Learning to Solve Orienteering Problem with Time Windows and Variable Profits
This addresses a specific optimization problem in logistics and routing, offering incremental improvements in efficiency and solution quality for domain applications.
The paper tackled the orienteering problem with time windows and variable profits (OPTWVP), a complex variant with discrete and continuous variables, by proposing a learning-based two-stage optimization method called DeCoST, which outperformed state-of-the-art solvers with up to 6.6x inference speedup on instances with fewer than 500 nodes.
The orienteering problem with time windows and variable profits (OPTWVP) is common in many real-world applications and involves continuous time variables. Current approaches fail to develop an efficient solver for this orienteering problem variant with discrete and continuous variables. In this paper, we propose a learning-based two-stage DEcoupled discrete-Continuous optimization with Service-time-guided Trajectory (DeCoST), which aims to effectively decouple the discrete and continuous decision variables in the OPTWVP problem, while enabling efficient and learnable coordination between them. In the first stage, a parallel decoding structure is employed to predict the path and the initial service time allocation. The second stage optimizes the service times through a linear programming (LP) formulation and provides a long-horizon learning of structure estimation. We rigorously prove the global optimality of the second-stage solution. Experiments on OPTWVP instances demonstrate that DeCoST outperforms both state-of-the-art constructive solvers and the latest meta-heuristic algorithms in terms of solution quality and computational efficiency, achieving up to 6.6x inference speedup on instances with fewer than 500 nodes. Moreover, the proposed framework is compatible with various constructive solvers and consistently enhances the solution quality for OPTWVP.