The multi-objective assignment problem is basically the N men –N tasks problem where a single task should be assigned to an individual with a view to optimizing the outcome. A common challenge is to address the conflicting objectives which produce Pareto–optimal solutions. This research attempts to solve this problem with the decision maker’s preferences through a genetic algorithm. While solving this problem, a new encoding scheme was used together with a partially matched crossover (PMX). The working principles of the proposed algorithm are 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. Another feature of this work is normalizing all the criteria into a single scale regardless of their measurement units and their demand of minimum or maximum, which reliefs us from careful attention in quantifying the quality criteria. Furthermore, the research is enriched by the incorporation of a decision maker’s preferences in different objectives.