DOCSLIB.ORG

AIMMS Optimization Modeling

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
AIMMS Optimization Modeling AIMMS Optimization Modeling AIMMS September 15, 2021 AIMMS Optimization Modeling AIMMS Johannes Bisschop Copyright c 1993–2019 by AIMMS B.V. All rights reserved. Email: [email protected] WWW: www.aimms.com Aimms is a registered trademark of AIMMS B.V. IBM ILOG CPLEX and CPLEX is a registered trademark of IBM Corporation. GUROBI is a registered trademark of Gurobi Optimization, Inc. Knitro is a registered trademark of Artelys. Windows and Excel are registered trademarks of Microsoft Corporation. TEX, LATEX, and AMS-LATEX are trademarks of the American Mathematical Society. Lucida is a registered trademark of Bigelow & Holmes Inc. Acrobat is a registered trademark of Adobe Systems Inc. Other brands and their products are trademarks of their respective holders. Information in this document is subject to change without notice and does not represent a commitment on the part of AIMMS B.V. The software described in this document is furnished under a license agreement and may only be used and copied in accordance with the terms of the agreement. The documentation may not, in whole or in part, be copied, photocopied, reproduced, translated, or reduced to any electronic medium or machine-readable form without prior consent, in writing, from AIMMS B.V. AIMMS B.V. makes no representation or warranty with respect to the adequacy of this documentation or the programs which it describes for any particular purpose or with respect to its adequacy to produce any particular result. In no event shall AIMMS B.V., its employees, its contractors or the authors of this documentation be liable for special, direct, indirect or consequential damages, losses, costs, charges, claims, demands, or claims for lost profits, fees or expenses of any nature or kind. In addition to the foregoing, users should recognize that all complex software systems and their docu- mentation contain errors and omissions. The authors, AIMMS B.V. and its employees, and its contractors shall not be responsible under any circumstances for providing information or corrections to errors and omissions discovered at any time in this book or the software it describes, whether or not they are aware of the errors or omissions. The authors, AIMMS B.V. and its employees, and its contractors do not recommend the use of the software described in this book for applications in which errors or omissions could threaten life, injury or significant loss. This documentation was typeset by AIMMS B.V. using LATEX and the Lucida font family. About Aimms Aimms was introduced as a new type of mathematical modeling tool in 1993— History an integrated combination of a modeling language, a graphical user inter- face, and numerical solvers. Aimms has proven to be one of the world’s most advanced development environments for building optimization-based decision support applications and advanced planning systems. Today, it is used by leading companies in a wide range of industries in areas such as sup- ply chain management, energy management, production planning, logistics, forestry planning, and risk-, revenue-, and asset- management. In addition, Aimms is used by universities worldwide for courses in Operations Research and Optimization Modeling, as well as for research and graduation projects. Aimms is far more than just another mathematical modeling language. True, What is Aimms? the modeling language is state of the art for sure, but alongside this, Aimms offers a number of advanced modeling concepts not found in other languages, as well as a full graphical user interface both for developers and end-users. Aimms includes world-class solvers (and solver links) for linear, mixed-integer, and nonlinear programming such as baron, cplex, conopt, gurobi, knitro, path, snopt and xa, and can be readily extended to incorporate other ad- vanced commercial solvers available on the market today. In addition, con- cepts as stochastic programming and robust optimization are available to in- clude data uncertainty in your models. Mastering Aimms is straightforward since the language concepts will be intu- Mastering itive to Operations Research (OR) professionals, and the point-and-click graph- Aimms ical interface is easy to use. Aimms comes with comprehensive documentation, available electronically and in book form. Aimms provides an ideal platform for creating advanced prototypes that are Types of Aimms then easily transformed into operational end-user systems. Such systems can applications than be used either as stand-alone applications, or optimization components. About Aimms vi Application developers and operations research experts use Aimms to build Stand-alone complex and large scale optimization models and to create a graphical end- applications user interface around the model. Aimms-based applications place the power of the most advanced mathematical modeling techniques directly into the hands of end-users, enabling them to rapidly improve the quality, service, profitabil- ity, and responsiveness of their operations. Independent Software Vendors and OEMs use Aimms to create complex and Optimization large scale optimization components that complement their applications and components web services developed in languages such as C++, Java, .NET, or Excel. Appli- cations built with Aimms-based optimization components have a shorter time- to-market, are more robust and are richer in features than would be possible through direct programming alone. Companies using Aimms include Aimms users ABN AMRO Merck Areva Owens Corning Bayer Perdig˜ao Bluescope Steel Petrobras BP Philips CST PriceWaterhouseCoopers ExxonMobil Reliance Gaz de France Repsol Heineken Shell Innovene Statoil Lufthansa Unilever Universities using Aimms include Budapest University of Technology, Carnegie Mellon University, George Mason University, Georgia Institute of Technology, Japan Advanced Institute of Science and Technology, London School of Eco- nomics, Nanyang Technological University, Rutgers University, Technical Uni- versity of Eindhoven, Technische Universit¨at Berlin, UIC Bioengineering, Uni- versidade Federal do Rio de Janeiro, University of Groningen, University of Pittsburgh, University of Warsaw, and University of the West of England. A more detailed list of Aimms users and reference cases can be found on our website www.aimms.com. Contents About Aimms v Contents vii Preface xiii What is in the Aimms documentation ............... xiii What’s in the Optimization Modeling guide ........... xvi The authors ............................... xviii Part I Introduction to Optimization Modeling 2 1 Background 2 1.1 Whatisamodel? ............................ 2 1.2 Why usemodels? ........................... 3 1.3 The role of mathematics ....................... 4 1.4 The modeling process ........................ 6 1.5 Application areas ........................... 7 1.5.1 Production ........................... 7 1.5.2 Production and inventory management ......... 8 1.5.3 Finance ............................. 9 1.5.4 Manpower planning ..................... 10 1.5.5 Agricultural economics ................... 11 1.6 Summary ................................ 12 2 Formulating Optimization Models 13 2.1 Formulating linear programming models ............. 13 2.1.1 Introduction ......................... 13 2.1.2 Example of a linear programming model ........ 14 2.1.3 Picturing the formulation and the solution ....... 17 2.2 Formulating mixed integer programming models ....... 23 2.3 Formulating nonlinear programming models .......... 27 2.4 Summary ................................ 31 Contents viii 3 Algebraic Representation of Models 32 3.1 Explicit form .............................. 32 3.2 Symbolic form ............................. 33 3.3 Symbolic-indexed form ........................ 34 3.4 Aimms form ............................... 37 3.5 Translating a verbal problem into a model ............ 39 3.6 Summary ................................ 40 4 Sensitivity Analysis 41 4.1 Introduction .............................. 41 4.2 Shadow prices ............................. 42 4.3 Reduced costs ............................. 45 4.4 Sensitivity ranges with constant objective function value . 48 4.5 Sensitivity ranges with constant basis ............... 49 4.6 Summary ................................ 51 5 Network Flow Models 52 5.1 Introduction .............................. 52 5.2 Example of a network flow model ................. 53 5.3 Network formulation ......................... 55 5.4 Solution and sensitivity analysis .................. 57 5.5 Pure network flow models ...................... 58 5.6 Other network models ........................ 60 5.7 Summary ................................ 61 Part II General Optimization Modeling Tricks 63 6 Linear Programming Tricks 63 6.1 Absolute values ............................ 63 6.2 A minimax objective ......................... 66 6.3 A fractional objective ......................... 67 6.4 A range constraint ........................... 68 6.5 A constraint with unknown-but-bounded coefficients ..... 69 6.6 A probabilistic constraint ...................... 71 6.7 Summary ................................ 74 7 Integer Linear Programming Tricks 75 7.1 A variable taking discontinuous values .............. 75 7.2 Fixedcosts ............................... 76 7.3 Either-or constraints ......................... 77 7.4 Conditional constraints ....................... 79 7.5 Special Ordered Sets ......................... 80 7.6 Piecewise linear formulations .................... 81 7.7 Elimination of products
Load more

Recommended publications
  • Specifying “Logical” Conditions in AMPL Optimization Models
    Specifying “Logical” Conditions in AMPL Optimization Models Robert Fourer AMPL Optimization www.ampl.com — 773-336-AMPL INFORMS Annual Meeting Phoenix, Arizona — 14-17 October 2012 Session SA15, Software Demonstrations Robert Fourer, Logical Conditions in AMPL INFORMS Annual Meeting — 14-17 Oct 2012 — Session SA15, Software Demonstrations 1 New and Forthcoming Developments in the AMPL Modeling Language and System Optimization modelers are often stymied by the complications of converting problem logic into algebraic constraints suitable for solvers. The AMPL modeling language thus allows various logical conditions to be described directly. Additionally a new interface to the ILOG CP solver handles logic in a natural way not requiring conventional transformations. Robert Fourer, Logical Conditions in AMPL INFORMS Annual Meeting — 14-17 Oct 2012 — Session SA15, Software Demonstrations 2 AMPL News Free AMPL book chapters AMPL for Courses Extended function library Extended support for “logical” conditions AMPL driver for CPLEX Opt Studio “Concert” C++ interface Support for ILOG CP constraint programming solver Support for “logical” constraints in CPLEX INFORMS Impact Prize to . Originators of AIMMS, AMPL, GAMS, LINDO, MPL Awards presented Sunday 8:30-9:45, Conv Ctr West 101 Doors close 8:45! Robert Fourer, Logical Conditions in AMPL INFORMS Annual Meeting — 14-17 Oct 2012 — Session SA15, Software Demonstrations 3 AMPL Book Chapters now free for download www.ampl.com/BOOK/download.html Bound copies remain available purchase from usual
    [Show full text]
  • A Practical Guide to Robust Optimization
    A Practical Guide to Robust Optimization Bram L. Gorissen, Ihsan Yanıkoğlu, Dick den Hertog Tilburg University, Department of Econometrics and Operations Research, 5000 LE Tilburg, Netherlands {b.l.gorissen,d.denhertog}@tilburguniversity.edu, [email protected] Abstract Robust optimization is a young and active research field that has been mainly developed in the last 15 years. Robust optimization is very useful for practice, since it is tailored to the information at hand, and it leads to computationally tractable formulations. It is therefore remarkable that real-life applications of robust optimization are still lagging behind; there is much more potential for real-life applications than has been exploited hitherto. The aim of this paper is to help practitioners to understand robust optimization and to successfully apply it in practice. We provide a brief introduction to robust optimization, and also describe important do’s and don’ts for using it in practice. We use many small examples to illustrate our discussions. 1 Introduction Real-life optimization problems often contain uncertain data. Data can be inherently stochas- tic/random or it can be uncertain due to errors. The reasons for data errors could be measure- ment/estimation errors that come from the lack of knowledge of the parameters of the mathematical model (e.g., the uncertain demand in an inventory model) or could be implementation errors that come from the physical impossibility to exactly implement a computed solution in a real-life set- ting. There are two approaches to deal with data uncertainty in optimization, namely robust and stochastic optimization. Stochastic optimization (SO) has an important assumption, i.e., the true probability distribution of uncertain data has to be known or estimated.
    [Show full text]
  • AIMMS 4 Release Notes
    AIMMS 4 Release Notes Visit our web site www.aimms.com for regular updates Contents Contents 2 1 System Requirements 3 1.1 Hardware and operating system requirements ......... 3 1.2 ODBC and OLE DB database connectivity issues ........ 4 1.3 Viewing help files and documentation .............. 5 2 Installation Instructions 7 2.1 Installation instructions ....................... 7 2.2 Solver availability per platform ................... 8 2.3 Aimms licensing ............................ 9 2.3.1 Personal and machine nodelocks ............. 9 2.3.2 Installing an Aimms license ................ 12 2.3.3 Managing Aimms licenses ................. 14 2.3.4 Location of license files ................... 15 2.4 OpenSSL license ............................ 17 3 Project Conversion Instructions 20 3.1 Conversion of projects developed in Aimms 3.13 and before 20 3.2 Conversionof Aimms 3 projects to Aimms 4 ........... 22 3.2.1 Data management changes in Aimms 4.0 ........ 24 4 Getting Support 27 4.1 Reporting a problem ......................... 27 4.2 Known and reported issues ..................... 28 5 Release Notes 29 What’s new in Aimms 4 ........................ 29 Chapter 1 System Requirements This chapter discusses the system requirements necessary to run the various System components of your Win32 Aimms 4 system successfully. When a particular requirements requirement involves the installation of additional system software compo- nents, or an update thereof, the (optional) installation of such components will be part of the Aimms installation procedure. 1.1 Hardware and operating system requirements The following list provides the minimum hardware requirements to run your Hardware Aimms 4 system. requirements 1.6 Ghz or higher x86 or x64 processor XGA display adapter and monitor 1 Gb RAM 1 Gb free disk space Note, however, that performance depends on model size and type and can vary.
    [Show full text]
  • Distributionally Robust Optimization for Engineering Design Under Uncertainty
    Distributionally Robust Optimization for Engineering Design under Uncertainty Michael G. Kapteyn∗ Massachusetts Institute of Technology, Cambridge, MA 02139, USA Karen E. Willcoxy The University of Texas at Austin, Austin, TX 78712, USA Andy B. Philpottz The University of Auckland, Auckland 1010, New Zealand This paper addresses the challenge of design optimization under uncertainty when the de- signer only has limited data to characterize uncertain variables. We demonstrate that the error incurred when estimating a probability distribution from limited data affects the out- of-sample performance (i.e., performance under the true distribution) of optimized designs. We demonstrate how this can be mitigated by reformulating the engineering design prob- lem as a distributionally robust optimization (DRO) problem. We present computationally efficient algorithms for solving the resulting DRO problem. The performance of the DRO approach is explored in a practical setting by applying it to an acoustic horn design prob- lem. The DRO approach is compared against traditional approaches to optimization under uncertainty, namely, sample-average approximation and a multi-objective optimization in- corporating a risk reduction objective. In contrast with the multi-objective approach, the proposed DRO approach does not use an explicit risk reduction objective but rather speci- fies a so-called ambiguity set of possible distributions, and optimizes against the worst-case distribution in this set. Our results show that the DRO designs in some cases significantly outperform those designs found using the sample-average or multi-objective approaches. I. Introduction The importance of considering the nature of the uncertain parameters in engineering design has long been established,1{3 the primary reason being that simply considering all parameters to be deterministic tends to over-fit designs to the chosen parameter values.
    [Show full text]
  • Spatially Explicit Techno-Economic Optimisation Modelling of UK Heating Futures
    Spatially explicit techno-economic optimisation modelling of UK heating futures A thesis submitted in fulfilment of the requirements for the Degree of Doctor of Philosophy UCL Energy Institute University College London Date: 3rd April 2013 Candidate: Francis Li Supervisors: Robert Lowe, Mark Barrett I, Francis Li, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. Francis Li, 3rd April 2013 2 For Eugenia 3 Abstract This thesis describes the use of a spatially explicit model to investigate the economies of scale associated with district heating technologies and consequently, their future technical potential when compared against individual building heating. Existing energy system models used for informing UK technology policy do not employ high enough spatial resolutions to map district heating potential at the individual settlement level. At the same time, the major precedent studies on UK district heating potential have not explored future scenarios out to 2050 and have a number of relevant low-carbon heat supply technologies absent from their analyses. This has resulted in cognitive dissonance in UK energy policy whereby district heating is often simultaneously acknowledged as both highly desirable in the near term but ultimately lacking any long term future. The Settlement Energy Demand System Optimiser (SEDSO) builds on key techno-economic studies from the last decade to further investigate this policy challenge. SEDSO can be distinguished from other models used for investigating UK heat decarbonisation by employing a unique combination of extensive spatial detail, technical modelling which captures key cost-related nonlinearities, and a least-cost constrained optimisation approach to technology selection.
    [Show full text]
  • AIMMS 4 Linux Release Notes
    AIMMS 4 Portable component Linux Intel version Release Notes for Linux Visit our web site www.aimms.com for regular updates Contents Contents 2 1 System Overview of the Intel Linux Aimms Component 3 1.1 Hardware and operating system requirements ......... 3 1.2 Feature comparison with the Win32/Win64 version ...... 3 2 Installation and Usage 5 2.1 Installation instructions ....................... 5 2.2 Solver availability per platform ................... 6 2.3 Licensing ................................ 6 2.4 Usage of the portable component ................. 10 2.5 The Aimms command line tool ................... 10 3 Getting Support 13 3.1 Reporting a problem ......................... 13 3.2 Known and reported issues ..................... 14 4 Release Notes 15 What’s new in Aimms 4 ........................ 15 Chapter 1 System Overview of the Intel Linux Aimms Component This chapter discusses the system requirements necessary to run the portable System Intel Linux Aimms component. The chapter also contains a feature comparison overview with the regular Windows version of Aimms. 1.1 Hardware and operating system requirements The following list of hardware and software requirements applies to the por- Hardware table Intel x64 Linux Aimms 4 component release. requirements Linux x64 Intel x64 compatible system Centos 6, Red Hat 6, or Ubuntu 12.04 Linux operating system 1 Gb RAM 1 Gb free disk space Note, however, that performance depends on model size and type and can Performance vary. It can also be affected by the number of other applications that are running concurrently with Aimms. In cases of a (regular) performance drop of either Aimms or other applications you are advised to install sufficiently additional RAM.
    [Show full text]
  • Notes 1: Introduction to Optimization Models
    Notes 1: Introduction to Optimization Models IND E 599 September 29, 2010 IND E 599 Notes 1 Slide 1 Course Objectives I Survey of optimization models and formulations, with focus on modeling, not on algorithms I Include a variety of applications, such as, industrial, mechanical, civil and electrical engineering, financial optimization models, health care systems, environmental ecology, and forestry I Include many types of optimization models, such as, linear programming, integer programming, quadratic assignment problem, nonlinear convex problems and black-box models I Include many common formulations, such as, facility location, vehicle routing, job shop scheduling, flow shop scheduling, production scheduling (min make span, min max lateness), knapsack/multi-knapsack, traveling salesman, capacitated assignment problem, set covering/packing, network flow, shortest path, and max flow. IND E 599 Notes 1 Slide 2 Tentative Topics Each topic is an introduction to what could be a complete course: 1. basic linear models (LP) with sensitivity analysis 2. integer models (IP), such as the assignment problem, knapsack problem and the traveling salesman problem 3. mixed integer formulations 4. quadratic assignment problems 5. include uncertainty with chance-constraints, stochastic programming scenario-based formulations, and robust optimization 6. multi-objective formulations 7. nonlinear formulations, as often found in engineering design 8. brief introduction to constraint logic programming 9. brief introduction to dynamic programming IND E 599 Notes 1 Slide 3 Computer Software I Catalyst Tools (https://catalyst.uw.edu/) I AIMMS - optimization software (http://www.aimms.com/) Ming Fang - AIMMS software consultant IND E 599 Notes 1 Slide 4 What is Mathematical Programming? Mathematical programming refers to \programming" as a \planning" activity: as in I linear programming (LP) I integer programming (IP) I mixed integer linear programming (MILP) I non-linear programming (NLP) \Optimization" is becoming more common, e.g.
    [Show full text]
  • Robust and Data-Driven Optimization: Modern Decision-Making Under Uncertainty
    Robust and Data-Driven Optimization: Modern Decision-Making Under Uncertainty Dimtris Bertsimas¤ Aur¶elieThieley March 2006 Abstract Traditional models of decision-making under uncertainty assume perfect information, i.e., ac- curate values for the system parameters and speci¯c probability distributions for the random variables. However, such precise knowledge is rarely available in practice, and a strategy based on erroneous inputs might be infeasible or exhibit poor performance when implemented. The purpose of this tutorial is to present a mathematical framework that is well-suited to the limited information available in real-life problems and captures the decision-maker's attitude towards uncertainty; the proposed approach builds upon recent developments in robust and data-driven optimization. In robust optimization, random variables are modeled as uncertain parameters be- longing to a convex uncertainty set and the decision-maker protects the system against the worst case within that set. Data-driven optimization uses observations of the random variables as direct inputs to the mathematical programming problems. The ¯rst part of the tutorial describes the robust optimization paradigm in detail in single-stage and multi-stage problems. In the second part, we address the issue of constructing uncertainty sets using historical realizations of the random variables and investigate the connection between convex sets, in particular polyhedra, and a speci¯c class of risk measures. Keywords: optimization under uncertainty; risk preferences; uncertainty sets; linear program- ming. 1 Introduction The ¯eld of decision-making under uncertainty was pioneered in the 1950s by Dantzig [25] and Charnes and Cooper [23], who set the foundation for, respectively, stochastic programming and ¤Boeing Professor of Operations Research, Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA 02139, [email protected] yP.C.
    [Show full text]
  • AIMMS Modeling Guide - Linear Programming Tricks
    AIMMS Modeling Guide - Linear Programming Tricks This file contains only one chapter of the book. For a free download of the complete book in pdf format, please visit www.aimms.com. Aimms 4 Copyright c 1993–2018 by AIMMS B.V. All rights reserved. AIMMS B.V. AIMMS Inc. Diakenhuisweg 29-35 11711 SE 8th Street 2033 AP Haarlem Suite 303 The Netherlands Bellevue, WA 98005 Tel.: +31 23 5511512 USA Tel.: +1 425 458 4024 AIMMS Pte. Ltd. AIMMS 55 Market Street #10-00 SOHO Fuxing Plaza No.388 Singapore 048941 Building D-71, Level 3 Tel.: +65 6521 2827 Madang Road, Huangpu District Shanghai 200025 China Tel.: ++86 21 5309 8733 Email: [email protected] WWW: www.aimms.com Aimms is a registered trademark of AIMMS B.V. IBM ILOG CPLEX and CPLEX is a registered trademark of IBM Corporation. GUROBI is a registered trademark of Gurobi Optimization, Inc. Knitro is a registered trademark of Artelys. Windows and Excel are registered trademarks of Microsoft Corporation. TEX, LATEX, and AMS-LATEX are trademarks of the American Mathematical Society. Lucida is a registered trademark of Bigelow & Holmes Inc. Acrobat is a registered trademark of Adobe Systems Inc. Other brands and their products are trademarks of their respective holders. Information in this document is subject to change without notice and does not represent a commitment on the part of AIMMS B.V. The software described in this document is furnished under a license agreement and may only be used and copied in accordance with the terms of the agreement. The documentation may not, in whole or in part, be copied, photocopied, reproduced, translated, or reduced to any electronic medium or machine-readable form without prior consent, in writing, from AIMMS B.V.
    [Show full text]
  • A New Robust Optimization Approach for Scheduling Under Uncertainty II
    Computers and Chemical Engineering 31 (2007) 171–195 A new robust optimization approach for scheduling under uncertainty II. Uncertainty with known probability distribution Stacy L. Janak, Xiaoxia Lin, Christodoulos A. Floudas∗ Department of Chemical Engineering, Princeton University, Princeton, NJ 08544-5263, USA Received 1 April 2005; received in revised form 3 May 2006; accepted 22 May 2006 Available online 1 August 2006 Abstract In this work, we consider the problem of scheduling under uncertainty where the uncertain problem parameters can be described by a known probability distribution function. A novel robust optimization methodology, originally proposed by Lin, Janak, and Floudas [Lin, X., Janak, S. L., & Floudas, C. A. (2004). A new robust optimization approach for scheduling under uncertainty: I. Bounded uncertainty. Computers and Chemical Engineering, 28, 1069–1085], is extended in order to consider uncertainty described by a known probability distribution. This robust optimization formulation is based on a min–max framework and when applied to mixed-integer linear programming (MILP) problems, produces “robust” solutions that are immune against data uncertainty. Uncertainty is considered in the coefficients of the objective function, as well as the coefficients and right-hand-side parameters of the inequality constraints in MILP problems. Robust optimization techniques are developed for uncertain data described by several known distributions including a uniform distribution, a normal distribution, the difference of two normal distributions, a general discrete distribution, a binomial distribution, and a poisson distribution. The robust optimization formulation introduces a small number of auxiliary variables and additional constraints into the original MILP problem, generating a deterministic robust counterpart problem which provides the optimal/feasible solution given the (relative) magnitude of the uncertain data, a feasibility tolerance, and a reliability level.
    [Show full text]
  • 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.
    [Show full text]
  • AIMMS Tutorial for Beginners - Solving the Model
    AIMMS Tutorial for Beginners - Solving the Model This file contains only one chapter of the book. For a free download of the complete book in pdf format, please visit www.aimms.com Aimms 3.13 Copyright c 1993–2012 by Paragon Decision Technology B.V. All rights reserved. Paragon Decision Technology B.V. Paragon Decision Technology Inc. Schipholweg 1 500 108th Avenue NE 2034 LS Haarlem Ste. # 1085 The Netherlands Bellevue, WA 98004 Tel.: +31 23 5511512 USA Fax: +31 23 5511517 Tel.: +1 425 458 4024 Fax: +1 425 458 4025 Paragon Decision Technology Pte. Ltd. Paragon Decision Technology 55 Market Street #10-00 Shanghai Representative Office Singapore 048941 Middle Huaihai Road 333 Tel.: +65 6521 2827 Shuion Plaza, Room 1206 Fax: +65 6521 3001 Shanghai China Tel.: +86 21 51160733 Fax: +86 21 5116 0555 Email: [email protected] WWW: www.aimms.com ISBN xx–xxxxxx–x–x Aimms is a registered trademark of Paragon Decision Technology B.V. IBM ILOG CPLEX and CPLEX is a registered trademark of IBM Corporation. GUROBI is a registered trademark of Gurobi Optimization, Inc. KNITRO is a registered trademark of Ziena Optimization, Inc. XPRESS-MP is a registered trademark of FICO Fair Isaac Corporation. Mosek is a registered trademark of Mosek ApS. Windows and Excel are registered trademarks of Microsoft Corporation. TEX, LATEX, and AMS-LATEX are trademarks of the American Mathematical Society. Lucida is a registered trademark of Bigelow & Holmes Inc. Acrobat is a registered trademark of Adobe Systems Inc. Other brands and their products are trademarks of their respective holders.
    [Show full text]