Hybridised differential evolution and equilibrium optimiser with learning parameters for mechanical and aircraft wing design

Multi-Strategy-Assisted Hybrid Crayfish-Inspired Optimization Algorithm for Solving Real-World Problems

In order to solve problems with the original crayfish optimization algorithm (COA), such as reduced diversity, local optimization, and insufficient convergence accuracy, a multi-strategy optimization algorithm for crayfish based on differential evolution, named the ICOA, is proposed. First, the elite chaotic difference strategy is used for population initialization to generate a more uniform crayfish population and increase the quality and diversity of the population. Secondly, the differential evolution strategy and the dimensional variation strategy are introduced to improve the quality of the crayfish population before its iteration and to improve the accuracy of the optimal solution and the local search ability for crayfish at the same time. To enhance the updating approach to crayfish exploration, the Levy flight strategy is adopted. This strategy aims to improve the algorithm's search range and local search capability, prevent premature convergence, and enhance population stability. Finally, the adaptive parameter strategy is introduced to improve the development stage of crayfish, so as to better balance the global search and local mining ability of the algorithm, and to further enhance the optimization ability of the algorithm, and the ability to jump out of the local optimal. In addition, a comparison with the original COA and two sets of optimization algorithms on the CEC2019, CEC2020, and CEC2022 test sets was verified by Wilcoxon rank sum test. The results show that the proposed ICOA has strong competition. At the same time, the performance of ICOA is tested against different high-performance algorithms on 6 engineering optimization examples, 30 high-low-dimension constraint problems and 2 large-scale NP problems. Numerical experiments results show that ICOA has superior performance on a range of engineering problems and exhibits excellent performance in solving complex optimization problems.

Multi‑strategy Equilibrium Optimizer: An improved meta-heuristic tested on numerical optimization and engineering problems

The Equilibrium Optimizer (EO) is a recently proposed intelligent optimization algorithm based on mass balance equation. It has a novel principle to deal with global optimization. However, when solving complex numerical optimization problems and engineering problems, the algorithm will get stuck into local optima and degrade accuracy. To address the issue, an improved Equilibrium Optimizer (IEO) based on multi-strategy optimization is proposed. First, Tent mapping is used to generate the initial location of the particle population, which evenly distributes the particle population and lays the foundation for diversified global search process. Moreover, nonlinear time parameter is used to update the position equation, which dynamically balances the exploration and exploitation phases of improved algorithm. Finally, Lens Opposition‑based Learning (LOBL) is introduced, which avoids local optimization by improving the population diversity of the algorithm. Simulation experiments are carried out on 23 classical functions, IEEE CEC2017 problems and IEEE CEC2019 problems, and the stability of the algorithm is further analyzed by Friedman statistical test and box plots. Experimental results show that the algorithm has good solution accuracy and robustness. Additionally, six engineering design problems are solved, and the results show that improved algorithm has high optimization efficiency achieves cost minimization.