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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.
estimation, local search, Statistics as Topic, traveling salesman problem, combinatorial optimization problems, Game Theory, flow shop scheduling problem, Computer Simulation, number of local optima, species estimation problem, Algorithms
estimation, local search, Statistics as Topic, traveling salesman problem, combinatorial optimization problems, Game Theory, flow shop scheduling problem, Computer Simulation, number of local optima, species estimation problem, Algorithms
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 24 | |
popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Top 10% | |
influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Top 10% |