Numeric Crunch Algorithm: a new metaheuristic algorithm for solving global and engineering optimization problems

In order to solve optimization problems, this paper introduces a new metaheuristic algorithm called the Numeric Crunch Algorithm (NCA), which employs the distribution behaviour of the population members and a novel hyperbolic acceleration function for convergence. Each generation's search space exploration and exploitation are ensured by the population's distribution behaviour around its members and their adaptively diversified boundaries, respectively. The convergence of the search solutions in the NCA was also accelerated by the random, adaptive parameters and hyperbolic function. A set of 68 test benchmark functions with (30, 100, 500, and 1000) dimensions was used to examine the NCA's effectiveness in terms of exploration, exploitation, local optimality avoidance, population fitness enhancement, and convergence rate. Firstly, the proposed NCA's behaviour is examined using a collection of 23 standard well-known benchmark functions, including unimodal, multimodal, and fixed-dimensional functions. Secondly, the proposed NCA's superiority is examined using the IEEE CEC-2015 and IEEE CEC-2017 benchmark suites. In addition to qualitatively examine NCA's superiority over other metaheuristics, Friedman and Wilcoxon rank-sum tests are performed. In terms of performance metrics, NCA ranked first. For application perspective, the NCA is tested on eight real-world constrained and unconstrained engineering design problems from IEEE CEC-2020 real-world optimization benchmark suits. The NCA algorithm's performance on benchmark functions and engineering design problems indicates that it can handle constrained and uncertain search spaces in real-world scenarios. The source code of the NCA algorithm is publicly available at https://github.com/Shivankur07/Numeric-Crunch-Algorithm.git.