An Enhanced Large Neighborhood Search Approach for the Capacitated Facility Location Problem with Incompatible Customers

2026-05-27

AI Summary

This study addresses the capacitated facility location problem with customer exclusion constraints, wherein certain pairs of customers cannot be served by the same facility—a condition commonly arising in hazardous material distribution or scenarios involving competing clients. To tackle this challenging variant, the authors propose an enhanced large neighborhood search algorithm incorporating three tailored destruction operators and leveraging an exact solver during the repair phase to optimally resolve subproblems. The method achieves new best-known solutions on all publicly available benchmark instances, consistently outperforming the current state-of-the-art metaheuristic approaches. These results demonstrate the algorithm’s superior efficacy and robustness in handling complex exclusion constraints while maintaining solution quality and computational efficiency.

Abstract

A new variant of the classic capacitated facility location problem, which considers incompatibilities between customers, has recently been introduced in the literature. This problem captures the situation where given pairs of customers cannot be served by the same facility. Such a feature is crucial for many practical cases of location problems, such as the presence of hazardous or polluting materials and contention between competing costumers. In this paper, we propose a Large Neighborhood Search (LNS) method to solve this problem. Within the framework of LNS, we introduce three different destroy operators, which are combined in a hybrid manner, and we use an exact solver in the repair phase. Different algorithmic components are investigated for the design of LNS. The experimental analysis shows that our new method outperforms existing state-of-the-art metaheuristics, providing new best solutions for all available benchmark instances.

Problem

• Capacitated Facility Location Problem
• Incompatible Customers
• Customer Incompatibility
• Facility Location
• Mutual Exclusion

Innovation

• Large Neighborhood Search
• Capacitated Facility Location Problem
• Incompatible Customers
• Hybrid Destroy Operators
• Exact Solver