An efficient procedure for finding best compromise solutions to the multi-objective assignment problem

In this paper, we consider the problem of determining a best compromise solution for the multi-objective assignment problem. Such a solution minimizes a scalarizing function, such as the weighted Tchebychev norm or reference point achievement functions. To solve this problem, we resort to a ranking (or k-best) algorithm which enumerates feasible solutions according to an appropriate weighted sum until a condition, ensuring that an optimal solution has been found, is met. The ranking algorithm is based on a branch and bound scheme. We study how to implement efficiently this procedure by considering different algorithmic variants within the procedure: choice of the weighted sum, branching and bounding schemes. We present an experimental analysis that enables us to point out the best variants, and we provide experimental results showing the remarkable efficiency of the procedure, even for large size instances.