Criteria Convolutions When Combining the Solutions of the Multicriteria Axial Assignment Problem

This paper is devoted to a classical NP-hard problem, known as the three-index axial assignment problem. Within the corresponding framework, the problem of combining feasible solutions is posed as an assignment problem on the set of solutions containing only the components of selected feasible solutions. The issues of combining solutions for the multicriteria problem with different criteria convolutions are studied. In the general case, the combination problem turns out to be NP-hard. Polynomial solvability conditions are obtained for the combination problem.