A genetic algorithm-based approach for unbalanced assignment problem in interval environment

Abstract

The goal of this paper is to propose an approach based on genetic algorithm for solving unbalanced assignment problem with lesser number of agents than the number of jobs under the assumption that the cost/time for assigning a job to an agent is interval number. Also an additional constraint on the maximum number of jobs allowable to agent(s) is considered. In the proposed approach, the existing real coded genetic algorithm is extended for interval valued fitness with the help of interval order relations (Bhunia and Samanta, 2014) and two different versions of algorithm based on two crossover operators is developed, one is newly proposed extended one-point crossover and the other, inverse exchange crossover. Then, to test the performance of different versions of the algorithm and also for the practical demonstration of the problem, three test problems are considered and solved. Finally, a fruitful conclusion is drawn regarding the performance of both the versions of genetic algorithm.