Urban water resources planning by using a modified particle swarm optimization algorithm

A new optimization algorithm by coupling the mutation process to the particle swarm optimization (PSO) is developed in this paper. This algorithm, entitled particle swarm optimization with mutation similarity (PSOMS), is successfully applied to an urban water resources management problem for the large city of Tabriz, Iran. The objective functions of the optimization problem are to minimize the cost, maximize water supply and minimize the environmental hazards. The constraints are physical limits such as pipelines capacity, ground water, the demand and the impact of conservation tools. Due to the parameters uncertainty, the water supply objective is modeled with fuzzy set theory and the objectives are then combined with compromise programming. The resulted single objective is solved using PSOMS, and its efficiency is then compared with the basic PSO and two kinds of genetic algorithms. Among them, PSOMS shows rapid convergence and suitable results compared to other methods. PSOMS is also improved to provide the Pareto frontier, which is needed to proper selecting of the optimal solutions in the uncertain conditions. Finally, the diversity of solutions is checked based on an indicator of the distances between different solutions, which show the efficiency of the PSOMS algorithm with respect to the genetic algorithm. Then by using the non-symmetric Kalai–Smorodinsky method a guideline is provided for comfort selection of the most preferred solution in the Pareto frontier. Based on these outcomes, the multi-objective PSOMS provides more appropriate results needed for urban systems management.