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

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

Emailcmariano@tlaloc.imta.mx

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

Email: emorales@campus.mor.itesm.mx

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.