We propose a method for solving mixed-integer nonlinear programs (MINLPs) to global optimality by discretization of occuring nonlinearities. The main idea is based on using piecewise linear functions to construct mixed-integer linear program (MIP) relaxations of the underlying MINLP. In order to find a global optimum of the given MINLP we develope an iterative algorithm which solves MIP relaxat...

Abstract : Two new methodologies for the global optimization of MINLP models, the Special structure Mixed Integer Nonlinear BB, SMIN– BB, and the General structure Mixed Integer Nonlinear BB, GMIN– BB, are presented. Their theoretical foundations provide guarantees that the global optimum solution of MINLPs involving twice–differentiable nonconvex functions in the continuous variables can be id...

â liquefied natural gas (lng) is the most economical way of transporting natural gas (ng) over long distances. liquefaction of ng by using vapor compression refrigeration system requires high operating and capital cost. due to lack of systematic design methods for multistage refrigeration cycles, the conventional approaches of determining optimal cycle configuration are mostly based on trial-an...

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...

An algorithm (M-SIMPSA) suitable for the optimization of mixed integer non-linear programming (MINLP) problems is presented. A recently proposed continuous non-linear solver (SIMPSA) is used to update the continuous parameters, and the Metropolis algorithm is used to update the complete solution vector of decision variables. The M-SIMPSA algorithm, which does not require feasible initial points...

This paper proposes a multiobjective, mixed-integer nonlinear programming (MINLP) model for the superstructure optimization of hydrocarbon biorefineries via gasification pathway under economic and environmental criteria. The proposed hydrocarbon biorefinery superstructure includes a number of major processing stages, such as drying of the cellulosic biomass feedstocks, air separation unit, gasi...

Recently, cogeneration systems (CGS) have been installed in various factories and buildings. CGS is usually connected to various facilities such as refrigerators, reservoirs, and cooling towers, and produces various energies for electric loads, air-conditioning loads, heating loads, and hot water loads (fig.1). Since daily load patterns of the various loads are different, optimal operational pl...

Structural multiplicity has a significant effect on the solution of an MINLP model for process synthesis problems. The optimization model may also have built-in redundancy that cannot always be directly derived from the multiplicity of the superstructure. A basic GDP representation (BGR) involving logical relations is defined, and can be constructed by applying a standard natural representation...

We are interested in methods to solve mixed-integer nonlinear optimal control problems (MIOCPs) constrained by ordinary differential equations and combinatorial constraints on some of the control functions. To solve these problems we use a first discretize, then optimize approach to get a specially structured mixed-integer nonlinear program (MINLP). We decompose this MINLP into an NLP and an MI...

In the context of convex mixed integer nonlinear programming (MINLP), we investigate how the outer approximation method and the generalized Benders decomposition method are affected when the respective nonlinear programming (NLP) subproblems are solved inexactly. We show that the cuts in the corresponding master problems can be changed to incorporate the inexact residuals, still rendering equiv...