Title: Pareto Frontier Approximation Network (PA-Net) Applied to Multi-objective TSP. Abstract: Multi-objective optimization is used in various areas of robotics like control, planning etc. Their solutions are dependent on multiple objective functions, which 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. For instance, the travelling salesman problem (TSP) is used in robotics for task/resource allocation. Often this allocation is influenced by multiple objective functions and is solved using Multi-objective travelling salesman problem (MOTSP). In this work, we present PA-Net, a network that generates good approximations of the Pareto front for the multi-objective optimization problems. Our training framework is applicable to other multi-objective optimization problems; however, in this work, we focus on solving MOTSP.  Firstly, MOTSP 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 better quality Pareto fronts with fast inference times as compared to other learning based and classical methods. Finally, we present the application of PA-Net to find optimal visiting order in coverage planning.