Modification of Species-Based Differential Evolution for Finding All Solutions of Systems of Nonlinear Equations

Abstract

Nowadays the root finding problem for nonlinear system equations is still one of the difficult problems in computational sciences. Many attempts using deterministic and meta-heuristic methods have been done with their advantages and disadvantages, but many of them have fail to converge to all possible roots.Differential Evolution (DE), a random search techniques using vector as an alternative solution in the search for finding all ofthe real roots from the system of nonlinear equations. Species-based is one of the methods niching the building sub-populations or species in the area with species-seed functions as its center. This study will describe the modification of existing species-based previously to reduce the computational complexity and run more efficiently. The results of the test function shows species-based modifications can localize all potential roots with one running the program