Prize-Collecting Traveling Salesman Problem: A Reinforcement Learning Approach

Prize-Collecting Traveling Salesman Problem (PC-TSP) is a new variation of TSP and is defined as follows. Given a weighted complete graph $G(V, E)$ where node $i\in V$ has an available prize of $p_{i}$, and two nodes $s, t\in V$, the goal of the traveling salesman is to find a route from $s$ to $t$ such that the sum of the prizes of all the nodes visited along the route reaches a pre-set quota while the distance along the route is minimized. In this paper, we propose a multi-agent reinforcement learning (MARL) framework for the PC-TSP. Our novel observation is that prize-collecting in PC-TSP is intrinsically related to cumulative reward maximization in reinforcement learning (RL). By integrating the prizes in PC-TSP into the reward model in RL, we design an efficient and effective MARL algorithm to solve the PC-TSP. Via extensive simulations under different network and RL parameters, we show that our learning algorithm delivers an average of 65.6% of less traveling distance compared to one existing handcrafted greedy algorithm. When changing the number of agents $m$ from 1 to 5, our algorithm reduces the prize-collecting learning time by up to 66.9%, demonstrating the effectiveness of multi-agent collaboration in reducing the prize-collecting learning time in PC-TSP.