Knee-based energy-saving measures selection using MOPSO and NSGA-II

This paper benchmarks two Evolutionary Multi-Objective Optimization (EMO) methods, namely Multi Objective Particle Swarm Optimization (MOPSO) and Non-Dominated Sorting Genetic Algorithm II (NSGA-II), for selecting Energy-Saving Measures (ESMs) in an audited Malaysian academic building under a bi-objective trade-off between annual energy saving and investment cost, while avoided CO₂ is computed from energy saving using the fixed grid-emission factor as a carbon metric. For each algorithm, 30 seeds generate Pareto fronts in the cost–energy saving plane, shown in 2D for clear comparison, and the resulting carbon metric is visualized as a 3D projection. A curvature-based knee is extracted to yield one implementable package per run. Knee packages are valued over a 10-year horizon using Simple Payback Period (SPP), discounted Return on Investment (ROI), Life-Cycle Cost (LCC), and Savings-to-Investment Ratio (SIR) under fixed site assumptions. Relative to the auditor’s package, the knee solutions cut Capital Expenditure (CAPEX) by approximately 87.3 % for MOPSO and 81.9 % for NSGA-II while sustaining around 21 % to 23 % of the auditor’s annual energy savings and CO₂ avoidance. Economic performance improves markedly at the knees: SPP shortens to 2.25 yr for MOPSO and 3.54 yr for NSGA-II; discounted ROI rises to 235.24 % and 110.43 %; SIR increases to 3.18 and 2.03; and LCC is favorable at -RM 92,816 and -RM 62,614, respectively. Across 30 paired seeds, paired Wilcoxon tests indicate statistically and practically significant between-method differences at the knee, with the strongest separation in LCC and SPP. Overall, the MOPSO knee offers the strongest financial profile, whereas the NSGA-II knee attains slightly higher annual savings and CO₂ avoidance.