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

In stochastic combinatorial optimization, problem parameters are affected by uncertainty; however, probability distributions describing the uncertainty are known or can be estimated. Stochastic routing problems, a prominent class of stochastic combinatorial optimization problems, involve finding an efficient way to distribute or collect goods across a logistic network. In order to tackle these problems, I considered a typical setting in which the cost of each solution is a random variable, and the goal is to find the solution with the minimum expected cost. It has been shown that, for some problems and for known probability distributions, the expectation can be computed analytically. Unfortunately, this typically involves complex analytical developments and computationally expensive procedures. Moreover, computing the expectation through the analytical computation approach is a highly problem-specific issue and it requires a deep understanding of the underlying probabilistic model. An alternative approach is empirical estimation, which estimates the expectation through Monte Carlo simulation. The main advantage of the empirical estimation approach over the analytical computation one is generality: a sample estimate of the expected cost of a given solution can be obtained by simply averaging sample cost estimates over a number of realizations of the random variable.