Efficient Modified Meta-Heuristic Technique for Unconstrained Optimization Problems

Abstract

In this paper, a new Modified Meta-Heuristic algorithm is proposed. This method contains some modifications to improve the performance of the simulated-annealing algorithm (SA). Most authors who deal with improving the SA algorithm presented some improvements and modifications to one or more of the five standard features of the SA algorithm. In this paper, we improve the SA algorithm by presenting some suggestions and modifications to all five standard features of the SA algorithm. Through these suggestions and modifications, we obtained a new algorithm that finds the approximate solution to the global minimum of a non-convex function. The new algorithm contains novel parameters, which are updated at each iteration. Therefore, the variety and alternatives in choosing these parameters demonstrated a noticeable impact on the performance of the proposed algorithm. Furthermore, it has multiple formulas by which the candidate solutions are generated. Diversity in these formulas helped the proposed algorithm to escape a local point while finding the global minimizer of a non-convex function. The efficiency of the proposed algorithm is reported through extensive numerical experiments on some well-known test problems. The performance profiles are used to evaluate and compare the performance of our proposed algorithm against the other five meta-heuristic algorithms. The comparison results between the performance of our suggested algorithm and the other five algorithms indicate that the proposed algorithm is competitive with, and in all cases superior to, the five algorithms in terms of the efficiency, reliability, and effectiveness for finding the global minimizers of non-convex functions. This superiority of the new proposed algorithm is due to those five modified standard features.

Adaptive Hybrid Mixed Two-Point Step Size Gradient Algorithm for Solving Non-Linear Systems

“…These problems need to be solved. A mathematical modelling technique is a critical tool that is utilized to formulate these problems as mathematical problems [1].…”

“…The author of [25] used Lemma 3.3 from [26] to prove that the sequence { F(x k ) } converges. Furthermore, the author of [25] presented a convergence analysis for their algorithm and the numerical results show that the algorithm in is computationally efficient to solve Problem (1).…”

“…Stanimirovic et al [27] proposed a new improved gradient descent iterations to solve Problem (1). They proposed new directions and step-size gradient methods by defining various parameters.…”

“…Waziri et al [28] proposed some hybrid derivative-free algorithms to solve Problem (1). They presented several parameters by which two methods were designed to deal with a nonlinear system of equations.…”

“…Abubakar et al [5] presented a new hybrid spectral-CG algorithm to find approximate solutions to Problem (1).…”