A Novel Adaptive Artificial Bee Colony Algorithm for Multi-Objective UFLP Problems

Abstract

Facility location decisions directly affect operational costs, service quality, and customer allocation. However, minimising total cost may result in an imbalanced distribution of customers among open facilities, requiring both objectives to be considered simultaneously. This study proposes a novel non-dominated sorting adaptive binary artificial bee colony algorithm with adaptive operator selection, called NSABC, for the bi-objective uncapacitated facility location problem. The first objective minimises facility opening and customer assignment costs, while the second minimises customer allocation imbalance among open facilities. NSABC integrates Pareto-based archiving, smart initialisation, adaptive operator selection, and diversity-preservation mechanisms to generate high-quality and diverse trade-off solutions. Computational experiments on 15 OR-Library CAP benchmark instances evaluate the algorithms using Hypervolume and Inverted Generational Distance as complementary Pareto-front performance indicators, together with paired two-sided Wilcoxon signed-rank tests and Holm correction. NSABC achieves higher mean Hypervolume values on most instances and lower mean IGD values on 14 of the 15 instances. The statistical analysis significantly favours NSABC on 11 instances according to Hypervolume and on 9 instances according to IGD, whereas NSGA-III is significantly favoured on only one instance according to IGD. The performance advantages of NSABC were observed across benchmark instances of different sizes and scales, indicating its effectiveness under varying problem structures. These findings indicate that NSABC is a competitive and statistically supported alternative to NSGA-III for bi-objective facility location problems involving both economic efficiency and balanced customer distribution.