Application of Ant Colony Programming Approach for Solving Systems of Stochastic Differential Equations

Abstract

Stochastic differential equations (SDE) have wide applications in natural phenomena, engineering, finance, and biological models. Obtaining analytic solutions for an SDE is often complex, and the complexity increases for an SDE system. The paper introduces ant colony programming (ACP) as a novel approach for solving SDE system. Ant colony programming was developed in two directions, the first is to add the Wiener process  as a variable to the terminals and functions, and the second is to construct the appropriate fitness function . ACP constructs mathematical expressions and evaluates them using the fitness function . The ACP proposed effectiveness has been demonstrated by applying to 2,3 and 4-dimensional SDE systems. The most important finding of this work is that ACP generates symbolic stochastic processes that represent solutions for SDE system. Methods for solving SDE systems are important tools for study phenomena that involve noise or randomness.