Solving Mixed Integer Programming Problems Using Automatic Reformulation

In this paper we describe computational experience in solving mixed 0-1 programming problems using strong valid inequalities as cutting planes. In particular we report on the solution to optimality of 18 medium- to large-size problems, including production planning problems with setup costs and capacity constraints, multilevel distribution planning problems, drainage and heating system design problems, and electricity generator scheduling problems. The solution approach uses the theory of strong valid inequalities that we developed in a series of earlier papers. Here we report specifically on the implementation of an experimental system, MPSARX, which consists of the SCICONIC mathematical programming system and an automatic reformulation executor (ARX) that use this theory, and on the results obtained with this system.