Elitist genetic algorithm approach for Assignment Problem

The name ‘Assignment Problem ’ (AP) originates from the classical problems where the objective is to find the optimum assignment of a number of tasks (jobs) to an equal number of facilities (or persons) at a minimum cost (or time) or maximum profit. In this paper, a new approach for solving an assignment problem (balanced) is proposed with the help of an elitist genetic algorithm (EGA) and also its computational behaviour is reported. The mathematical formulation of the problem indicates that this problem is a 0-1 programming problem. To solve this problem, an EGA with new types of initialization, crossover, mutation and existing rank-based selection has been developed. As special cases, different types of assignment problems like unbalanced assignment problem, maximization assignment problem, restricted assignment problem have been reported and illustrated with some numerical examples.