The economic dispatch (ED) problem is a major challenge in power system optimization. In this article, an Enhanced Social Group Optimization (ESGO) algorithm is presented for solving the economic dispatch problem with or without wind units, considering various characteristics related to valve-point effects, ramp-rate constraints, prohibited operating zones, and transmission power losses. The Social Group Optimization (SGO) algorithm models the social dynamics of individuals within a group—through mechanisms of collective learning, behavioral adaptation, and information exchange—and leverages these interactions to guide the population efficiently towards optimal solutions. ESGO extends SGO along three complementary directions: redefining the update relations of the original SGO, introducing stochastic operators into the heuristic mechanisms, and dynamically updating the generated solutions. These modifications aim to achieve a more robust balance between exploration and exploitation, enable flexible adaptation of search steps, and rapidly integrate improved-fitness solutions into the evolutionary process. ESGO is evaluated in six distinct cases, covering systems with 6, 40, 110, and 220 units, to demonstrate its ability to produce competitive solutions as well as its performance in terms of stability, convergence, and computational efficiency. The numerical results show that, in the vast majority of the analyzed cases, ESGO outperforms SGO and other known or improved metaheuristic algorithms in terms of cost and stability. It incorporates wind generation results at an operating cost reduction of approximately 10% compared to the thermal-only system, under the adopted linear wind power model. Moreover, relative to the size of the analyzed systems, ESGO exhibits a reduced average execution time and requires a small number of function evaluations to obtain competitive solutions.
Secui et al. (Sun,) studied this question.