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

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.