What is Interval Programming

This chapter presents how Genetic Algorithm (GA) is effectively employed to Goal Programming (GP) formulation of an agricultural planning problem having interval model parameters and a set of chance constraints for optimal production of seasonal crops in uncertain environment. In model formulation, the planned-interval goals associated with objectives of the problem are converted into their equivalent two-objective deterministic goals. The chance constraints are also converted into their deterministic equivalents to solve the problem by using GP methodology. In goal achievement function, minimization of deviational variables associated with model goals is evaluated on the basis of priorities by employing a GA scheme to reach optimal decision. In the decision process, sensitivity analysis with variations of priority structure of goals is performed, and then the notion of Euclidean distance function is used to identify the priority structure under which optimal production of crops can be obtained in the decision environment. A case example is considered to demonstrate the approach.