Irrigation networks Optimization using expanded particle swarm algorithm and linear programming

The issue of choosing the best arrangement for pipes’ diameter and optimal pump head, by considering the minimization of entire system cost, has been taken into account by hydraulic engineers over the past years. In this study, mixed integer linear programming (MILP) algorithm, as well as developed and mutated particle swarm Meta heuristic algorithm (DMPSO) is used to optimize the pressurized irrigation for a network consists of 16 tubes and 17 nodes. The objective function of the MILP includes the annual fixed cost of irrigation network diameter, and the annual cost of energy. The hydraulic constraints of the equation include the node pressure head and the flow rate constraints in the pipes. Input data includes the network map, the cost of pipes in all commercial sizes, the cost of the production facilities of pressure (such as pumps, etc.) and the limitations of the high and low hydraulic boundaries. Output is the optimal diameter of the pipes, operation pressure heads and total annual cost equivalent to the pipeline in the irrigation network. The results of hydraulic analysis with dynamic coupling between MATLAB software and EPANET have been evaluated. The optimal solution for Esmailabad irrigation network was obtained by the proposed fractional evolution particle swarm, mutated algorithm and integrated linear integer programming. Then, the experimental method was compared with the above results and it was determined that the fractional and mixed integer linear programming, have reduced the total cost of the experimental method by the value of 10.68% and 12.5%, respectively. In addition, according to the percentage of reduced values by the methods, it was found out that MILP is better than DMPSO with the least difference in network, but the DMPSO algorithm is faster with less memory response.