Comparative Evaluation of Multi-Objective Evolutionary Algorithms for Utility-Scale Smart Grid Operation

Abstract

This paper presents a benchmark-oriented multi-objective optimization framework for renewable energy allocation under scarcity conditions in utility-scale smart grid environments. The problem is formulated over a $\mathbf{2 4}$-hour horizon with hourly resolution and incorporates time-varying demand, intermittent renewable generation, capped grid import capacity, and economically penalized energy shortages. Two conflicting objectives are considered: minimization of total operational cost and minimization of unmet demand. Three evolutionary multi-objective optimization algorithms, NSGA-II, MOEA/D, and SPEA2, are evaluated under identical modeling assumptions. Algorithm performance is assessed using Hypervolume, Inverted Generational Distance, and execution time, with reference fronts obtained from extended optimization runs. Results show that SPEA2 achieves strong convergence performance in terms of hypervolume $\left(7.89 \times 10^{12}\right)$ and IGD $\left(1.47 \times 10^{6}\right)$, while NSGA-II provides competitive solution diversity at lower computational cost (3.45 s). MOEA/D produces feasible non-dominated solutions but exhibits weaker convergence under scarcity-driven conditions. The framework is intended as a reproducible benchmark for algorithmic comparison rather than a system-specific operational model.