Applying simulated annealing to the multidimensional assignment problem

The multidimensional assignment problem (MAP) is a combinatorial optimization problem that is known to be NP-hard, and therefore, heuristic methods are generally used to find good solutions to it. The problem has many recognized applications such as multi-agent path planning, data association, and multi-searcher problems. Simulated annealing has proven to be effective in solving many combinatorial optimization problems, but we find no references in the literature in which simulated annealing is applied to the MAP. In this chapter, we evaluate a simulated annealing algorithm for solving the MAP and report experimental results using several controlling factors in the algorithm. These factors include the cooling schedule and initial temperature, the neighborhood definition, and the method of finding a starting solution. A design of experiments approach is used to find the most effective controlling factors in the algorithm. Algorithm performance measures include time to solution and quality of solution. For a small problem, the algorithm finds the optimal solution in every case tested. For a large problem, the algorithm finds results that average 1.2 units from the optimal solution. The results show that simulated annealing is an effective method for solving the MAP.