This paper proposes a novel hybridization of two metaheuristic algorithms to solve the real-parameter single objective numerical optimization problems. The proposed Three-stage Cyclic Hybrid SFS and L-SHADE (3-sCHSL) algorithm integrates the high-level interactions of Stochastic Fractal Search (SFS) and L-SHADE algorithms in a single framework. Furthermore, a guided control population initialization strategy is injected in 3-sCHSL to address the stagnation and diversity loss issues as the evolution process evolves. The performance of the proposed algorithm is tested under different complexity levels of different transformations of the CEC 2021 benchmark suite with dimension 20. The experimental results demonstrated the efficiency and competitiveness of the proposed algorithm against recent state-of-the-art algorithms. In addition, 3-sCHSL achieved a superior performance when evaluating two engineering design problems.

Real-life problems can be expressed as optimization problems. These problems pose a challenge for researchers to design efficient algorithms that are capable of finding optimal solutions with the least budget. Stochastic Fractal Search (SFS) proved its powerfulness as a metaheuristic algorithm through the large research body that used it to optimize different industrial and engineering tasks. Nevertheless, as with any meta-heuristic algorithm and according to the “No Free Lunch” theorem, SFS may suffer from immature convergence and local minima trap. Thus, to address these issues, a popular Differential Evolution variant called Success-History based Adaptive Differential Evolution (SHADE) is used to enhance SFS performance in a unique three-phase hybrid framework. Moreover, a local search is also incorporated into the proposed framework to refine the quality of the generated solution and accelerate the hybrid algorithm convergence speed. The proposed hybrid algorithm, namely eMpSDE, is tested against a diverse set of varying complexity optimization problems, consisting of well-known standard unconstrained unimodal and multimodal test functions and some constrained engineering design problems. Then, a comparative analysis of the performance of the proposed hybrid algorithm is carried out with the recent state of art algorithms to validate its competitivity.