Heuristics for the probabilistic traveling salesman problem with deadlines based on quasi-parallel Monte Carlo sampling

The Probabilistic Traveling Salesman Problem with Deadlines (PTSPD) is a Stochastic Vehicle Routing Problem with a computationally demanding objective function. In this work we propose an approximation for that objective function based on Monte Carlo Sampling and using the novel approach of quasi-parallel evaluation of samples. We perform comprehensive computational studies that reveal the efficiency of this approximation. Additionally, we examine different Local Search Algorithms and present a Random Restart Local Search Algorithm for solving the PTSPD together with an extensive computational study on a large set of benchmark instances.