Mathematical Programming Based Bounds

Abstract

An important method of assessing the effectiveness of any heuristic is to compare it to the value of a lower bound on the cost of an optimal solution. In many cases this is not an easy task; constructing strong lower bounds on the optimal solution may be as difficult as solving the problem. An attractive approach for generating a lower bound on the optimal solution to an NP-Complete problem is the following mathematical programming approach. First, formulate the problem as an integer program; then relax the integrality constraint and solve the resulting linear program.