Comparative Benchmarking of Multi-Objective Algorithms for Renewable Energy System Design Using Pareto Front Quality Metrics

Abstract

Selecting the best multi-objective algorithms for photovoltaic energy storage system (PV-ESS) design remains challenging due to limited benchmarking across renewable energy studies. This study addresses this gap through a systematic evaluation of four widely used multi-objective optimization algorithms: NSGA-II, Multi-Objective Particle Swarm Optimization (MOPSO), weighted-sum scalarization, and ε-constraint methods. Performance assessment utilized three Pareto front quality metrics: Inverted Generational Distance (IGD) for convergence quality, hypervolume (HV) for objective-space coverage, and spacing for solution distribution uniformity. The algorithms were tested on PV-ESS design problems in three developing economies (Nigeria, South Africa, India) under identical problem formulations and computational resources. NSGA-II achieved superior performance across all metrics in all three case studies. For convergence quality, NSGA-II attained a mean IGD of 0.0083, outperforming MOPSO by 29%, ε-constraint by 64%, and weighted-sum by 131%. For objective-space coverage, NSGA-II achieved a mean HV of 0. 700, representing 10–16% better coverage than other methods. For solution distribution, NSGA-II showed a mean spacing of 0.076, indicating 30–117% more uniform Pareto fronts. Computational efficiency analysis revealed that NSGA-II’s runtime is between 5.5 and 7.8 h per case, providing better quality–time ratios compared to ε-constraint methods (which are 18 times slower), while avoiding MOPSO’s premature convergence. Statistical validation confirmed NSGA-II’s superiority, with p < 0.01 across all quality metrics. These results establish NSGA-II as the best algorithm for lifecycle-aware PV-ESS optimization, offering quantitative, evidence-based guidance for practitioners selecting optimization tools for renewable energy system design. The demonstrated performance leads to $ 45,000–$ 60,000 lifecycle cost savings per MW/MWh of system capacity through improved Pareto front identification.