A heuristic approach to solve multidimensional assignment problem

Here a general methodology is proposed to solve both the balanced and the unbalanced multidimensional assignment problems (MAP) using any existing soft computing technique. Since MAP belongs to NP hard class, it cannot be solved in a reasonable time window by any analytical approach. This limitation forces the researchers to follow heuristic approaches for finding optimal/near-optimal solution of a MAP with moderate size. Here an approach is proposed where potential solutions of the problem are taken in coded form and a rule is defined to generate corresponding actual solutions (assignment) from that coded solution. A heuristic approach (Genetic Algorithm/Particle swarm Optimization) is applied to a randomly generated set of such coded solutions to find optimal assignment. Experimental studies show that both the algorithms provide optimal solutions for considerably large size problems following this approach in a reasonable number of function evaluations.