Lévy Opposition-Based Learning Bat Algorithm for Solving the Economic Load Dispatch Problem

Abstract

This paper proposes the Lévy Opposition-Based Learning-Bat Algorithm (LOBL-BA) as a solution to the Economic Load Dispatch (ELD) problem with Valve-Point Effect (VPE) and Prohibited Operating Zones (POZ). The standard Bat Algorithm (BA) suffers from slow convergence and limited exploration, making it prone to becoming trapped in local optima. To address these limitations, three enhancements are introduced. First, a random inertia weight strategy improves search capability. Second, Lévy Opposition-Based Learning (LOBL) is incorporated to balance exploration and exploitation, enabling more effective handling of complex optimization problems. Third, a Sine Function-Driven Local Search (SFDLS) mechanism refines candidate solutions and strengthens the algorithm's ability to escape local optima. The proposed LOBL-BA is thoroughly validated on 6-unit, 13-unit, 15-unit, and 40-unit power systems. The results clearly demonstrate that it achieves significantly greater fuel cost minimization for the ELD problem with VPE and POZ, with its performance benchmarked against several established algorithms, including BA, FPA, GWO, MVO, SCA, AOA, WSO, RIME, and others from the literature. Across all test cases, the proposed algorithm consistently achieves the optimal fuel cost.