PBI-BFS-MaOA: A Many-Objective Evolutionary Algorithm with PBI-Based Boundary-Front Selection

Thiago Santos; Sebastião Xavier

doi:10.33333/lajc.vol13n2.04

Authors

Thiago Santos Federal University of Ouro Preto (UFOP) https://orcid.org/0000-0002-2435-2786
Sebastião Xavier Federal University of Ouro Preto (UFOP) https://orcid.org/0009-0004-2765-0764

DOI:

https://doi.org/10.33333/lajc.vol13n2.04

Keywords:

many-objective optimization, environmental selection, reference directions, penalty-based boundary intersection

Abstract

Reference-guided many-objective evolutionary algorithms frequently lose discrimination when Pareto dominance becomes sparse and the last accepted front must be truncated. In this situation, front ranking preserves the global search structure, but the boundary-front decision becomes weakly determined, especially as the number of objectives increases. This paper addresses that limitation through PBI-BFS-MaOA, a many-objective evolutionary algorithm that retains Pareto ranking over feasible solutions and applies a survival rule based on cumulative ideal-nadir normalization, penalty-based boundary intersection association, active-niche filtering, and occupancy-aware survivor insertion. These mechanisms are activated only in the critical front, where convergence and directional coverage must be balanced simultaneously. The method is evaluated on DTLZ1-DTLZ4 and WFG1-WFG4 with objective counts M in {5, 8, 10} by using the averaged Hausdorff distance Δ_p, Wilcoxon signed-rank tests, Friedman rank analysis, and runtime measurements. The results show the best mean Δ_p on 13 of the 24 benchmark instances, with stronger performance on the DTLZ suite and on WFG3 at higher dimensions, while runtime remains between NSGA-III and CMOEA-CD.

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Author Biographies

Thiago Santos, Federal University of Ouro Preto (UFOP)

An Associate Professor at the Federal University of Ouro Preto (UFOP), Ouro Preto, Brazil, he holds a Ph.D. in Mathematics and serves as Chief Coordinator of both the Mathematics Education Research Group (GEEMA) and the Applied Mathematics Group of the Department. His research interests span multi-objective optimization, evolutionary computation, and mathematics education — three domains whose convergence underlies his broader commitment to advancing rigorous, computationally informed approaches to both theory and practice. In optimization and computational intelligence, his work is centered on the conception and analysis of metaheuristic algorithms capable of simultaneously navigating multiple conflicting objectives, with far-reaching applications across engineering and the applied sciences. He is equally invested in mathematics education research, bringing sustained scholarly attention to pedagogical innovation, curriculum architecture, and the epistemological barriers students encounter when engaging with advanced mathematical reasoning. Through this integrative research agenda, he contributes substantively to the theoretical foundations of computational methods while championing more effective and intellectually meaningful approaches to the teaching and learning of mathematics at the university level
Sebastião Xavier, Federal University of Ouro Preto (UFOP)

An Associate Professor at the Federal University of Ouro Preto (UFOP), he holds a B.S., M.Sc., and Ph.D. in Mathematics from the Federal University of Minas Gerais (UFMG), with specialized expertise in Dynamical Systems and real foliations. Building on an extensive teaching background that spans basic education through graduate levels, he has played a pivotal role in the institutional development of UFOP’s mathematics programs and the training of future educators through the Mathematics Education Research Group (GEEMA). His primary scientific research is in the field of Optimization, with a focus on multiobjective optimization and evolutionary strategies, where his efforts are dedicated to bridging the gap between rigorous theoretical foundations and practical applications

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