Differential evolution algorithm for crop planning: Single and multi-objective optimization model

Abstract

Single objective optimization for maximizing total net benefit from farming is 
presented in this study. Differential evolution algorithm which is a family of 
evolutionary algorithm for fast optimization is employed for the model. The 
single objective optimization is used to find a better solution using the results 
of multi-objective optimization of crop planning where three objectives are 
considered. The objectives are to maximize both total net benefit and agricultural 
output while minimizing the total irrigation water used. The methodology adopted 
in this study is used to assist in choosing a solution when many non dominated 
solutions are presented by a multi-objective optimization. The other two objectives 
are used as constraints of the problem while maximizing the total net benefit only. 
The ten strategies of differential evolution are tested with this model. DE/rand/1/bin 
generated a maximum total net benefit of ZAR 1,330,000 after 1,207 iterations from 
a planting area of 771,000 m(2) using 704694 m(3) of irrigation water while multi-objective 
differential evolution algorithm (MDEA1) generated the total net benefit of ZAR 1,304,600. 
It is concluded that this methodology can be used to generate better results than using a 
multi-objective model only. It is also suggested that each objective can be solved separately 
to get better solutions than the ones generated by multi-objective models using the same 
procedure with suitable modifications.