Decomposition Strategies and Multi-shot ASP Solving for Job-shop Scheduling

TL;DR

This paper explores decomposition strategies combined with multi-shot Answer Set Programming to improve job-shop scheduling solutions, demonstrating significant quality improvements over single-shot methods within limited runtime.

Contribution

It introduces novel decomposition and overlapping techniques for multi-shot ASP solving, enhancing solution quality for complex job-shop scheduling problems.

Findings

Multi-shot ASP outperforms single-shot in quality within limited time.

Decomposition into time windows improves scheduling efficiency.

Overlapping and compression techniques mitigate partial schedule limitations.

Abstract

The Job-shop Scheduling Problem (JSP) is a well-known and challenging combinatorial optimization problem in which tasks sharing a machine are to be arranged in a sequence such that encompassing jobs can be completed as early as possible. In this paper, we investigate problem decomposition into time windows whose operations can be successively scheduled and optimized by means of multi-shot Answer Set Programming (ASP) solving. From a computational perspective, decomposition aims to split highly complex scheduling tasks into better manageable subproblems with a balanced number of operations such that good-quality or even optimal partial solutions can be reliably found in a small fraction of runtime. We devise and investigate a variety of decomposition strategies in terms of the number and size of time windows as well as heuristics for choosing their operations. Moreover, we incorporate time window overlapping and compression techniques into the iterative scheduling process to counteract optimization limitations due to the restriction to window-wise partial schedules. Our experiments on different JSP benchmark sets show that successive optimization by multi-shot ASP solving leads to substantially better schedules within tight runtime limits than single-shot optimization on the full problem. In particular, we find that decomposing initial solutions obtained with proficient heuristic methods into time windows leads to improved solution quality.