Progressive Focus Search for the Static and Stochastic VRPTW with both Random Customers and Reveal Times

Michael Saint-Guillain, Christine Solnon, Yves Deville

Static stochastic VRPs aim at modeling real-life VRPs by considering uncertainty on data. In particular, the SS-VRPTW-CR considers stochastic customers with time windows and does not make any assumption on their reveal times, which are stochastic as well. Based on customer request probabilities, we look for an a priori solution composed preventive vehicle routes, minimizing the expected number of unsatisfied customer requests at the end of the day. A route describes a sequence of strategic vehicle relocations, from which nearby requests can be rapidly reached. Instead of reoptimizing online, a so-called recourse strategy defines the way the requests are handled, whenever they appear. In this paper, we describe a new recourse strategy for the SS-VRPTW-CR, improving vehicle routes by skipping useless parts. We show how to compute the expected cost of a priori solutions, in pseudo-polynomial time, for this recourse strategy. We introduce a new meta-heuristic, called Progressive Focus Search (PFS), which may be combined with any local-search based algorithm for solving static stochastic optimization problems. PFS accelerates the search by using approximation factors: from an initial rough simplified problem, the search progressively focuses to the actual problem description. We evaluate our contributions on a new, real-world based, public benchmark.

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