Comparison of Several Kinds of Lagrangian Relaxation Algorithm Strategies for Solving Unit Combination Problems

In order to find an algorithm with the highest efficiency for solving the unit combination problem, the characteristics of the unit combination problem are discussed in this paper. The advantages and disadvantages of the current mainstream methods for solving the unit combination problem are comprehensively analyzed, and it is concluded that the current methods for solving the unit combination problem are difficult to balance computational efficiency and computational accuracy. The Lagrangian relaxation method absorbs the constraints into the objective function by introducing Lagrangian multipliers to reduce the difficult constraints in the unit combination problem, which reduces the size of the unit combination problem and overcomes the problem of "dimensional disaster". The computational analysis of different number of unit combinations and the analysis of the pairwise gap also confirm that the Lagrangian relaxation method can better deal with the unit combination problem.