Adaptive Geometry Based Meta-Learning for Multi-Objective Combinatorial Optimization Problems

In recent years, neural heuristics leveraging deep reinforcement learning have exhibited considerable promise in addressing multi-objective combinatorial optimization problems (MOCOPs). Nonetheless, challenges persist in attaining both high learning efficiency and optimal solution quality. To address this issue, we propose a novel multi-objective optimization algorithm grounded in information geometry and machine learning principles, which integrates adaptive gradient descent with meta-reinforcement learning techniques to effectively tackle MOCOPs. In this paper, we present a meta-learning framework aimed at enhancing model performance in multi-objective combinatorial optimization through tensor remodeling, preconditioned gradient descent, and entropy regularization strategies. Experimental results demonstrate that the proposed method yields significant performance improvements across several classic multi-objective combinatorial optimization challenges, including the Multi-objective Traveling Salesman Problem (MOTSP), Multi-objective Vehicle Routing Problem (MOCVRP), and Multi-objective Knapsack Problem (MOKP).