Optimization under Uncertainty in the Prize-Collecting Traveling Salesman Problem: An Artificial Intelligence and Simheuristics Approach

C. Tobar-Fernández, Ana Dolores López Sánchez, Jesús Sánchez-Oro

Keywords: Traveling Salesman Problem, Traveling Repairman Problem, Prize-Collecting Traveling Salesman Problem, Simheuristic, Machine Learning, Stochastic Optimization

TL;DR: This paper explores how combining Machine Learning with simheuristics can improve decision-making for the Prize-Collecting Traveling Salesman Problem (PCTSP) under demand uncertainty.

Abstract: This research addresses the Prize-Collecting Traveling Salesman Problem (PCTSP) under demand uncertainty, a challenge in route optimization where unmet demands incur penalties. Traditional deterministic models fail to capture real-world variability. In this context, a new methodology is proposed that integrates Artificial Intelligence (AI) and simheuristic techniques, which arise from the combination of simulations with heuristics, to improve decision making in uncertain environments. Specifically, Machine Learning models are used to predict demand by obtaining an approximation to the most affine deterministic world assumption, while clustering methods generate realistic demand scenarios. All this giving a more realistic approach replacing the classical ones with Monte Carlo simulations. A simheuristic approach combining GRASP with simulations will be used, aided by Machine Learning methods to improve the evaluation of solutions under stochastic conditions.

Submission Number: 5