In this paper we survey recent work on the perspective reformulation approach that generates tight, tractable relaxations for convex mixed integer nonlinear programs (MINLP)s. This preprocessing technique is applicable to cases where the MINLP contains binary indicator variables that force continuous decision variables to take the value 0, or to belong to a convex set. We derive from first prin...

Branch-and-Bound (B&B) is perhaps the most fundamental algorithm for the global solution of convex Mixed-Integer Nonlinear Programming (MINLP) problems. It is well-known that carrying out branching in a non-simplistic manner can greatly enhance the practicality of B&B in the context of Mixed-Integer Linear Programming (MILP). No detailed study of branching has heretofore been carried out for MI...

Abstract: In order to improve the efficiency for solving MINLP problems, we present in this paper three computational strategies. These include multiple-generation cuts, hybrid methods and partial surrogate cuts for the Outer Approximation and Generalized Benders Decomposition. The properties and convergence of the strategies are analyzed. Five new MINLP algorithms are described based on the pr...

Many optimization problems involve integer and continuous variables that can be modeled as mixed integer nonlinear programming (MINLP) problems. This has led to a wide range of applications, in particular in some engineering areas. Here, we provide a brief overview on MINLP, and present a simple idea for a future nonconvex MINLP solution technique.

Primal heuristics are an important component of state-of-the-art codes for mixed integer nonlinear programming (MINLP). In this article we give a compact overview of primal heuristics for MINLP that have been suggested in the literature of recent years. We sketch the fundamental concepts of different classes of heuristics and discuss specific implementations. A brief computational experiment sh...

In this work, we propose a new algorithm for addressing the simultaneous design and control problem through the robust and efficient solution of a Mixed-Integer Dynamic Optimization (MIDO) problem. The algorithm is based on the transformation of the MIDO problem into a Mixed-Integer Nonlinear Programming (MINLP) program through the discretization of the MIDO problem. In this approach both the m...

Coordinated voltage and VAR control (VVC) can provide major economic benefits for distribution utilities. Incorporating distributed generations (DG) for VVC can improve the efficiency and reliability of distribution systems. This paper presents an approach to formulate and solve distribution system VVC with DG units as a mixed integer non-linear programming (MINLP) problem. The method can be ut...

This paper will attempt to show that one of the trends in the area of process synthesis is its gradual evolution towards the mathematical programming approach. This is in part due to the fundamental understanding that has been gained on the nature of the synthesis problems over the last twenty years. However, another major part has to do with the development of new and more powerful mathematica...

Bioprocess optimization by genetically modifying the microorganism characteristics is an intensively investigated subject due to the immediate economic interest. A large variety of alternatives using elaborated experimental procedures, accompanied by in-silico cell design based on topological and dynamic models have emerged. The present study investigates the possibility of using a mixed-intege...

Process synthesis often involves the solution of large nonlinear discretecontinuous optimization problems, which are usually formulated as mixedinteger nonlinear programming (MINLP) or generalized disjunctive programming (GDP) problems and solved with MINLP solvers. This paper presents an efficient solution method for these problems named successive relaxed MINLP (SR-MINLP), where the model for...