N(CO)$^2$: Neural Combinatorial Optimization with Chance Constraints to Solve Stochastic Orienteering

2026-06-16

AI Summary

This work addresses the challenge of path planning for the Stochastic Orienteering Problem (SOP) under uncertainty by proposing a reinforcement learning–based neural combinatorial optimization method integrated with chance constraints. For the first time, chance constraints are embedded directly into an end-to-end trainable neural solver, eliminating the need for handcrafted heuristics and enabling the model to adaptively learn robust routing policies from data alone. The approach effectively balances exploration and exploitation during policy learning. Experimental results demonstrate that the proposed model exhibits strong generalization across diverse SOP instances and achieves performance comparable to state-of-the-art mixed-integer linear programming methods.

Abstract

Neural combinatorial optimization (NCO) offers a promising alternative to traditional heuristic-based methods for solving complex graph optimization problems by proposing to learn heuristics through data. This class of problems frequently arises in automation, as it can be used to model a variety of applications. While NCO has been extensively studied for deterministic combinatorial optimization problems, there are only a few works that aim to solve stochastic combinatorial optimization problems. In this work, we present N(CO)$^2$: Neural Combinatorial Optimization with Chance cOnstraints to solve the Stochastic Orienteering Problem (SOP) without the use of hand-crafted heuristics. By integrating a reinforcement learning (RL) framework, the model optimizes path selection under uncertainty, effectively balancing exploration and exploitation. Empirical results demonstrate that our method generalizes well across diverse SOP instances, achieving competitive performance compared to the state-of-the-art mixed-integer linear program (MILP) for the task. The proposed approach reduces human effort in heuristic design while enabling adaptive and efficient decision-making in uncertain environments.

Problem

• Stochastic Orienteering Problem
• Chance Constraints
• Neural Combinatorial Optimization
• Uncertainty

Innovation

• Neural Combinatorial Optimization
• Chance Constraints
• Stochastic Orienteering Problem
• Reinforcement Learning
• Uncertainty-aware Decision Making