Neural Combinatorial Optimization for Stochastic Flexible Job Shop Scheduling Problems

TL;DR

This paper introduces a neural combinatorial optimization method with an attention-based scenario processing module to effectively solve stochastic flexible job shop scheduling problems, outperforming existing methods.

Contribution

It presents a novel attention-based scenario processing module and a training paradigm for stochastic JSPs, extending neural optimization to handle stochasticity explicitly.

Findings

Outperforms existing methods on stochastic JSP benchmarks.

Effective generalization across different scenario numbers and distributions.

Supports multiple objectives like expected makespan and Value-at-Risk.

Abstract

Neural combinatorial optimization (NCO) has gained significant attention due to the potential of deep learning to efficiently solve combinatorial optimization problems. NCO has been widely applied to job shop scheduling problems (JSPs) with the current focus predominantly on deterministic problems. In this paper, we propose a novel attention-based scenario processing module (SPM) to extend NCO methods for solving stochastic JSPs. Our approach explicitly incorporates stochastic information by an attention mechanism that captures the embedding of sampled scenarios (i.e., an approximation of stochasticity). Fed with the embedding, the base neural network is intervened by the attended scenarios, which accordingly learns an effective policy under stochasticity. We also propose a training paradigm that works harmoniously with either the expected makespan or Value-at-Risk objective. Results demonstrate that our approach outperforms existing learning and non-learning methods for the flexible JSP problem with stochastic processing times on a variety of instances. In addition, our approach holds significant generalizability to varied numbers of scenarios and disparate distributions.