A New Computer Oriented Technique for Solving Linear Programming Problem Using Bender's Decomposition Method
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Julia, My New Friend for Computing and Optimization? Pierre Haessig, Lilian Besson
Julia, my new friend for computing and optimization? Pierre Haessig, Lilian Besson To cite this version: Pierre Haessig, Lilian Besson. Julia, my new friend for computing and optimization?. Master. France. 2018. cel-01830248 HAL Id: cel-01830248 https://hal.archives-ouvertes.fr/cel-01830248 Submitted on 4 Jul 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. « Julia, my new computing friend? » | 14 June 2018, IETR@Vannes | By: L. Besson & P. Haessig 1 « Julia, my New frieNd for computiNg aNd optimizatioN? » Intro to the Julia programming language, for MATLAB users Date: 14th of June 2018 Who: Lilian Besson & Pierre Haessig (SCEE & AUT team @ IETR / CentraleSupélec campus Rennes) « Julia, my new computing friend? » | 14 June 2018, IETR@Vannes | By: L. Besson & P. Haessig 2 AgeNda for today [30 miN] 1. What is Julia? [5 miN] 2. ComparisoN with MATLAB [5 miN] 3. Two examples of problems solved Julia [5 miN] 4. LoNger ex. oN optimizatioN with JuMP [13miN] 5. LiNks for more iNformatioN ? [2 miN] « Julia, my new computing friend? » | 14 June 2018, IETR@Vannes | By: L. Besson & P. Haessig 3 1. What is Julia ? Open-source and free programming language (MIT license) Developed since 2012 (creators: MIT researchers) Growing popularity worldwide, in research, data science, finance etc… Multi-platform: Windows, Mac OS X, GNU/Linux.. -
Solving Mixed Integer Linear and Nonlinear Problems Using the SCIP Optimization Suite
Takustraße 7 Konrad-Zuse-Zentrum D-14195 Berlin-Dahlem fur¨ Informationstechnik Berlin Germany TIMO BERTHOLD GERALD GAMRATH AMBROS M. GLEIXNER STEFAN HEINZ THORSTEN KOCH YUJI SHINANO Solving mixed integer linear and nonlinear problems using the SCIP Optimization Suite Supported by the DFG Research Center MATHEON Mathematics for key technologies in Berlin. ZIB-Report 12-27 (July 2012) Herausgegeben vom Konrad-Zuse-Zentrum f¨urInformationstechnik Berlin Takustraße 7 D-14195 Berlin-Dahlem Telefon: 030-84185-0 Telefax: 030-84185-125 e-mail: [email protected] URL: http://www.zib.de ZIB-Report (Print) ISSN 1438-0064 ZIB-Report (Internet) ISSN 2192-7782 Solving mixed integer linear and nonlinear problems using the SCIP Optimization Suite∗ Timo Berthold Gerald Gamrath Ambros M. Gleixner Stefan Heinz Thorsten Koch Yuji Shinano Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany, fberthold,gamrath,gleixner,heinz,koch,[email protected] July 31, 2012 Abstract This paper introduces the SCIP Optimization Suite and discusses the ca- pabilities of its three components: the modeling language Zimpl, the linear programming solver SoPlex, and the constraint integer programming frame- work SCIP. We explain how these can be used in concert to model and solve challenging mixed integer linear and nonlinear optimization problems. SCIP is currently one of the fastest non-commercial MIP and MINLP solvers. We demonstrate the usage of Zimpl, SCIP, and SoPlex by selected examples, give an overview of available interfaces, and outline plans for future development. ∗A Japanese translation of this paper will be published in the Proceedings of the 24th RAMP Symposium held at Tohoku University, Miyagi, Japan, 27{28 September 2012, see http://orsj.or. -
[20Pt]Algorithms for Constrained Optimization: [ 5Pt]
SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s Algorithms for Constrained Optimization: The Benefits of General-purpose Software Michael Saunders MS&E and ICME, Stanford University California, USA 3rd AI+IoT Business Conference Shenzhen, China, April 25, 2019 Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 1/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s SOL Systems Optimization Laboratory George Dantzig, Stanford University, 1974 Inventor of the Simplex Method Father of linear programming Large-scale optimization: Algorithms, software, applications Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 2/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s SOL history 1974 Dantzig and Cottle start SOL 1974{78 John Tomlin, LP/MIP expert 1974{2005 Alan Manne, nonlinear economic models 1975{76 MS, MINOS first version 1979{87 Philip Gill, Walter Murray, MS, Margaret Wright (Gang of 4!) 1989{ Gerd Infanger, stochastic optimization 1979{ Walter Murray, MS, many students 2002{ Yinyu Ye, optimization algorithms, especially interior methods This week! UC Berkeley opened George B. Dantzig Auditorium Optimization Software 3rd AI+IoT Business Conference, Shenzhen, April 25, 2019 3/39 SOL Optimization 1970s 1980s 1990s 2000s 2010s Summary 2020s Optimization problems Minimize an objective function subject to constraints: 0 x 1 min '(x) st ` ≤ @ Ax A ≤ u c(x) x variables 0 1 A matrix c1(x) B . C c(x) nonlinear functions @ . A c (x) `; u bounds m Optimization -
Numericaloptimization
Numerical Optimization Alberto Bemporad http://cse.lab.imtlucca.it/~bemporad/teaching/numopt Academic year 2020-2021 Course objectives Solve complex decision problems by using numerical optimization Application domains: • Finance, management science, economics (portfolio optimization, business analytics, investment plans, resource allocation, logistics, ...) • Engineering (engineering design, process optimization, embedded control, ...) • Artificial intelligence (machine learning, data science, autonomous driving, ...) • Myriads of other applications (transportation, smart grids, water networks, sports scheduling, health-care, oil & gas, space, ...) ©2021 A. Bemporad - Numerical Optimization 2/102 Course objectives What this course is about: • How to formulate a decision problem as a numerical optimization problem? (modeling) • Which numerical algorithm is most appropriate to solve the problem? (algorithms) • What’s the theory behind the algorithm? (theory) ©2021 A. Bemporad - Numerical Optimization 3/102 Course contents • Optimization modeling – Linear models – Convex models • Optimization theory – Optimality conditions, sensitivity analysis – Duality • Optimization algorithms – Basics of numerical linear algebra – Convex programming – Nonlinear programming ©2021 A. Bemporad - Numerical Optimization 4/102 References i ©2021 A. Bemporad - Numerical Optimization 5/102 Other references • Stephen Boyd’s “Convex Optimization” courses at Stanford: http://ee364a.stanford.edu http://ee364b.stanford.edu • Lieven Vandenberghe’s courses at UCLA: http://www.seas.ucla.edu/~vandenbe/ • For more tutorials/books see http://plato.asu.edu/sub/tutorials.html ©2021 A. Bemporad - Numerical Optimization 6/102 Optimization modeling What is optimization? • Optimization = assign values to a set of decision variables so to optimize a certain objective function • Example: Which is the best velocity to minimize fuel consumption ? fuel [ℓ/km] velocity [km/h] 0 30 60 90 120 160 ©2021 A. -
ILOG AMPL CPLEX System Version 9.0 User's Guide
ILOG AMPL CPLEX System Version 9.0 User’s Guide Standard (Command-line) Version Including CPLEX Directives September 2003 Copyright © 1987-2003, by ILOG S.A. All rights reserved. ILOG, the ILOG design, CPLEX, and all other logos and product and service names of ILOG are registered trademarks or trademarks of ILOG in France, the U.S. and/or other countries. JavaTM and all Java-based marks are either trademarks or registered trademarks of Sun Microsystems, Inc. in the United States and other countries. Microsoft, Windows, and Windows NT are either trademarks or registered trademarks of Microsoft Corporation in the U.S. and other countries. All other brand, product and company names are trademarks or registered trademarks of their respective holders. AMPL is a registered trademark of AMPL Optimization LLC and is distributed under license by ILOG.. CPLEX is a registered trademark of ILOG.. Printed in France. CO N T E N T S Table of Contents Chapter 1 Introduction . 1 Welcome to AMPL . .1 Using this Guide. .1 Installing AMPL . .2 Requirements. .2 Unix Installation . .3 Windows Installation . .3 AMPL and Parallel CPLEX. 4 Licensing . .4 Usage Notes . .4 Installed Files . .5 Chapter 2 Using AMPL. 7 Running AMPL . .7 Using a Text Editor . .7 Running AMPL in Batch Mode . .8 Chapter 3 AMPL-Solver Interaction . 11 Choosing a Solver . .11 Specifying Solver Options . .12 Initial Variable Values and Solvers. .13 ILOG AMPL CPLEX SYSTEM 9.0 — USER’ S GUIDE v Problem and Solution Files. .13 Saving temporary files . .14 Creating Auxiliary Files . .15 Running Solvers Outside AMPL. .16 Using MPS File Format . -
Open Source Tools for Optimization in Python
Open Source Tools for Optimization in Python Ted Ralphs Sage Days Workshop IMA, Minneapolis, MN, 21 August 2017 T.K. Ralphs (Lehigh University) Open Source Optimization August 21, 2017 Outline 1 Introduction 2 COIN-OR 3 Modeling Software 4 Python-based Modeling Tools PuLP/DipPy CyLP yaposib Pyomo T.K. Ralphs (Lehigh University) Open Source Optimization August 21, 2017 Outline 1 Introduction 2 COIN-OR 3 Modeling Software 4 Python-based Modeling Tools PuLP/DipPy CyLP yaposib Pyomo T.K. Ralphs (Lehigh University) Open Source Optimization August 21, 2017 Caveats and Motivation Caveats I have no idea about the background of the audience. The talk may be either too basic or too advanced. Why am I here? I’m not a Sage developer or user (yet!). I’m hoping this will be a chance to get more involved in Sage development. Please ask lots of questions so as to guide me in what to dive into! T.K. Ralphs (Lehigh University) Open Source Optimization August 21, 2017 Mathematical Optimization Mathematical optimization provides a formal language for describing and analyzing optimization problems. Elements of the model: Decision variables Constraints Objective Function Parameters and Data The general form of a mathematical optimization problem is: min or max f (x) (1) 8 9 < ≤ = s.t. gi(x) = bi (2) : ≥ ; x 2 X (3) where X ⊆ Rn might be a discrete set. T.K. Ralphs (Lehigh University) Open Source Optimization August 21, 2017 Types of Mathematical Optimization Problems The type of a mathematical optimization problem is determined primarily by The form of the objective and the constraints. -
MODELING LANGUAGES in MATHEMATICAL OPTIMIZATION Applied Optimization Volume 88
MODELING LANGUAGES IN MATHEMATICAL OPTIMIZATION Applied Optimization Volume 88 Series Editors: Panos M. Pardalos University o/Florida, U.S.A. Donald W. Hearn University o/Florida, U.S.A. MODELING LANGUAGES IN MATHEMATICAL OPTIMIZATION Edited by JOSEF KALLRATH BASF AG, GVC/S (Scientific Computing), 0-67056 Ludwigshafen, Germany Dept. of Astronomy, Univ. of Florida, Gainesville, FL 32611 Kluwer Academic Publishers Boston/DordrechtiLondon Distributors for North, Central and South America: Kluwer Academic Publishers 101 Philip Drive Assinippi Park Norwell, Massachusetts 02061 USA Telephone (781) 871-6600 Fax (781) 871-6528 E-Mail <[email protected]> Distributors for all other countries: Kluwer Academic Publishers Group Post Office Box 322 3300 AlI Dordrecht, THE NETHERLANDS Telephone 31 78 6576 000 Fax 31 786576474 E-Mail <[email protected]> .t Electronic Services <http://www.wkap.nl> Library of Congress Cataloging-in-Publication Kallrath, Josef Modeling Languages in Mathematical Optimization ISBN-13: 978-1-4613-7945-4 e-ISBN-13:978-1-4613 -0215 - 5 DOl: 10.1007/978-1-4613-0215-5 Copyright © 2004 by Kluwer Academic Publishers Softcover reprint of the hardcover 1st edition 2004 All rights reserved. No part ofthis pUblication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photo-copying, microfilming, recording, or otherwise, without the prior written permission ofthe publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Permissions for books published in the USA: P"§.;r.m.i.§J?i..QD.§.@:w.k~p" ..,.g.Qm Permissions for books published in Europe: [email protected] Printed on acid-free paper. -
Introduction to the COIN-OR Optimization Suite
The COIN-OR Optimization Suite: Algegraic Modeling Ted Ralphs COIN fORgery: Developing Open Source Tools for OR Institute for Mathematics and Its Applications, Minneapolis, MN T.K. Ralphs (Lehigh University) COIN-OR October 15, 2018 Outline 1 Introduction 2 Solver Studio 3 Traditional Modeling Environments 4 Python-Based Modeling 5 Comparative Case Studies T.K. Ralphs (Lehigh University) COIN-OR October 15, 2018 Outline 1 Introduction 2 Solver Studio 3 Traditional Modeling Environments 4 Python-Based Modeling 5 Comparative Case Studies T.K. Ralphs (Lehigh University) COIN-OR October 15, 2018 Algebraic Modeling Languages Generally speaking, we follow a four-step process in modeling. Develop an abstract model. Populate the model with data. Solve the model. Analyze the results. These four steps generally involve different pieces of software working in concert. For mathematical programs, the modeling is often done with an algebraic modeling system. Data can be obtained from a wide range of sources, including spreadsheets. Solution of the model is usually relegated to specialized software, depending on the type of model. T.K. Ralphs (Lehigh University) COIN-OR October 15, 2018 Modeling Software Most existing modeling software can be used with COIN solvers. Commercial Systems GAMS MPL AMPL AIMMS Python-based Open Source Modeling Languages and Interfaces Pyomo PuLP/Dippy CyLP (provides API-level interface) yaposib T.K. Ralphs (Lehigh University) COIN-OR October 15, 2018 Modeling Software (cont’d) Other Front Ends (mostly open source) FLOPC++ (algebraic modeling in C++) CMPL MathProg.jl (modeling language built in Julia) GMPL (open-source AMPL clone) ZMPL (stand-alone parser) SolverStudio (spreadsheet plug-in: www.OpenSolver.org) Open Office spreadsheet R (RSymphony Plug-in) Matlab (OPTI) Mathematica T.K. -
Largest Small N-Polygons: Numerical Results and Conjectured Optima
Largest Small n-Polygons: Numerical Results and Conjectured Optima János D. Pintér Department of Industrial and Systems Engineering Lehigh University, Bethlehem, PA, USA [email protected] Abstract LSP(n), the largest small polygon with n vertices, is defined as the polygon of unit diameter that has maximal area A(n). Finding the configuration LSP(n) and the corresponding A(n) for even values n 6 is a long-standing challenge that leads to an interesting class of nonlinear optimization problems. We present numerical solution estimates for all even values 6 n 80, using the AMPL model development environment with the LGO nonlinear solver engine option. Our results compare favorably to the results obtained by other researchers who solved the problem using exact approaches (for 6 n 16), or general purpose numerical optimization software (for selected values from the range 6 n 100) using various local nonlinear solvers. Based on the results obtained, we also provide a regression model based estimate of the optimal area sequence {A(n)} for n 6. Key words Largest Small Polygons Mathematical Model Analytical and Numerical Solution Approaches AMPL Modeling Environment LGO Solver Suite For Nonlinear Optimization AMPL-LGO Numerical Results Comparison to Earlier Results Regression Model Based Optimum Estimates 1 Introduction The diameter of a (convex planar) polygon is defined as the maximal distance among the distances measured between all vertex pairs. In other words, the diameter of the polygon is the length of its longest diagonal. The largest small polygon with n vertices is the polygon of unit diameter that has maximal area. For any given integer n 3, we will refer to this polygon as LSP(n) with area A(n). -
Computing in Operations Research Using Julia
Computing in Operations Research using Julia Miles Lubin and Iain Dunning MIT Operations Research Center INFORMS 2013 { October 7, 2013 1 / 25 High-level, high-performance, open-source dynamic language for technical computing. Keep productivity of dynamic languages without giving up speed. Familiar syntax Python+PyPy+SciPy+NumPy integrated completely. Latest concepts in programming languages. 2 / 25 Claim: \close-to-C" speeds Within a factor of 2 Performs well on microbenchmarks, but how about real computational problems in OR? Can we stop writing solvers in C++? 3 / 25 Technical advancements in Julia: Fast code generation (JIT via LLVM). Excellent connections to C libraries - BLAS/LAPACK/... Metaprogramming. Optional typing, multiple dispatch. 4 / 25 Write generic code, compile efficient type-specific code C: (fast) int f() { int x = 1, y = 2; return x+y; } Julia: (No type annotations) Python: (slow) function f() def f(): x = 1; y = 2 x = 1; y = 2 return x + y return x+y end 5 / 25 Requires type inference by compiler Difficult to add onto exiting languages Available in MATLAB { limited scope PyPy for Python { incompatible with many libraries Julia designed from the ground up to support type inference efficiently 6 / 25 Simplex algorithm \Bread and butter" of operations research Computationally very challenging to implement efficiently1 Matlab implementations too slow to be used in practice High-quality open-source codes exist in C/C++ Can Julia compete? 1Bixby, Robert E. "Solving Real-World Linear Programs: A Decade and More of Progress", Operations Research, Vol. 50, pp. 3{15, 2002. 7 / 25 Implemented benchmark operations in Julia, C++, MATLAB, Python. -
AMPL Academic Price List These Prices Apply to Purchases by Degree-Awarding Institutions for Use in Noncommercial Teaching and Research Activities
AMPL Optimization Inc. 211 Hope Street #339 Mountain View, CA 94041, U.S.A. [email protected] — www.ampl.com +1 773-336-AMPL (-2675) AMPL Academic Price List These prices apply to purchases by degree-awarding institutions for use in noncommercial teaching and research activities. Products covered by academic prices are full-featured and have no arbitrary limits on problem size. Single Floating AMPL $400 $600 Linear/quadratic solvers: CPLEX free 1-year licenses available: see below Gurobi free 1-year licenses available: see below Xpress free 1-year licenses available: see below Nonlinear solvers: Artelys Knitro $400 $600 CONOPT $400 $600 LOQO $300 $450 MINOS $300 $450 SNOPT $320 $480 Alternative solvers: BARON $400 $600 LGO $200 $300 LINDO Global $700 $950 . Basic $400 $600 (limited to 3200 nonlinear variables) Web-based collaborative environment: QuanDec $1400 $2100 AMPL prices are for the AMPL modeling language and system, including the AMPL command-line and IDE development tools and the AMPL API programming libraries. To make use of AMPL it is necessary to also obtain at least one solver having an AMPL interface. Solvers may be obtained from us or from another source. As listed above, we offer many popular solvers for direct purchase; refer to www.ampl.com/products/solvers/solvers-we-sell/ to learn more, including problem types supported and methods used. Our prices for these solvers apply to the versions that incorporate an AMPL interface; a previously or concurrently purchased copy of the AMPL software is needed to use these versions. Programming libraries and other forms of these solvers are not included. -
Real-Time Trajectory Planning to Enable Safe and Performant Automated Vehicles Operating in Unknown Dynamic Environments
Real-time Trajectory Planning to Enable Safe and Performant Automated Vehicles Operating in Unknown Dynamic Environments by Huckleberry Febbo A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Mechanical Engineering) at The University of Michigan 2019 Doctoral Committee: Associate Research Scientist Tulga Ersal, Co-Chair Professor Jeffrey L. Stein, Co-Chair Professor Brent Gillespie Professor Ilya Kolmanovsky Huckleberry Febbo [email protected] ORCID iD: 0000-0002-0268-3672 c Huckleberry Febbo 2019 All Rights Reserved For my mother and father ii ACKNOWLEDGEMENTS I want to thank my advisors, Prof. Jeffrey L. Stein and Dr. Tulga Ersal for their strong guidance during my graduate studies. Each of you has played pivotal and complementary roles in my life that have greatly enhanced my ability to communicate. I want to thank Prof. Peter Ifju for telling me to go to graduate school. Your confidence in me has pushed me farther than I knew I could go. I want to thank Prof. Elizabeth Hildinger for improving my ability to write well and providing me with the potential to assert myself on paper. I want to thank my friends, family, classmates, and colleges for their continual support. In particular, I would like to thank John Guittar and Srdjan Cvjeticanin for providing me feedback on my articulation of research questions and ideas. I will always look back upon the 2018 Summer that we spent together in the Rackham Reading Room with fondness. Rackham . oh Rackham . I want to thank Virgil Febbo for helping me through my last month in Michigan.