Ant-Q Algorithm for the Solution of Multiple Objective Irrigation Water Distribution Network Design

Carlos Eduardo Mariano Instituto Mexicano de Tecnología del Agua, Paseo Cuauhnahuac 8532, Col. Progreso, 62550 Jiutepec, Morelos, MEXICO.

E. M. Morales, Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Morelos, Paseo de la Reforma 182-A, Col. Lomas de Cuernavaca 62020 Cuernavaca, Morelos, MEXICO

The difficulty of solving multiple objective optimization problems with traditional techniques, have urge researchers to use alternative approaches. Ant-Q algorithms have shown good results in the solution of combinatorial optimization problems, however little work has been done for multiple objective problems. Their distributed characteristics, theoretical background, and representation capabilities make them good candidates for the solution of multiple objective optimization problems. In this paper we describe a system, called MOAQ (Multiple Objective Ant Q), that can solve multiple objective optimization problems via cooperation between families of ants. Each family find solutions which depends on the solutions of the rest of the families creating a negotiation mechanism and finding compromise solutions for all the objectives involved.

MOAQ is used to solve the water distribution network design problem which is a non-linear multiple objective optimization problem. Specifically, a family of ants looks for the minimum distance network layout connecting all the hydraulic nodes that supply water to each plot in an agricultural region. The proposed network must guarantee that the mayor transport of water travels the minimal distance, in order to minimized the network costs. Ants, in a second family, select a crop for each plot in the region. This selection determines the required water for each plot and its productivity, trying to maximize the global productivity without exceeding the irrigation water disposability and not violating the restrictions of the problem. Dependencies between solutions are included in the reward functions of each family producing compromise solutions between the objectives involved.