Summary: An \(M\)-elite coevolutionary algorithm (MECA) is proposed for high-dimensional unconstrained numerical optimization problems based on the concept of coevolutionary algorithms and elitist strategies. In the MECA, the individual with high fitness, called elite population, is considered to play a dominant role in the evolutionary process. The whole population is divided into two subpopulations which are an elite population composed of \(M\) elites and a common population including other individuals, and team members are selected to form \(M\) teams by \(M\) elites acting as the cores of the \(M\) teams (named core elites), respectively. If the team member selected is another elite individual, it will exchange information with the core elite with the cooperating operation defined in the paper; if the team member is chosen from the common population, it will be led by the core elite with the leading operation.
The cooperating and the leading operation above are defined by different combinations of several crossover operators or mutation operators. The algorithm is proved to converge to the global optimization solution with probability one. Tests on 15 benchmark problems show that the algorithm can find the global optimal solution or near-optimal solution for most problems tested. Compared with three existing algorithms, the MECA achieves an improved accuracy with the same number of function evaluations. Additionally, the runtime of the MECA is less even compared with the standard genetic algorithm with the same parameter setting. Moreover, the parameters of the MECA are analyzed in experiments and the results show that the MECA is insensitive to parameters and easy to use.