Solving Multi-Objective Assignment Problem with Decision Maker’s Preferences by Using Genetic Algorithm

Abstract

The multi-objective assignment problem is basically the N men –N tasks problem, where a single task has to be assigned to an individual with a view of optimizing the outcomes. A common challenge is to address the conflicting objectives which produce Pareto–optimal solutions. The main feature of the work is- normalizing all the criteria into a single scale regardless of their measurement units and their demand of minimum or maximum, which reliefs the researchers from careful attention in quantifying the quality criteria. The methodology also included the decision maker’s preferences regarding the objectives. While solving the problem through a genetic algorithm, a new encoding scheme is used together with a partially matched crossover (PMX). The working principle of the proposed algorithm is illustrated with a numerical example and its effectiveness has been compared with some well-established methodologies. It is found that the proposed algorithm provides a better solution with minimal computational effort.