Solving differential equations with artificial bee colony programming

Abstract

Relying on artificial bee colony programming (ABCP), we present in this paper, for the first time, a novel methodology for solving differential equations. The three-phase evolving process of ABCP is managed to apply on the issue of recovering the exact solution of differential equations through a well-posed problem. In fact, the original ABCP model which has been initially developed for symbolic regression cannot be used directly as differential problems might have multiple outputs. Moreover, the definition of fitness function is a critical problem-dependent issue for model design. In this sense, a problem-specific ABCP algorithm is worked out in the present contribution. With the proposed algorithm, solution with multiple outputs can evolve under a multiple-tree framework toward the exact solution. For fitness function evaluation, different forms are derived for ordinary and partial differential equations by performing experiments with multiple runs. Results on several differential equations are reported and compared to other advanced methods to assess the feasibility and the potential of the proposed method. A computational performance evaluation is provided for the considered examples and completed with an additional study on the impact of key control parameters.