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

Abstract

Reference-guided many-objective evolutionary algorithms often lose selection pressure when Pareto dominance becomes scarce and the final accepted front must be truncated. We propose PBI-BFS-MaOA, a many-objective evolutionary algorithm that preserves Pareto ranking for feasible solutions and modifies only the survival decision on the boundary front. The method combines cumulative ideal–nadir normalization, penalty-based boundary intersection association, active-niche filtering, and occupancy-aware survivor insertion. These operations are activated where convergence and directional coverage must be decided simultaneously. We evaluate the algorithm on DTLZ1–DTLZ4 and WFG1–WFG4 with M ∈ {5, 8, 10} objectives, using the averaged Hausdorff distance Δp, Wilcoxon signed-rank tests, Friedman rank analysis, and runtime measurements. PBI-BFS-MaOA obtains the best mean Δp in 13 of 24 benchmark instances, with its strongest gains on highdimensional DTLZ cases and degenerate WFG3 instances, while its runtime remains between NSGA-III and CMOEA-CD.