Learning to Solve Orienteering Problem with Time Windows and Variable Profits

2026-03-06

AI Summary

This work addresses the computational bottleneck in the Orienteering Problem with Time Windows and Variable Profits (OPTWVP), where the coupling of discrete path selection and continuous service time allocation impedes solution efficiency. To this end, we propose DeCoST, a two-stage decoupled optimization framework. In the first stage, a parallel decoding architecture jointly predicts a route and initial service times; in the second stage, service times are globally optimized via linear programming, augmented with structural estimation to capture long-range dependencies. DeCoST is the first framework to effectively decouple and co-optimize discrete and continuous variables in OPTWVP, offering global optimality guarantees for the second-stage solution while remaining compatible with diverse constructive solvers. Experiments demonstrate that DeCoST outperforms existing constructive and metaheuristic methods in solution quality and achieves up to a 6.6× speedup in inference time on instances with fewer than 500 nodes.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Orienteering Problem
• Time Windows
• Variable Profits
• Discrete-Continuous Optimization
• Combinatorial Optimization

Innovation

• Decoupled optimization
• Learning-based solver
• Orienteering problem with time windows
• Service-time allocation
• Linear programming