New relaxation algorithm for three-dimensional assignment problem

The valid solution algorithm for multi-dimensional assignment problem is a difficult point in optimization field. This paper proposes a new relaxation algorithm to solve three-dimensional assignment problem by fusing a certain number of good solutions of 2-dimensional (2-D) assignment problems which are relaxed from 3-D assignment problem. The new algorithm constructs the optimal solution by assigning the solution components with high frequency appearing in the good solutions of 2-D assignment problems according to an order from high to low under feasible constraints. So the calculation complexity is decreased, and the data association accuracy of targets is improved to some extent. Simulation results show that the new algorithm is feasible and effective.