+1) Evolutionary Algorithm on combinatorial problems like finding minimum spanning trees, shortest paths, or Euler tours. * Carola Winzen is a recipient of the Google Europe Fellowship in Randomized Algorithms, and this work is supported in part by this Google Fellowship.

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“…A lot of progress has been made in analyzing simple evolutionary algorithms with respect to their runtime behavior on artificial pseudo-boolean functions [4,10] as well as some well-known combinatorial optimization problems [8,15,18,19,21,24]. We contribute to this line of research and study the minimum s-t-cut problem in a given graph with weights on the edges.…”

Section: Introductionmentioning

confidence: 99%

Computing Minimum Cuts by Randomized Search Heuristics

2009

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We study the minimum s-t-cut problem in graphs with costs on the edges in the context of evolutionary algorithms. Minimum cut problems belong to the class of basic network optimization problems that occur as crucial subproblems in many real-world optimization problems and have a variety of applications in several different areas. We prove that there exist instances of the minimum s-t-cut problem that cannot be solved by standard single-objective evolutionary algorithms in reasonable time. On the other hand, we develop a bi-criteria approach based on the famous maximum-flow minimum-cut theorem that enables evolutionary algorithms to find an optimal solution in expected polynomial time.

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Evolutionary Algorithms and the Maximum Matching Problem

Cited by 151 publications

References 14 publications

Refined runtime analysis of a basic ant colony optimization algorithm

Refined runtime analysis of a basic ant colony optimization algorithm

Multiplicative Drift Analysis

Computing Minimum Cuts by Randomized Search Heuristics

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