Pareto Frontier Approximation Network (PA-Net) to Solve Bi-objective TSP

Travelling salesperson problem (TSP) is a classic resource allocation problem used to find an optimal order of doing a set of tasks while minimizing (or maximizing) an associated objective function. It is widely used in robotics for applications such as planning, scheduling etc. In this work, we solve TSP for two objectives using reinforcement learning. Often in multi objective optimization problems, the associated objective functions can be conflicting in nature. In such cases, the optimality is defined in terms of Pareto optimality. A set of these Pareto Optimal solutions in the objective space form a Pareto front (or frontier). Each solution has its own trade off. In this work, we present PA-Net, a network that generates good approximations of the Pareto front for the bi-objective travelling salesperson problem (BTSP). Firstly, BTSP is converted into a constrained optimization problem. We then train our network to solve this constrained problem using the Lagrangian relaxation and policy gradient. With PA-Net we are able to generate good quality Pareto fronts with fast inference times. Finally, we present the application of PA-Net to find optimal visiting order in a robotic navigation task/coverage planning.