An improved genetic algorithm based approach to solve constrained knapsack problem in fuzzy environment

In this paper, we have proposed an improved genetic algorithm (GA) to solve constrained knapsack problem in fuzzy environment. Some of the objects among all the objects are associated with a discount. If at least a predetermined quantity of the object(s) (those are associated with a discount) is selected, then an amount (in $) is considered as discount. The aim of the model is to maximize the total profit of the loaded/selected objects with obtaining minimum discount price (predetermined). For the imprecise model, profit and weight (for each of the objects) have been considered as fuzzy number. This problem has been solved using two types of fuzzy systems, one is credibility measure and another is graded mean integration approach. We have presented an improved GA to solve the problem. The genetic algorithm has been improved by introducing ‘refining’ and ‘repairing’ operations. Computational experiments with different randomly generated data sets are given in experiment section. Some sensitivity analysis have also been made and presented in experiment section.