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چکیده
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Finding the best solutions in complicated designs with many variables is a common challenge in engineering, and it takes a lot of computing power. Traditional gradient-based methods often struggle with these tasks because they can get stuck in local optima and require a lot of computing power [1]. Meta-heuristic algorithms are very useful tools because they are flexible and can search for solutions effectively across a wide range of possibilities. Many different algorithms have been created by mimicking natural processes, social behaviors of animals, and the principles of evolution. Some of these include the Genetic Algorithm (GA) [2], Particle Swarm Optimization (PSO) [3], Ant Colony Optimization (ACO) [4], City Councils Evolution (CCE) [5]. A key idea in optimization theory, called the "No Free Lunch" theorem, states that there isn't one algorithm that can work better than all the others for every type of problem [6]. A method that works really well for one type of problem might not work at all for a different type. This highlights the ongoing requirement for research and the creation of new meta-heuristic strategies to address the changing challenges of complex optimization problems.
Current scientific inquiry is directed along three primary pathways: the conception of original algorithms, the improvement of current methods, and the strategic amalgamation of multiple techniques [7]. A particularly fruitful direction has been the creation of hybrid meta-heuristics, which aim to capitalize on the complementary strengths of individual solvers to achieve more powerful and reliable optimization. The efficacy of this paradigm is evidenced by a growing body of successful hybrid models, including: the combination of firefly algorithm with particle swarm optimization (PSO) [8], the hybridization of the sine-cosine algorithm (SCA) with differential evolution (DE) [9], the integration of particle swarm optimization (PSO) with the gray wolf optimizer (GWO) [10], the hybridiz
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