Optimizing Irrigation Water Allocation and Multicrop Planning Using Discrete PSO Algorithm

Abstract

This study presents a linear and a mixed-integer linear (MIL) model for optimizing an irrigation water allocation and a multicrop planning problem. The main objective was to maximize net benefit for all cultivated crops within irrigated areas in a reservoir-irrigation system in Iran. The linear model was optimized with linear programming (LP) method and continuous particle swarm optimization (CPSO) algorithm to make a detailed comparison between the LP method and CPSO algorithm results. The optimal solution obtained by the CPSO algorithm and LP method in the linear model were comparable. However, the optimal allocated areas for both crops and orchards in the linear model obtained by the LP method and CPSO algorithm were not directly applicable in real crop planning situations. Consequently, the MIL model was developed for which a discrete particle swarm optimization (DPSO) algorithm was used to obtain an applicable and allowable solution for the problem. Contrary to LP and CPSO, the DPSO algorithm was competent to deal with the MIL model. The results showed that the discrete nature of cropping area variables in the MIL model had a significant effect on assigned areas and reservoir operation policies. It was found that the inapplicable assigned area by the LP method and CPSO algorithm for some crops was eliminated from optimum selected cropping areas by the DPSO algorithm. The statistical assessment showed that the CPSO and DPSO algorithms were both able to limit the variations of annual net benefit within the acceptable range of no more than 2%. The number of function evaluations for obtaining optimal annual net benefit and the standard deviation of the results in 50 independent runs in the MIL model was 167,000 and 0.81, respectively by the DPSO algorithm as compared with 200,000 and 1.09 by the CPSO algorithm in the linear model. Thus, the DPSO algorithm could direct the objective function value in a faster way and with more accuracy than CPSO algorithm.