Branch-and-Cut Algorithmic Framework for 0−1 Mixed-Integer Convex Nonlinear Programs

Abstract

With widespread use of mixed-integer modeling for continuous and discontinuous nonlinear chemical processes, a robust mixed-integer nonlinear optimization algorithm is strongly demanded for the design and operation of chemical processes that achieve greater profits and also satisfy environmental and safety constraints. In this article, an extensive evaluation of a branch-and-cut algorithmic framework for 0−1 mixed-integer convex nonlinear programs, called MINO for Mixed-Integer Nonlinear Optimizer, is presented. The numerical performances of MINO are tested against four sets of medium-sized practical application problems from the fields of operations research and chemical engineering. The effects of the nonlinear programming (NLP) solvers, the cut generating and maintaining strategy, the node selection method, and the frequency of cut generation are examined, in order to handle MINLP problem with different mathematical structures. Preliminary computational results show that MINO exhibits a capability for handling practical MINLP problems that is comparable to that of the commercial solvers SBB and DICOPT, and it shows better performance for some problems for which either commercial solver encounters convergence problem within a CPU time limit of 6 h.