Chaotic Gradient Based Optimizer for Solving Multidimensional Unconstrained and Constrained Optimization Problems

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.