Riesz s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{s}$$\end{document}-Energy Regularized Bi-Objective Maxi

Abstract

This article presents the Energy-Regularized Bi-Objective Maximal Covering Location Problem (ERBOMCLP), an extension of the classical Maximal Covering Location Problem (MCLP) that incorporates spatial dispersion among selected facilities. The classical MCLP maximizes covered demand under a fixed facility budget and service radius, but may place facilities in spatial clusters when high-demand areas are concentrated. ERBOMCLP addresses this limitation by augmenting coverage maximization with a Riesz s-energy objective that penalizes short inter-facility distances. To solve the model, we develop a memetic Non-dominated Sorting Genetic Algorithm II (NSGA-II) with binary fixed-cardinality encoding, problem-specific crossover and mutation operators, coverage-oriented local search, archive management, and a set-convergence-based termination criterion for detecting approximation-boundary stabilization. Experiments on ERBOMCLP instances derived from a real-world MCLP dataset show that the main memetic variant improves selected-solution coverage and often gives competitive or lower Riesz s-energy, while the spread of the Pareto front approximation remains instance dependent. A controlled hypervolume experiment with a Riesz-nonincreasing local-search rule further improves standard dominated hypervolume on the tested instances, at the cost of substantially more objective evaluations. The study connects potential-theoretic dispersion modeling with facility-location decision support for settings where high demand coverage is primary and dispersion is a complementary proxy for geographic balance.