Approximate Solution by Ant Colony Programming to Symmetrical Drop Suspended Equilibrium Equation

Abstract

The paper presents the Ant Colony Programming (ACP) method as a solver for Differential Equations of a suspended symmetric drop. The Ant Colony method developed by Gambardella Dorigo in 1997 has been applied in Routing, Scheduling, Constraint Satisfaction, Graph Coloring, and such other optimization problems. The Differential Equation Solution can be expressed as an expression containing Terminals and Functions and both are represented as a graph with nodes and edges. In this graph, each node (city) represents a function or terminal, the information flow represents pheromone quantity disposed by ants while walking. An initial quantity of pheromone is disposed on links between nodes. After that and until termination criteria, ants construct solutions (paths) from the source to the destination by visiting nodes, and deposing (updating) pheromones quantity at links of the path. This is one of the advantages of Ant Colony Programming, i.e. the diversification by local pheromone update. The select step is fundamental, too. In this step, the ant reflects the performance of the link in the cost path according to fitness value. The simulation experiments show that Ant Colony Programming method can obtain very good results in finding solution.