Estimation-based metaheuristics for stochastic combinatorial optimization: case studies in sochastic routing problems

Stochastic combinatorial optimization problems are combinatorial optimization problems where part of the problem data are probabilistic. The focus of this thesis is on stochastic routing problems, a class of stochastic combinatorial optimization problems that arise in distribution management. Stochastic routing problems involve finding the best solution to distribute goods across a logistic network. In the problems we tackle, we consider a setting in which the cost of a solution is described by a random variable; the goal is to find the solution that minimizes the expected cost. Solving such stochastic routing problems is a challenging task because of two main factors. First, the number of possible solutions grows exponentially with the instance size. Second, computing the expected cost of a solution is computationally very expensive. To tackle stochastic routing problems, stochastic local search algorithms such as iterative improvement algorithms and metaheuristics are quite promising because they offer effective strategies to tackle the combinatorial nature of these problems. However, a crucial factor that determines the success of these algorithms in stochastic settings is the trade-off between the computation time needed to search for high quality solutions in a large search space and the computation time spent in computing the expected cost of solutions obtained during the search. To compute the expected cost of solutions in stochastic routing problems, two classes of approaches have been proposed in the literature: analytical computation and empirical estimation. The former exactly computes the expected cost using closed-form expressions; the latter estimates the expected cost through Monte Carlo simulation.Many previously proposed metaheuristics for stochastic routing problems use the analytical computation approach. However, in a large number of practical stochastic routing problems, due to the presence of complex constraints, the use of the analytical computation approach is difficult, time consuming or even impossible. Even for the prototypical stochastic routing problems that we consider in this thesis, the adoption of the analytical computation approach is computationally expensive. Notwithstanding the fact that the empirical estimation approach can address the issues posed by the analytical computation approach, its adoption in metaheuristics to tackle stochastic routing problems has never been thoroughly investigated. In this thesis, we study two classical stochastic routing problems: the probabilistic traveling salesman problem (PTSP) and the vehicle routing problem with stochastic demands and customers (VRPSDC). The goal of the thesis is to design, implement, and analyze effective metaheuristics that use the empirical estimation approach to tackle these two problems. The main results of this thesis are: 1) The empirical estimation approach is a viable alternative to the widely-adopted analytical computation approach for the PTSP and the VRPSDC; 2) A principled adoption of the empirical estimation approach in metaheuristics results in high performing algorithms for tackling the PTSP and the VRPSDC. The estimation-based metaheuristics developed in this thesis for these two problems define the new state-of-the-art.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished