An Improved Multi-Strategy Crayfish Optimization Algorithm for Solving Numerical Optimization Problems

The crayfish optimization algorithm (COA), proposed in 2023, is a metaheuristic optimization algorithm that is based on crayfish’s summer escape behavior, competitive behavior, and foraging behavior. COA has a good optimization performance, but it still suffers from the problems of slow convergence speed and sensitivity to the local optimum. To solve these problems, an improved multi-strategy crayfish optimization algorithm for solving numerical optimization problems, called IMCOA, is proposed to address the shortcomings of the original crayfish optimization algorithm for each behavioral strategy. Aiming at the imbalance between local exploitation and global exploration in the summer heat avoidance and competition phases, this paper proposes a cave candidacy strategy and a fitness–distance balanced competition strategy, respectively, so that these two behaviors can better coordinate the global and local optimization capabilities and escape from falling into the local optimum prematurely. The directly foraging formula is modified during the foraging phase. The food covariance learning strategy is utilized to enhance the population diversity and improve the convergence accuracy and convergence speed. Finally, the introduction of an optimal non-monopoly search strategy to perturb the optimal solution for updates improves the algorithm’s ability to obtain a global best solution. We evaluated the effectiveness of IMCOA using the CEC2017 and CEC2022 test suites and compared it with eight algorithms. Experiments were conducted using different dimensions of CEC2017 and CEC2022 by performing numerical analyses, convergence analyses, stability analyses, Wilcoxon rank–sum tests and Friedman tests. Experiments on the CEC2017 and CEC2022 test suites show that IMCOA can strike a good balance between exploration and exploitation and outperforms the traditional COA and other optimization algorithms in terms of its convergence speed, optimization accuracy, and ability to avoid premature convergence. Statistical analysis shows that there is a significant difference between the performance of the IMCOA algorithm and other algorithms. Additionally, three engineering design optimization problems confirm the practicality of IMCOA and its potential to solve real-world problems.