Learning to Solve Orienteering Problem with Time Windows and Variable Profits

TL;DR

This paper introduces DeCoST, a learning-based two-stage optimization method for the complex orienteering problem with time windows and variable profits, improving solution quality and speed over existing methods.

Contribution

DeCoST effectively decouples discrete and continuous variables in OPTWVP, enabling efficient learning and optimization with proven global optimality for the second stage.

Findings

Outperforms state-of-the-art solvers in solution quality

Achieves up to 6.6x faster inference speed

Enhances solution quality across various constructive solvers

Abstract

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.