<p>The Sine Cosine Algorithm (SCA) excels in local search capabilities for solving real optimization problems. However, its strong local search ability and rotational invariance often lead to convergence at local optima. In this paper, we introduce a hybrid single-objective optimization algorithm, the Improved Sine Cosine Algorithm, and the Population-Based Incremental Learning Algorithm (ISCAPBIL). First, the Improved Sine Cosine Algorithm (ISCA) is developed by incorporating the hyperbolic sinusoidal cosine function, which dynamically interferes with individual positions to enhance optimization accuracy. Additionally, the Levy flight function is embedded within ISCA to improve its exploratory capabilities. The combination of ISCA and PBIL leverages their respective strengths, with ISCA performing local searches and PBIL handling global searches. This integration achieves a dynamic balance between global and local search processes. Our experimental results demonstrated that ISCAPBIL effectively avoided local optima, significantly improving solution accuracy compared to other algorithm variants. Moreover, when applied to the economic load scheduling problem in power systems, ISCAPBIL exhibited superior optimization efficiency and potential for practical application. The Economic Load Dispatch (ELD) problem is a core optimization task in power systems that aims to minimize generation costs while satisfying demand balance and various operational constraints. However, ELD is often formulated as a complex nonlinear optimization problem, influenced by high dimensionality and constraints, making it challenging for traditional methods to achieve efficient solutions. To address these challenges, we proposed a hybrid algorithm combining the improved Sine Cosine Algorithm (SCA) and Population Incremental Learning (PIL). By leveraging the strengths of both techniques, the proposed algorithm achieved a balance between global exploration and local exploitation. The algorithm was applied to several benchmark ELD problems, and the results demonstrated its superiority in terms of convergence speed and solution quality compared to other methods.</p>
