Solution of Simultaneous Non-Linear Equations using Genetic Algorithms

The solution of Systems of Simultaneous Non-Linear Equations (SNLE) remains a complex and as yet not closed problem. Although analytical methods to tackle such problems do exist, they are limited in scope and, in general, demand certain prior knowledge of the functions under study. In this paper we propose a novel method to numerically solve such systems by using a Genetic Algorithm (GA). In order to show the generality of the method we first prove a theorem which allows us to equate the SNLE problem to that of minimizing a linear combination of the equations to be solved, subject to a set of constraints. Then we describe a rugged GA (the so-called Vasconcelos GA or VGA) which has been proved to perform optimally in a controlled but unbounded problem space. Next, we show how the VGA may be efficiently utilized to adapt its behavior (which is inherently adequate to solve unconstrained minimization problems) to a constrained solution space. Finally, we offer some examples of systems of non-linear equations which were solved using the proposed methodology.