A Method to Solve Conditional Optimization Problems with Quadratic Objective Functions on the Set of Permutations

The problem with a quadratic objective function and additional linear constraints is considered on the set of permutations. A solution method is proposed, which consists of two stages. At the first stage, the set of support solutions is found. A quadratic function is composed for the corresponding transposition, and sub-problems with additional constraints are generated. A set of supporting solutions that satisfy the constraints of the main problem can be found in the course of their solution. The second stage is to find the optimal solution from the subset of optimal solutions and the set of feasible solutions.