Partially constrained ant colony optimization algorithm for the solution of constrained optimization problems: Application to storm water network design

This paper exploits the unique feature of the Ant Colony Optimization Algorithm (ACOA), namely incremental solution building mechanism, to develop partially constraint ACO algorithms for the solution of optimization problems with explicit constraints. The method is based on the provision of a tabu list for each ant at each decision point of the problem so that some constraints of the problem are satisfied. The application of the method to the problem of storm water network design is formulated and presented. The network nodes are considered as the decision points and the nodal elevations of the network are used as the decision variables of the optimization problem. Two partially constrained ACO algorithms are formulated and applied to a benchmark example of storm water network design and the results are compared with those of the original unconstrained algorithm and existing methods. In the first algorithm the positive slope constraints are satisfied explicitly and the rest are satisfied by using the penalty method while in the second one the satisfaction of constraints regarding the maximum ratio of flow depth to the diameter are also achieved explicitly via the tabu list. The method is shown to be very effective and efficient in locating the optimal solutions and in terms of the convergence characteristics of the resulting ACO algorithms. The proposed algorithms are also shown to be relatively insensitive to the initial colony used compared to the original algorithm. Furthermore, the method proves itself capable of finding an optimal or near-optimal solution, independent of the discretisation level and the size of the colony used.