Applied Mathematics & Information Sciences

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By successively employing the interval search method, we developed the proposed algorithm MPSO, introducing three creative position vectors to replace the three worst fitness particles among the population in the PSO, to overcome the premature convergence situation that occurs when a problem with a large number of variables and (or) multiple optima is solved. The results obtained by applying the MPSO and the PSO on 6 benchmark functions show that, except for the randomly shifted Rosenbrock functions, the MPSO can successfully secure a solution that is close to the exact solution for each of the remaining five functions.We also showed that all benchmark functions are solvable by the MPSO if the maximum number of generations is raised to be as high as possible. With regard to the PSO′s performance for the three different numbers of variables, it fails to obtain a solution that is close to the exact solution for all of the tested functions except for the Sphere function with 30 variables.

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