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About 10,000 papers for “mixed-integer linear programming”

Mixed-Integer Linear Programming

Ignacio E. Grossmann · Cambridge University Press eBooks · 2021

Based on the author's forty years of teaching experience, this unique textbook covers both basic and advanced concepts of optimization theory and methods for process systems engineers. Topics covered include continuous, discrete and logic optimization (linear, nonlinear, mixed-integer and generalized disjunctive programming), optimization under uncertainty (stochastic programming and flexibility analysis), and decomposition techniques (Lagrangean and Benders decomposition). Assuming only a basic background in calculus and linear algebra, it enables easy understanding of mathematical reasoning, and numerous examples throughout illustrate key concepts and algorithms. End-of-chapter exercises involving theoretical derivations and small numerical problems, as well as in modeling systems like GAMS, enhance understanding and help put knowledge into practice. Accompanied by two appendices containing web links to modeling systems and models related to applications in PSE, this is an essential text for single-semester, graduate courses in process systems engineering in departments of chemical engineering.

Cited by 0

Multiparametric Mixed‐Integer Linear Programming

Vivek Dua, Michael C. Georgiadis · 2007

This chapter contains sections titled: Parametric Mixed-Integer Linear Programming Multiparametric Mixed-Integer Linear Programming. Branch and Bound Approach Multiparametric Mixed-Integer Linear Programming. Parametric and Integer Cuts Numerical Example Concluding Remarks Appendix A. Definition of an Infeasible Region Literature

Cited by 2

MILP: Mixed-Integer Linear Programming

Amirhossein Hajimiragha, Michael Fowler, Claudio Cañizares · 2009

This paper investigates the feasibility of electrolytic hydrogen production for the transport sector during off-peak periods in Ontario. This analysis is based on the existing electricity system infrastructure and its planned future development up to 2025. First, a simplified but realistic zonal based model for Ontario’s electricity transmission network is developed. Then, based on Ontario’s Integrated Power System Plan (IPSP), a zonal pattern of generation capacity procurement in Ontario from 2008 to 2025 is proposed, specifying the total effective generation capacity in each zone that contributes to base-load energy. Finally, an optimization model is developed to find the optimal size of hydrogen production plants to be developed in different zones, as well as optimal hydrogen transportation routes to achieve a feasible hydrogen economy penetration in Ontario up to 2025. The proposed model is shown to be an effective planning tool for electrolysis based hydrogen economy studies. The results of the present study demonstrate that the present and projected electricity grid in Ontario can be optimally exploited for hydrogen production, achieving 1.2 % to 2.8 % levels of hydrogen economy penetration by 2025 without any additional grid or power generation investments beyond those currently planned.

Cited by 0

Integer Processing for Mixed Integer Linear Programming Problems

Hardi Tambunan, Herman Mawengkang · INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH · 2025

The mixed integer nonlinear programming problem addressed in this paper refers to mathematical pro­gramming with continuous and discrete variables and linearities in the ob­jective function and constraints. The purpose of this article is to create an approach to solving MILP problems for integer search through active constraints, and neighborhoods, in order to reduce iterations. The study of the criteria for selecting non-basic variables for use in the integer processes has been conducted using active constraint and neighborhood approaches. The number of integration steps will be limited if the number of integer variables in the problem is finite. However, the integer processes not necessarily depend on the number of integer variables, as many integer variables may have integer values ​​in a continuous optimal solution.

Cited by 0Open access

Integer Processing for Mixed Integer Linear Programming Problems

Hardi Tambunan, Herman Mawengkang · Zenodo (CERN European Organization for Nuclear Research) · 2025

The mixed integer nonlinear programming problem addressed in this paper refers to mathematical pro­gramming with continuous and discrete variables and linearities in the ob­jective function and constraints. The purpose of this article is to create an approach to solving MILP problems for integer search through active constraints, and neighborhoods, in order to reduce iterations. The study of the criteria for selecting non-basic variables for use in the integer processes has been conducted using active constraint and neighborhood approaches. The number of integration steps will be limited if the number of integer variables in the problem is finite. However, the integer processes not necessarily depend on the number of integer variables, as many integer variables may have integer values in a continuous optimal solution.

Cited by 0Open access

Mixed-Time Mixed-Integer Linear Programming Scheduling Model

Joakim Westerlund, Mattias Hästbacka, Sebastian Forssell et al. · Industrial & Engineering Chemistry Research · 2007

This paper presents a novel mixed-time mixed-integer linear programming (MILP) scheduling model for industrial problems where intermediate storage handling is of particular concern. The proposed model is a crossbreed between a continuous-time and a discrete-time model where a continuous-time representation is incorporated in a discrete-time grid. The mixed-time formulation is useful in the modeling of multi-stage multi-product production processes using intermediate storages with nonlinear optimal storage profiles. The model is combining useful features from continuous-time models, flexibility, and solution efficiency, with the functional reference grid for the time representation, included in discrete-time representations. The model is able to handle both short-term and periodic problems. The main purpose of the presented model is not to challenge existing models on solution efficiency or quality on theoretical problems but to present a model that is very useful in the modeling of industrial scheduling problems where intermediate storage handling is of importance. The proposed model is able to solve industrial problems which, according to our knowledge, have not previously been solvable by existing models. The novelty with the proposed model is that an entirely continuous-time representation is incorporated in a uniform time grid. In practice this means that despite the continuous-time representation, aging profiles or highly nonlinear storage inventory profiles may, for example, be addressed with the proposed model.

Cited by 23