Abstract

The application of differential evolution (DE) algorithm to a constrained optimization problem of irrigation water use is presented in this study. Irrigation water, amounting to 10 Mm³ is optimized to irrigate 2500 ha of land where 16 different crops are planted on different areas of land. The crops are assumed not rain-fed but depend only on irrigation water. The DE which is an evolutionary based optimization algorithm, with codes written in MATLAB is used to solve the problem. Also a comparative study using linear programming (LP) is performed. The results are compared to study the effectiveness of the DE algorithm. The different areas of land where the crops are to be planted to maximize the total income (TI) in monetary terms (South African Rand, ZAR) are optimized. It is found that a TI of ZAR 46 060 000 can be derived without any constraint violation using DE. Also ZAR 46 060 200 can be derived using LP. Ten strategies of DE are tested with this problem varying the population size (NP), crossover constant (CR) and weighting factor (F). It is found that strategy 1, DE/rand-1-bin, with values of NP, CR and F of 160, 0.95 and 0.5 respectively, obtains the best solution most efficiently. DE is considered comparable to LP in solving this optimization problem.

Key words: Irrigation planning, linear programming, constrained optimization, differential evolution, evolutionary algorithm.