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Optimization Techniques (Doctorate Program in Power Systems or in Engineering Systems Modeling, year 2021-22)

News:

Operational Research Methods and Applications

Operational Research: scientific approach to the solution of problems in the management of complex systems.

Operations Research & Analytics: enable organizations to turn complex challenges into substantial opportunities by transforming data into information, and information into insights for making better decisions and improving results

L. Escudero y M.A. López SEIO y la historia de la IO en España Boletín de Estadística e Investigación Operativa 28 (1): 24-55, Feb 2012

F. Petropoulos et al. Operational Research: Methods and Applications March 2023

The current table reflects in a realistic way the course development during the several sessions. It allows the student to know in advance what is going to happen in each session in order to prepare the subject and to organize its work adequately.

Date

Theory

Additional readings

Applications

Jan 31, 22

Syllabus of the subject.
Hand out of the class notes and web page for slides.

Algebraic modeling languages.

FAQs About O.R. & Analytics

Feb 7, 22

Optimization Cases

Feb 14, 22

LINEAR PROGRAMMING.
Graphical simplex method. Algebraic simplex. Tabular form. Duality. Primal-dual interior point method.

Mathematical Programming Glossary

Linear Programming FAQ (2005)

2015 Linear Programming Software Survey

COmputational INfrastructure for Operations Research Projects

Good Optimization Modeling Practices with GAMS

Good Optimization Modeling Practices with Pyomo

Feb 21, 22

MIXED INTEGER LINEAR PROGRAMMING.
Branch and bound. Preprocessing. Branch and cut.
Modeling of Mixed Integer Linear Programming Problems. Piecewise linear. Convex and concave regions. Special ordered sets. Reformulation.

Feb 28, 22

STOCHASTIC OPTIMIZATION.
Generation expansion planning case study.

A. Ramos, A. Alonso-Ayuso, G. Pérez (eds.) Optimización bajo Incertidumbre Universidad Pontificia Comillas Madrid, España 2008 ISBN 8484682516

Red Temática de Optimización bajo Incertidumbre (ReTOBI)

Stochastic Programming Resources

Stochastic Optimization Cases

Stochastic Programming (SP) with GAMS

Mar 7, 22

Manufacturing case study. Decision tree and scenario tree.

Open Models

Mar 14, 22

Two-stage and multistage linear optimization. Hydrothermal coordination problem case study

Mar 21, 22

ROBUST OPTIMIZATION.
Static Robust Optimization.

Mar 28, 22

Adaptative Robust Optimization (ARO) for generation expansion planning. Comparison with stochastic optimization

Apr 4, 22

DECOMPOSITION TECHNIQUES.
Benders decomposition. Fixed cost transportation problem. Nested Benders decomposition.

G. Hechme-Doukopoulos, S. Brignol-Charousset, J. Malick, C. Lemaréchal The short-term electricity production management problem at EDF Optima (84) 2-7 Oct 2010

Benders decomposition. GAMS code

Apr 25, 22

Danztig-Wolfe decomposition. Lagrangian relaxation. Fixed cost transportation problem. Unit commitment solved by LR

Danztig-Wolfe decomposition. GAMS code
Lagrangean relaxation. GAMS code

May 9, 22

SCENARIO TREE
Characterization. Generation

May 18, 22

EQUILIBRIUM MODELING AND NONLINEAR PROGRAMMING (NLP).
Definition of nonlinear programs and standard optimization techniques
Convexity, Lagrangian, KKT conditions. Illustrative examples

Nonlinear Programming FAQ (2007)

1998 Nonlinear Programming Software Survey

May 23, 22

Simple equilibrium models and solution techniques. Mixed complementarity problems.

May 30, 22

Student presentations