Local optima topology for the k-coloring problem
Discrete Applied Mathematics - Special volume: viewpoints on optimization
Artificial Intelligence
How to detect all maxima of a function
Theoretical aspects of evolutionary computing
Non-parametric Estimation of Properties of Combinatorial Landscapes
Proceedings of the Applications of Evolutionary Computing on EvoWorkshops 2002: EvoCOP, EvoIASP, EvoSTIM/EvoPLAN
Production scheduling and rescheduling with genetic algorithms
Evolutionary Computation
On confidence intervals for the number of local optima
EvoWorkshops'03 Proceedings of the 2003 international conference on Applications of evolutionary computing
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The solution of many combinatorial optimization problems is carried out by metaheuristics, which generally make use of local search algorithms. These algorithms use some kind of neighborhood structure over the search space. The performance of the algorithms strongly depends on the properties that the neighborhood imposes on the search space. One of these properties is the number of local optima. Given an instance of a combinatorial optimization problem and a neighborhood, the estimation of the number of local optima can help not only to measure the complexity of the instance, but also to choose the most convenient neighborhood to solve it. In this paper we review and evaluate several methods to estimate the number of local optima in combinatorial optimization problems. The methods reviewed not only come from the combinatorial optimization literature, but also from the statistical literature. A thorough evaluation in synthetic as well as real problems is given. We conclude by providing recommendations of methods for several scenarios.