Abstract
<title>Abstract</title> <p>Economic dispatch and environmental dispatch are two fundamental single-objective optimizationproblems in modern power system operation. The presence of valve-point loadingeffects on the generators’ cost curves renders these problems strongly non-convex, nonsmooth,and multimodal, defeating classical gradient-based methods. This paper presentsa comprehensive study of the Phototropic Growth Algorithm (PGA) applied to two staticsingle-objective formulations of the combined economic and environmental dispatch problemon a large-scale 40-unit thermal benchmark system. The first case minimizes the totalfuel cost only, while the second minimizes the total pollutant emissions only, both underidentical realistic constraints (power balance with lossless network, generator capacity limits,and valve-point loading effects). PGA is a recent nature-inspired metaheuristic thatmimics the directional growth of plants toward a light source, translating the differentialelongation of illuminated and shaded cells into an exploration–exploitation strategy. Constraintviolations are handled through boundary correction and penalty functions. Theproposed methodology is evaluated through fifty independent runs to assess robustness,with performance assessed via convergence analysis, statistical dispersion, and feasibilityverification. The numerical results show that PGA achieves smooth and stable convergence,with low dispersion across independent runs, and outperforms several recentmetaheuristics in both objective value and execution time, confirming its effectiveness forsingle-objective dispatch problems in non-convex thermal power systems.</p>