Ant colony extended: Search in solution spaces with a countably infinite number of solutions

Abstract

Ant Colony Extended (ACE) is a new framework that allows to apply the ant colony paradigm [1] to solve combinatorial optimization problems, in which the values of each variable are taken from a finite set, and the set of possible solutions is countably infinite. Previously, we applied ACE to autonomous ship manoeuvre planning [2], where the objective was to minimize the time of a manoeuvre. In this problem, as in the TSP and others, the value of the cost function increases monotonically as new elements are added to the solution sequence. We want to check the algorithm for problems that do not exhibit this feature. For this purpose we select a set of multi-modal functions to minimize with ACE: Griewank's function (F2), Shekel's foxholes (F3), Michalewicz' function (F4) and Langerman's function (F5). All functions are taken from [4]. These functions have many local minima, where algorithms may get stuck.We select the Simple Genetic Algorithm (SGA), and Differential Evolution (DE) to perform a comparison of local minima avoidance. © 2010 Springer-Verlag Berlin Heidelberg.