Computational Experience with Logmip Solving Linear and Nonlinear Disjunctive Programming Problems

The objectives of this paper are to give a brief overview of the code LogMIP and to report numerical experience on a set of test problems. LOGMIP is currently the only code for disjunctive programming, which has implemented the research work done on this area on the last decade. Major motivations in the development of LogMIP have been to facilitate problem formulation of discrete/continuous optimization problems, and to improve the efficiency and robustness of the solution of these problems, particularly for the nonlinear case. LOGMIP is a software system linked to GAMS for solving problems that are formulated as disjunctive/hybrid programs (Vecchietti and Grossmann, 1999). For linear problems the disjunctive/hybrid model can be automatically reformulated as a mixed-integer (MIP) formulation using either a big-M reformulation, or a convex hull reformulation (Balas, 1979) depending on the choice selected by the user. The other option for solving nonlinear problems is the Logic-Based Outer-Approximation (LBOA) (Turkay and Grossmann, 1996). Computational experience on a set of linear and non-linear problems is reported. These problems correspond to the synthesis of process flowsheets, synthesis, retrofit and design of batch plants, scheduling of a multi-product pipeline, jobshop scheduling, and strip packing problem.