Solving Non-smooth Arc Routing Problems Throughout Biased-Randomized Heuristics
In non-smooth optimization problems the objective function to minimize or maximize is non-smooth and usually non-convex either, which is a frequent characteristic of real-life optimization problems. In this chapter we discuss the arc routing problem with a non-smooth cost function, and propose a randomized algorithm for solving it. Our approach employs non-uniform probability distributions to add a biased random behavior to the well-known savings heuristic. By doing so, a large set of alternative good solutions can be quickly obtained in a natural way and without complex configuration processes. Since the solution-generation process is based on the criterion of maximizing the savings, it does not need to assume any particular property of the objective function. Therefore, the procedure can be especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregulars solution space, for which the traditional optimization methods -both of exact and approximate nature- may fail to reach their full potential. The results obtained so far suggest that using biased probability distributions to randomize classical heuristics can be successfully applied in non-smooth optimization.
KeywordsRandomized algorithms Combinatorial optimization Heuristics Arc routing problem
The research of the first, third and fourth authors has been partially supported by the Spanish Ministry of Science and Innovation (TRA2010-21644-C03) and by the Ibero-American Programme for Science, Technology and Development (CYTED2010-511RT0419) in the context of the ICSO-HAROSA Programme of the IN3 (http://dpcs.uoc.edu).
The research of the second author has been partially supported by the Spanish Ministry of Science and Technology (MTM2011-29064-C03-01).
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