A Novel Adaptive Hybrid Metaheuristic For Unconstrained and Engineering Optimization Problems

Abstract

This study presents AHO-DE-Powell, a hybrid continuous optimization framework that extends Adaptive Hybrid Optimization (AHO) by integrating two complementary search mechanisms: Differential Evolution (DE) for periodic diversity restoration and bounded Powell derivative-free refinement for intensified local exploitation. The parent AHO mechanism is retained as the principal population-search engine and employs four stochastic position-update strategies, probabilistic dual-leader guidance, and a nonlinear power-changing exploration coefficient. In the proposed architecture, DE/rand/1 mutation with binomial crossover is periodically applied to the worst 20% of the population, whereas Powell refinement is periodically applied only to the current best solution. The resulting sequential architecture separates global exploration, diversity recovery, and local numerical refinement.The computational study comprises ten 10-dimensional analytical benchmark functions—Sphere, Rastrigin, Ackley, Rosenbrock, Griewank, Schwefel, Zakharov, Lévy, Michalewicz, and Dixon–Price—and two classical constrained engineering-design problems, namely welded-beam and pressure-vessel optimization. For the benchmark study, 30 agents, 300 iterations, and five independent runs with seeds 0–4 were used. The engineering experiments employed 40 agents and 500 iterations. Numerical results show substantial improvement over the parent AHO on several difficult landscapes, particularly Rastrigin, Ackley, Rosenbrock, Zakharov, Lévy, and Dixon–Price, while also demonstrating that the hybrid is not uniformly superior on every landscape. On the engineering problems, the proposed method produced feasible solutions close to established reference values. The results support the effectiveness of combining adaptive population search, evolutionary diversity injection, and derivative-free local refinement within a single sequential optimization framework.