Finding the Optimal Solution to the Problem of Conditional Optimization on the Graph of the set of Placements

Abstract

The model of the problem of conditional optimization on the set of partial permutations is formulated. The linear form of the objective function is obtained by interpreting the elements of the set of partial permutations as points of the Euclidean space. A combinatorial polytope of allocations is considered for which there is a graph of the set of partial permutations An algorithm for solving this problem is proposed and its practical applicability is demonstrated. The proposed algorithm for solving the conditional optimization problem provides for the representation of the admissible of the Set of Partial Permutations in the form of a graph, which significantly reduces the search path for the optimal solution, as evidenced by the practical example considered.