A Social Group Optimization Algorithm Using the Laplace Operator for the Economic Dispatch Problem

The economic dispatch (ED) problem focuses on the optimal scheduling of thermal generating units in a power system to minimize fuel costs while satisfying operational constraints. This article proposes a modified version of the social group optimization (SGO) algorithm to address the ED problem with various practical characteristics (such as valve-point effects, transmission losses, prohibited operating zones, and multi-fuel sources). SGO is a population-based metaheuristic algorithm with strong exploration capabilities, but for certain types of problems, it may stagnate in a local optimum due to a potential imbalance between exploration and exploitation. The new version, named SGO-L, retains the structure of the SGO but incorporates a Laplace operator derived from the Laplace distribution into all the iterative solution update equations. This adjustment generates more effective search steps in the solution space, improving the exploration–exploitation balance and overall performance in terms of solution stability and quality. SGO-L is validated on four power systems of small (six-unit), medium (10-unit), and large (40-unit and 110-unit) sizes with diverse characteristics. The efficiency of SGO-L is compared with SGO and other metaheuristic algorithms. The experimental results demonstrate that the proposed SGO-L algorithm is more robust than well-known algorithms (such as particle swarm optimization, genetic algorithms, differential evolution, and cuckoo search algorithms) and other competitor algorithms mentioned in the study. Moreover, the non-parametric Wilcoxon statistical test indicates that the new SGO-L version is more promising than the original SGO in terms of solution stability and quality. For example, the standard deviation obtained by SGO-L shows significantly lower values (6.02 × 10−9 USD/h for the six-unit system, 7.56 × 10−5 USD/h for the 10-unit system, 75.89 USD/h for the 40-unit system, and 4.80 × 10−3 USD/h for the 110-unit system) compared to SGO (0.44 USD/h for the six-unit system, 50.80 USD/h for the 10-unit system, 274.91 USD/h for the 40-unit system, and 1.04 USD/h for the 110-unit system).