Faster Evolutionary Algorithms by Superior Graph Representation

Doerr, Benjamin; Klein, Christian; Storch, Tobias

doi:10.1109/foci.2007.372176

Cited by 24 publications

(22 citation statements)

References 11 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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“…One of the first papers in this direction is [14], where evolutionary algorithms for sorting and shortest path problems are proposed and analyzed. Other results on evolutionary algorithms for combinatorial optimization problems include a series of papers on the Eulerian cycle problem [4]- [6], [11], minimum spanning trees [12], [13] or maximal matchings [8].…”

Section: Introductionmentioning

confidence: 99%

A tight analysis of the (1 + 1)-EA for the single source shortest path problem

Doerr¹,

Happ²,

Klein³

2007

2007 IEEE Congress on Evolutionary Computation

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Abstract-We conduct a rigorous analysis of the (1 + 1) evolutionary algorithm for the single source shortest path problem proposed by Scharnow, Tinnefeld and Wegener (Journal of Mathematical Modelling and Algorithms, 2004). We prove a tight bound of Θ(n 2 max{log(n), }) on the optimization time, where is the maximum number of edges of a shortest path with minimum number of edges from the source to another vertex. Using various tools from probability theory we show that these bounds not only hold in expectation, but also with high probability. We are optimistic that these tools can also be used to analyze the run-time of evolutionary algorithms for other problems.

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“…Recently, two different kinds of graph representation have been studied. In this way, firstly, the expected runtime has been lowered to Θ(m 2 log m) [47] . Secondly, by considering adjacency lists representations, the expected runtime has been further reduced to Θ(m log m) [48] .…”

Section: Problems In Pmentioning

confidence: 99%

Time complexity of evolutionary algorithms for combinatorial optimization: A decade of results

Oliveto

Yao

2007

Int J Automat Comput

182

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Computational time complexity analyzes of evolutionary algorithms (EAs) have been performed since the mid-nineties. The first results were related to very simple algorithms, such as the (1+1)-EA, on toy problems. These efforts produced a deeper understanding of how EAs perform on different kinds of fitness landscapes and general mathematical tools that may be extended to the analysis of more complicated EAs on more realistic problems. In fact, in recent years, it has been possible to analyze the (1+1)-EA on combinatorial optimization problems with practical applications and more realistic population-based EAs on structured toy problems. This paper presents a survey of the results obtained in the last decade along these two research lines. The most common mathematical techniques are introduced, the basic ideas behind them are discussed and their elective applications are highlighted. Solved problems that were still open are enumerated as are those still awaiting for a solution. New questions and problems arisen in the meantime are also considered.

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Faster Evolutionary Algorithms by Superior Graph Representation

Abstract: Abstract-

Cited by 24 publications

References 11 publications

Refined runtime analysis of a basic ant colony optimization algorithm

Refined runtime analysis of a basic ant colony optimization algorithm

A tight analysis of the (1 + 1)-EA for the single source shortest path problem

Time complexity of evolutionary algorithms for combinatorial optimization: A decade of results

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