An application of extended elitist non-dominated sorting Genetic Algorithm in multi-objective linear programming problem of tea industry with interval objectives

In this paper, we have modeled a decision making problem of a tea industry as a multi-objective optimization problem in interval environment. The goal of this problem is to maximize the overall profit as well as to minimize the total production cost subject to the given resource constraints depending on budget, storage space and allotted processing times in different machines. For this purpose, the problem has been formulated as a multi-objective integer linear programming problem with interval objectives. To solve the problem, we have proposed extended elitist non-dominated sorting genetic algorithm (ENSGA-II) for integer variables with interval fitness, crowded tournament selection, intermediate crossover, one neighborhood mutation and elitism. To develop this algorithm, we have proposed modified non-dominated sorting and crowding distance based on interval mathematics and interval order relations. Finally, to test the performance of the proposed algorithm, a numerical example has been solved.