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The Runge-Kutta Optimization (RUNGE) algorithm is a recently proposed metaphor-free metaheuristic optimizer borrowing practical mathematical foundations of the famous Runge-Kutta differential equation solver. Despite its relatively new emergence, this algorithm has several applications in various branches of scientific fields. However, there is still much room for improvement as it suffers from premature convergence resulting from inefficient search space exploration. To overcome this algorithmic drawback, this research study proposes a brand-new quasi-dynamic opposition-based learning (QDOPP) mechanism to be implemented in a standard Runge-Kutta optimizer to eliminate the local minimum points over the search space. Enhancing the asymmetric search hyperspace by taking advantage of various positions of the current solution within the domain is the critical novelty to enrich general diversity in the population, significantly improving the algorithm's overall exploration capability. To validate the effectivity of the proposed RUNGE-QDOPP method, thirty-four multidimensional optimization benchmark problems comprised of unimodal and multimodal test functions with various dimensionalities have been solved, and the corresponding results are compared against the predictions obtained from the other opposition-based learning variants as well as some state-of-art literature optimizers. Furthermore, six constrained engineering design problems with different functional characteristics have been solved, and the respective results are benchmarked against those obtained for the well-known optimizers. Comparison of the solution outcomes with literature optimizers for constrained and unconstrained test problems reveals that the proposed QDOPP has significant advantages over its counterparts regarding solution accuracy and efficiency. [ABSTRACT FROM AUTHOR]

This research study proposes a novel mutation scheme mainly based on the manipulation equations of Tangent Search Optimization and mutualism phase of Symbiotic Organism Search algorithms to be implemented on the Equilibrium Optimization algorithm to enhance the solution diversity among the population individuals. Beneficial coordination between these governing search mechanisms enables maintaining diversity in the population. It eliminates the stagnation towards the local sub-optimal solutions over the search domain, significantly alleviating the inherent drawbacks of Equilibrium Optimizer. To assess the efficiency of the proposed diversity-enhanced Equilibrium Optimization algorithm (DEQUIL) on unconstrained problems, thirty-four multidimensional optimization test instances comprised of unimodal and multimodal benchmark problems have been solved, and respective performances are verified against those obtained from well-reputed new emerged metaheuristic algorithms. A comprehensive comparison based on the decisive metrics, including statistical analysis, performance index analysis, scalability tests, diversity analysis, and convergence rates demonstrates the effectiveness of the hybrid search methodology. Later, fourteen real-world constrained engineering problems with varying complexities were solved by the proposed DEQUIL method. The prediction performance of DEQUIL is compared with a wide range of available literature optimizers to scrutinize the improvements in problem-solving capabilities and seen that it can successfully cope with the complex constrained design problems outperforming the majority of the compared algorithm in most design cases. [ABSTRACT FROM AUTHOR]

Gradient-based optimizer (GRAD) belongs to the recently developed population-based metaheuristic algorithms inspired by the development of Newton-type methods. Despite its new emergence, there are many successful applications of this optimizer in the existing literature; however, chaos integrated version of this algorithm has not been extensively studied yet. In his study, twenty-one different chaotic maps have been incorporated into the standard GRAD algorithm to maintain a reliable balance between exploration and exploitation mechanisms, which is not robustly constructed within the original algorithm. First ninety-nine thirty dimensional artificially generated optimization benchmark problems comprised of sixty-eight multimodal and thirty-one unimodal functions have been solved by these chaotic variants of the GRAD algorithm to determine the five best performing methods between them. Clear dominancy of the chaotic algorithms is clearly observed over the entire range of benchmark cases in terms of solution accuracy and robustness. Then, to validate the optimization capability of the chaos integrated GRAD algorithms, the best method among them is tested on fourteen constrained real world engineering problems, and its respective feasible results are benchmarked against those obtained from cutting edge metaheuristic optimizer. It is seen that the chaotic GRAD algorithm is able to effectively compete with other state-of-art algorithms on both solving unconstrained and constrained engineering problems. Moreover, it is observed that the Chebyshev chaotic map improved GRAD algorithm outperforms its contemporaries in both unconstrained and constrained cases. [ABSTRACT FROM AUTHOR]