Differential evolution algorithm for solving multi-objective crop planning model

This study presents four strategies of a novel evolutionary algorithm, multi-objective differential evolution algorithm (MDEA). The four strategies namely, MDEA1, MDEA2, MDEA3 and MDEA4 are adapted to solve the multi-objective crop planning model with multiple constraints in a farmland in the Vaalharts irrigation scheme (VIS) in South Africa. The three objectives of the model are to minimize the total irrigation water (m²) and to maximize both the total net income in South African Rand (ZAR) from farming and the total agricultural output in tons. The total area of the farm is 771,000 m² and supplied with 704,694 m² of irrigation water annually. Numerical results produce non-dominated solutions which converge to Pareto optimal fronts. MDEA1 and MDEA2 strategies with binomial crossover method are better for solving the crop planning problem presented than MDEA3 and MDEA4 strategies with exponential crossover method. MDEA1 found a solution with the highest total net income of ZAR 1,304,600 with the corresponding total agricultural output, total irrigation water and total planting areas of 316.26 tons, 702,000 m³ and 725,000 m², respectively. The planting areas for the crops in the solution are 73,463 m² for maize, 551,660 m² for groundnut, 50,000 m² for Lucerne and 50,000 m² for Peacan nut. It can be concluded that MDEA is a good algorithm for solving crop planning problem especially in water deficient areas like South Africa.