A New Heuristic Method for General Mixed Integer Linear Programs: A Report on Work in Progress (Abstract)

Abstract

For linear integer programs, the method to be described starts with the continuous optimum and maintains primal feasibility. Instead of modifying the constraints of the original problem, the method modifies the objective function. A new, non-linear, objective function is set up, based on the original objective function and on two integrality measures. A lattice is constructed in the interior of the constraint polyhedron to enable us to move around inside this region. The simplex method is used to search for the maximum of the derived objective function which is so constructed that a maximum is likely to coincide with an integer solution to the problem. If a maximum is found which is also an integer solution, the parameters of the objective function are changed, and a search for a better integer solution is begun. If a maximum is found which is not an integer solution, the parameters are changed and the search continues. The search stops when no change of parameters will open up new areas of search. The effect of varying the parameters is to stretch or squeeze the derived objective function so that we can escape from local optima that are not integer solutions, and so that we can escape from integer solutions that are not global optima.