Heuristic Procedures for the Synthesis of Cutting Hyperplanes in Iterative Algorithms for Solving Mixed Linear Programming with Boolean Variables Problems

Abstract

The main provisions for one of the promising directions of methods development of mixed integer linear programming are presented. The method is based on an iterative application of a cutting-plane procedure that takes into account, as fully as possible, the properties of the problems being solved. Heuristic procedures are applied for the synthesis of cutting-planes as an intermediate step substantiating the construction of a solution tree. The properties of the generated algorithms are experimentally investigated, the prospects and ways of developing the method and expanding the classes of discrete optimization problems to be solved are determined. The material is illustrated with simple visual examples.