Optimization Model for Production Systems of Irrigation Improvement Projects Using Nonlinear Programming and Genetic Algorithms

Abstract

This work presents the formulation of an optimization model for agricultural production systems under irrigation conditions in the region of Cusco - Peru. The model is based on the evaluation of various analytical and heuristic methods where the non-linear programming method was the most appropriate because it requires an objective function and restrictions. This is consistent with the indispensable restrictions for the proposed model, which arise from its interaction with the market under real conditions. From this interaction one of the most relevant variables is the sale price, for whose determination a new mathematical model is proposed; taking into account, fluctuations in supply and demand are considered. Therefore, the contribution of the new proposed optimization model is based on that it allows knowing the conditions assumed to maximize profit and minimize production costs. Then the losses that affect the economy of the agricultural producer can be anticipated. Likewise, the new optimization model allows the construction of scenarios by modifying variables and restrictions to project the behavior of the economy for various products. The results of the optimization model are consistent and comply with the Kuhn Tucker conditions; therefore, these are considered valid. Within this framework, the model was evaluated using genetic algorithms, with the result that the sexual selection operator has the best performance for obtaining the optimum in non-linear problems under restrictions.