An intelligent quasi-oppositional HBO technique to solve non-smooth non-convex economic dispatch problem

In this paper, a modified heap-based optimization (HBO) known as the quasi-oppositional heap-based optimization (QOHBO) method is endeavored to tackle the challenging problem of non-convex economic load dispatch problem (ELDP) in large-scale power systems. The QOHBO method leverages a heap data structure to emulate the concept of corporate ranking hierarchy. The mathematical model of HBO is based on the three strategies; first, the interaction between subordinates and their direct superior; second, interactions between contemporaries; third, the employees' self-contribution is adopted to perform both the exploration and exploitation in the search space. To enhance the solution quality and computational efficiency in solving ELDP, we integrate the concept of quasi-oppositional learning into HBO. The proposed QOHBO technique effectively addresses various constraints, including transmission line losses, valve-point loading effects, generator generation limits, prohibited operating zones, power demand compliance, and ramp rate limits. The feasibility of the QOHBO to solve ELDP is evaluated by conducting ten distinct case studies across nine diverse test systems, featuring generating units ranging from three to 140. Comparative analysis with existing techniques from the literature highlights the superior performance of our proposed method in solving large-scale ELD problems. Subsequently, non-parametric alternative tests specifically the Wilcoxon rank-sum test and the Friedman test has been conducted to verify the efficacy of the proposed QOHBO. Moreover, extensive statistical analysis reveals that the QOHBO technique has the ability to consistently provide quality solutions and its robustness when compared to other state-of-the-art approaches.