Deep Reinforcement Learning Model for Robust Travel Salesman Problem via Multiobjective Optimization Framework

Deep Reinforcement Learning (DRL) has gained significant attention for its ability to solve combinatorial optimization problems, including the Traveling Salesman Problem (TSP). While traditional approaches assume known and deterministic cost coefficients, real-world scenarios often involve uncertainty, such as traffic conditions or varying travel times. To address this, we introduce a Multiobjective Robust Combinatorial Optimization (MO-RCO) model that incorporates robustness as an additional objective. By transforming a classical robust combinatorial optimization (RCO) problem into a multiobjective framework, MO-RCO allows decision-makers to explore optimal solutions via a Pareto front, while utilizing pre-trained multiobjective models to estimate robust solutions for new uncertain instances. This enables our method to balance optimality and robustness and provide a scalable solution for new RCO problems. Our results demonstrate the efficiency of MO-RCO in solving the min-max TSP with budget uncertainty, showcasing its potential for real-world applications in robust decision-making.