We develop a novel superstructure of algal biorefinery processes for biological carbon sequestration and utilization, encompassing off-gas purification, algae cultivation, harvesting and dewatering, lipid extraction, remnant treatment, biogas utilization, and algal oil upgrading stages. Based on the superstructure, we propose a mixed-integer nonlinear programming (MINLP) model to minimize the u...

In this paper, we propose a new model for designing integrated forward/reverse logistics based on pricing policy in direct and indirect sales channel. The proposed model includes producers, disposal center, distributers and final customers. We assumed that the location of final customers is fixed. First, a deterministic mixed integer linear programming model is developed for integrated logistic...

The general problem in topology optimization is correctly formulated as a doublemin mixed integer nonlinear programming (MINLP) problem based on the minimum total potential energy principle. It is proved that for linear elastic structures, the alternative iteration leads to a Knapsack problem, which is considered to be NP-hard in computer science. However, by using canonical duality theory (CDT...

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...

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...

We consider strategies for integrated design and control 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) rogram. In this approach, both the manipulated and controlled variables are discretized using a simultaneous dynamic optimizati...

This paper treats the solution of nonlinear optimization problems involving discrete decision variables, also known as generalized disjunctive programming (GDP) or mixed-integer nonlinear programming (MINLP) problems, that arise in process engineering. The key idea is to eliminate the discrete decision variables by adding a set of continuous variables and constraints that represent the discrete...

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...

We define difficult optimization problems as problems which cannot be solved to optimality or to any guaranteed bound by any standard solver within a reasonable time limit. The problem class we have in mind are mixed integer programming (MIP) problems. Optimization and especially mixed integer optimization is often appropriate and frequently used to model real world optimization problems. While...