The analysis of evolutionary algorithms on sorting and shortest paths problems
 Jens Scharnow,
 Karsten Tinnefeld,
 Ingo Wegener
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The analysis of evolutionary algorithms is up to now limited to special classes of functions and fitness landscapes. E.g., it is not possible to characterize the set of TSP instances (or another NPhard combinatorial optimization problem) which are solved by a generic evolutionary algorithm (EA) in an expected time bounded by some given polynomial. As a first step from artificial functions to typical problems from combinatorial optimization, we analyze simple EAs on wellknown problems, namely sorting and shortest paths. Although it cannot be expected that EAs outperform the wellknown problem specific algorithms on these simple problems, it is interesting to analyze how EAs work on these problems. The following results are obtained:
 Sorting is the maximization of “sortedness” which is measured by one of several wellknown measures of presortedness. The different measures of presortedness lead to fitness functions of quite different difficulty for EAs.
 Shortest paths problems are hard for all types of EA, if they are considered as singleobjective optimization problems, whereas they are easy as multiobjective optimization problems.
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 Title
 The analysis of evolutionary algorithms on sorting and shortest paths problems
 Journal

Journal of Mathematical Modelling and Algorithms
Volume 3, Issue 4 , pp 349366
 Cover Date
 20050101
 DOI
 10.1007/s1085200525840
 Print ISSN
 15701166
 Online ISSN
 15729214
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 randomized search heuristics
 evolutionary algorithms
 analysis of expected run time
 sorting
 shortest paths
 68W20
 68W40
 Authors

 Jens Scharnow ^{(1)}
 Karsten Tinnefeld ^{(1)}
 Ingo Wegener ^{(1)}
 Author Affiliations

 1. FB Informatik, LS2, University of Dortmund, 44221, Dortmund, Germany