Energy-Based Multi-Objective Black Hole Optimization with Angle Quantization and Crowding Distance for Multi-Objective Optimization Problems

Abstract

Multi-objective optimization (MOO) is a technique that deals with many conflicting goals that seek Pareto-optimal trade-off solutions. Although well-known Multi-Objective Evolutionary Algorithms (MOEAs), including NSGA-II, NSGA-III, MOPSO, and MOEA/D, are still actively used, issues of adaptive exploration-exploitation ratio and distribution control continue to be observed in some problem landscapes. The proposed algorithm EMOBHO-AQCD, is a physics-based bi-objective optimization model that combines three coordinated mechanisms to achieve adaptive search regulation (1), directional diversity control (2), and local density preservation (3). The algorithm represents optimization as a gravitational interaction system whereby elite solutions actively dynamically control search pressure depending on improvement-based energy updates. The suggested approach is compared to four established algorithms (NSGA-II, NSGA-III, MOPSO, and MOEA/D) and three proposed variants (MOBHO, EMOBHO, and EMOBHO-AQCD) on six classical bi-objective benchmark problems based on several performance indicators and non-parametric statistical confirmation (Wilcoxon signed-rank test with Cohen's d effect size analysis at α = 0.05). Findings show that EMOBHO-AQCD is always improving on its predecessors (EMOBHO and MOBHO) and is equally efficient as the major algorithms like NSGA-II and MOPSO in a number of benchmarks. Dominance robustness on low-to-moderate dimensional problems is confirmed by strong set coverage (SC1 = 0.83-1.00), whereas diversity metrics indicate a specified convergence-distribution trade-off profile. Higher-dimensional problems of ZDT are known to be of performance limitation, thus explaining the scope of operations of the proposed framework. In general, EMOBHO-AQCD offers a competitive and bi-objective optimization method, which has specific advantages in stability of dominance and directional coverage, and has a clear and transparent scaling limits in the studied benchmark domain.