Negative hypervolume improvement assisted infill criterion for multi-objective efficient global optimization and its applications

Abstract

This study introduces a novel hypervolume enhancement approach derived from negative hypervolume improvement (NHVI) concepts, addressing inherent limitations in conventional strategies that generate extensive zero-gradient regions detrimental to late-stage optimization efficiency. In contrast to traditional methodologies that nullify dominated regions, our proposed strategy systematically calculates negative improvements within these domains. This critical modification transforms problematic zero-gradient plateaus into negatively inclined hypervolume regions that actively drive optimization momentum, effectively accelerating the entire multi-objective optimization process. The research implements this negative hypervolume improvement paradigm within multi-objective Efficient Global Optimization (EGO) frameworks. The method's efficacy is rigorously validated against a comprehensive suite of standard multi-objective benchmarks, challenging many-objective test cases, and an aerodynamic airfoil optimization case study. Across all numerical tests, the proposed algorithm demonstrated statistically significant superiority, and in the engineering application, comparative analysis reveals that the enhanced algorithm produces a 485% increase in Pareto solution density (from 7 to 41 solutions) while maintaining superior solution quality. These empirical results substantiate the strategy's effectiveness in addressing real-world engineering challenges, particularly demonstrating its capacity to improve optimization precision through systematic gradient management. The demonstrated performance enhancements highlight the methodology's practical significance for complex multi-objective engineering applications requiring both computational efficiency and solution quality.