| Eigenvalue complementarity problem is developed from classical matrix eigenvalue problem,and it is closely related to nonlinear equations solving,nonlinear complementarity problem,variational inequality,differentiable optimization and other research directions.The eigenvalue complementarity problem has important applications in dynamics research of structural and mechanical systems and stability analysis of frictional and elastic systems.Therefore,research on the theory of eigenvalue complementarity and efficient numerical solution methods not only has profound theoretical significance but also has potential applications prospect.ABC algorithm is a new artificial intelligence optimization algorithm.It is based on the living habits of bees,using the simulation of bees in the nature of division of labor and cooperation to collect honey,sharing honey source data,to find the best honey source process.It has good optimization ability,and shows better performance than the basic differential evolution algorithm and particle swarm optimization algorithm in solving optimal problems.It is widely used in business travel problems,integer programming problems,nonlinear equations and nonlinear equations solving problems.In this paper,FB function is used to transform the eigenvalue complementary problem into a nonlinear equation system which can be solved by ABC algorithm and IABC algorithm.Secondly,by virtue of the constructed fitness function,the nonlinear equations are transformed into an optimization problem,and then the EICP-ABC algorithm and the EICP-IABC algorithm are constructed to solve the above optimization problem.Markov theory and convergence criterion of stochastic optimization algorithm are used to prove that the algorithm is globally convergent according to probability.Finally,the effectiveness of the algorithm is verified by numerical experiments,and the EICP-ABC algorithm and EICP-IABC algorithm are better than the SSNM algorithm in terms of convergence ratio and iteration number. |
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