New AI Solver Achieves Near-Optimal Solutions for Joint Routing-Assignment Problems

A team led by Qilong Yuan at the Singapore Institute of Technology has introduced a highly efficient solver for the Joint Routing-Assignment (JRA) problem, a complex optimization challenge that combines assignment and routing decisions. The new solver addresses limitations in existing methods, offering near-optimal solutions for large-scale instances. The JRA problem, which is relevant to robotics, logistics, and manufacturing, involves assigning items to placeholders while determining an optimal path that visits each location. Previous exact solvers have struggled with computational inefficiency for large problems, while heuristic methods often fall short of achieving true optimality. The new approach employs a Partial Path Reconstruction (PPR) method, which identifies key item-placeholder pairs to form a smaller subproblem, and is solved efficiently to refine the global solution. Additionally, a Large-α constraint is incorporated to further enhance solution optimality. Experimental results on benchmark datasets (n=300, 500, and 1000) demonstrate that the proposed method consistently delivers near-optimal solutions, achieving an average deviation of 0.00% from the ground truth while maintaining high computational efficiency. The PPR method and Large-α constraint also show potential for broader applications, including the classical Traveling Salesman Problem (TSP) and related routing and logistics optimization challenges. Future research will focus on extending the Large-α solver for multiple running trials to handle even larger problem sizes.