A Preprocessing That Combines Heuristic and Surrogate Constraint Analysis to Fix Variables in TSP

A preprocessing procedure that uses a local guided search defined in terms of a neighborhood structure to get a feasible solution (UB) and the Osorio and Glover[18, 20] exploiting of surrogate constraints and constraint pairing is applied to the traveling salesman problem. The surrogate constraint is obtained by weighting the original problem constraints by their associated dual values in the linear relaxation of the problem. The objective function is made a constraint less or equal than a feasible solution (UB). The surrogate constraint is paired with this constraint to obtain a combined equation where negative variables are replaced by complemented variables and the resulting constraint is used to fix variables to zero or one before solving the problem.