Using the COIN-OR Server
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Xpress Nonlinear Manual This Material Is the Confidential, Proprietary, and Unpublished Property of Fair Isaac Corporation
R FICO Xpress Optimization Last update 01 May, 2018 version 33.01 FICO R Xpress Nonlinear Manual This material is the confidential, proprietary, and unpublished property of Fair Isaac Corporation. Receipt or possession of this material does not convey rights to divulge, reproduce, use, or allow others to use it without the specific written authorization of Fair Isaac Corporation and use must conform strictly to the license agreement. The information in this document is subject to change without notice. If you find any problems in this documentation, please report them to us in writing. Neither Fair Isaac Corporation nor its affiliates warrant that this documentation is error-free, nor are there any other warranties with respect to the documentation except as may be provided in the license agreement. ©1983–2018 Fair Isaac Corporation. All rights reserved. Permission to use this software and its documentation is governed by the software license agreement between the licensee and Fair Isaac Corporation (or its affiliate). Portions of the program may contain copyright of various authors and may be licensed under certain third-party licenses identified in the software, documentation, or both. In no event shall Fair Isaac Corporation or its affiliates be liable to any person for direct, indirect, special, incidental, or consequential damages, including lost profits, arising out of the use of this software and its documentation, even if Fair Isaac Corporation or its affiliates have been advised of the possibility of such damage. The rights and allocation of risk between the licensee and Fair Isaac Corporation (or its affiliates) are governed by the respective identified licenses in the software, documentation, or both. -
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. -
Hydraulic Optimization Demonstration for Groundwater Pump
Figure 5-18: Shallow Particles, Contain Shallow 20-ppb Plume, & 500 gpm for Deep 20-ppb plume (1573 gpm, 3 new wells, 1 existing well) Injection Well Well Layer 1 Well Layer 2 30000 25000 20000 15000 10000 5000 0 0 5000 10000 15000 A "+" symbol indicates that a particle starting at that location is captured by one of the remediation wells, based on particle tracking with MODPATH. Shallow particles originate half-way down in layer 1. Figure 5-19: Deep Particles, Contain Shallow 20-ppb Plume, & 500 gpm for Deep 20-ppb plume (1573 gpm, 3 new wells, 1 existing well) Injection Well Well Layer 1 Well Layer 2 30000 25000 20000 15000 10000 5000 0 0 5000 10000 15000 A "+" symbol indicates that a particle starting at that location is captured by one of the remediation wells, based on particle tracking with MODPATH. Deep particles originate half-way down in layer 2. Figure 5-20: Shallow Particles, Contain Shallow 20-ppb & 50-ppb Plumes, & 500 gpm for Deep 20-ppb plume (2620 gpm, 6 new wells, 0 existing wells) Injection Well Well Layer 1 Well Layer 2 30000 25000 20000 15000 10000 5000 0 0 5000 10000 15000 A "+" symbol indicates that a particle starting at that location is captured by one of the remediation wells, based on particle tracking with MODPATH. Shallow particles originate half-way down in layer 1. Figure 5-21: Deep Particles, Contain Shallow 20-ppb & 50-ppb Plumes, & 500 gpm for Deep 20-ppb plume (2620 gpm, 6 new wells, 0 existing wells) Injection Well Well Layer 1 Well Layer 2 30000 25000 20000 15000 10000 5000 0 0 5000 10000 15000 A "+" symbol indicates that a particle starting at that location is captured by one of the remediation wells, based on particle tracking with MODPATH. -
SDDP.Jl: a Julia Package for Stochastic Dual Dynamic Programming
Optimization Online manuscript No. (will be inserted by the editor) SDDP.jl: a Julia package for Stochastic Dual Dynamic Programming Oscar Dowson · Lea Kapelevich Received: date / Accepted: date Abstract In this paper we present SDDP.jl, an open-source library for solving multistage stochastic optimization problems using the Stochastic Dual Dynamic Programming algorithm. SDDP.jl is built upon JuMP, an algebraic modelling lan- guage in Julia. This enables a high-level interface for the user, while simultaneously providing performance that is similar to implementations in low-level languages. We benchmark the performance of SDDP.jl against a C++ implementation of SDDP for the New Zealand Hydro-Thermal Scheduling Problem. On the bench- mark problem, SDDP.jl is approximately 30% slower than the C++ implementa- tion. However, this performance penalty is small when viewed in context of the generic nature of the SDDP.jl library compared to the single purpose C++ imple- mentation. Keywords julia · stochastic dual dynamic programming 1 Introduction Solving any mathematical optimization problem requires four steps: the formula- tion of the problem by the user; the communication of the problem to the com- puter; the efficient computational solution of the problem; and the communication of the computational solution back to the user. Over time, considerable effort has been made to improve each of these four steps for a variety of problem classes such linear, quadratic, mixed-integer, conic, and non-linear. For example, con- sider the evolution from early file-formats such as MPS [25] to modern algebraic modelling languages embedded in high-level languages such as JuMP [11], or the 73-fold speed-up in solving difficult mixed-integer linear programs in seven years by Gurobi [16]. -
ILOG AMPL CPLEX System Version 10.0 User's Guide
ILOG AMPL CPLEX System Version 10.0 User’s Guide Standard (Command-line) Version Including CPLEX Directives January 2006 COPYRIGHT NOTICE Copyright © 1987-2006, by ILOG S.A., 9 Rue de Verdun, 94253 Gentilly Cedex, France, and ILOG, Inc., 1080 Linda Vista Ave., Mountain View, California 94043, USA. All rights reserved. General Use Restrictions This document and the software described in this document are the property of ILOG and are protected as ILOG trade secrets. They are furnished under a license or nondisclosure agreement, and may be used or copied only within the terms of such license or nondisclosure agreement. No part of this work may be reproduced or disseminated in any form or by any means, without the prior written permission of ILOG S.A, or ILOG, Inc. Trademarks 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. All other company and product names are trademarks or registered trademarks of their respective holders. Java 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 United States and other countries. document version 10.0 CO N T E N T S Table of Contents Chapter 1 Welcome to AMPL . 9 Using this Guide. .9 Installing AMPL . .10 Requirements. .10 Unix Installation . .10 Windows Installation . .11 AMPL and Parallel CPLEX. -
Polyhedral Outer Approximations in Convex Mixed-Integer Nonlinear
Jan Kronqvist Polyhedral Outer Approximations in Polyhedral Outer Approximations in Convex Mixed-Integer Nonlinear Programming Approximations in Convex Polyhedral Outer Convex Mixed-Integer Nonlinear Programming Jan Kronqvist PhD Thesis in Process Design and Systems Engineering Dissertations published by Process Design and Systems Engineering ISSN 2489-7272 Faculty of Science and Engineering 978-952-12-3734-8 Åbo Akademi University 978-952-12-3735-5 (pdf) Painosalama Oy Åbo 2018 Åbo, Finland 2018 2018 Polyhedral Outer Approximations in Convex Mixed-Integer Nonlinear Programming Jan Kronqvist PhD Thesis in Process Design and Systems Engineering Faculty of Science and Engineering Åbo Akademi University Åbo, Finland 2018 Dissertations published by Process Design and Systems Engineering ISSN 2489-7272 978-952-12-3734-8 978-952-12-3735-5 (pdf) Painosalama Oy Åbo 2018 Preface My time as a PhD student began back in 2014 when I was given a position in the Opti- mization and Systems Engineering (OSE) group at Åbo Akademi University. It has been a great time, and many people have contributed to making these years a wonderful ex- perience. During these years, I was given the opportunity to teach several courses in both environmental engineering and process systems engineering. The opportunity to teach these courses has been a great experience for me. I want to express my greatest gratitude to my supervisors Prof. Tapio Westerlund and Docent Andreas Lundell. Tapio has been a true source of inspiration and a good friend during these years. Thanks to Tapio, I have been able to be a part of an inter- national research environment. -
Performance of Optimization Software - an Update
Performance of Optimization Software - an Update INFORMS Annual 2011 Charlotte, NC 13-18 November 2011 H. D. Mittelmann School of Math and Stat Sciences Arizona State University 1 Services we provide • Guide to Software: "Decision Tree" • http://plato.asu.edu/guide.html • Software Archive • Software Evaluation: "Benchmarks" • Archive of Testproblems • Web-based Solvers (1/3 of NEOS) 2 We maintain the following NEOS solvers (8 categories) Combinatorial Optimization * CONCORDE [TSP Input] Global Optimization * ICOS [AMPL Input] Linear Programming * bpmpd [AMPL Input][LP Input][MPS Input][QPS Input] Mixed Integer Linear Programming * FEASPUMP [AMPL Input][CPLEX Input][MPS Input] * SCIP [AMPL Input][CPLEX Input][MPS Input] [ZIMPL Input] * qsopt_ex [LP Input][MPS Input] [AMPL Input] Nondifferentiable Optimization * condor [AMPL Input] Semi-infinite Optimization * nsips [AMPL Input] Stochastic Linear Programming * bnbs [SMPS Input] * DDSIP [LP Input][MPS Input] 3 We maintain the following NEOS solvers (cont.) Semidefinite (and SOCP) Programming * csdp [MATLAB_BINARY Input][SPARSE_SDPA Input] * penbmi [MATLAB Input][MATLAB_BINARY Input] * pensdp [MATLAB_BINARY Input][SPARSE_SDPA Input] * sdpa [MATLAB_BINARY Input][SPARSE_SDPA Input] * sdplr [MATLAB_BINARY Input][SDPLR Input][SPARSE_SDPA Input] * sdpt3 [MATLAB_BINARY Input][SPARSE_SDPA Input] * sedumi [MATLAB_BINARY Input][SPARSE_SDPA Input] 4 Overview of Talk • Current and Selected(*) Benchmarks { Parallel LP benchmarks { MILP benchmark (MIPLIB2010) { Feasibility/Infeasibility Detection benchmarks -
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. -
Julia: a Modern Language for Modern ML
Julia: A modern language for modern ML Dr. Viral Shah and Dr. Simon Byrne www.juliacomputing.com What we do: Modernize Technical Computing Today’s technical computing landscape: • Develop new learning algorithms • Run them in parallel on large datasets • Leverage accelerators like GPUs, Xeon Phis • Embed into intelligent products “Business as usual” will simply not do! General Micro-benchmarks: Julia performs almost as fast as C • 10X faster than Python • 100X faster than R & MATLAB Performance benchmark relative to C. A value of 1 means as fast as C. Lower values are better. A real application: Gillespie simulations in systems biology 745x faster than R • Gillespie simulations are used in the field of drug discovery. • Also used for simulations of epidemiological models to study disease propagation • Julia package (Gillespie.jl) is the state of the art in Gillespie simulations • https://github.com/openjournals/joss- papers/blob/master/joss.00042/10.21105.joss.00042.pdf Implementation Time per simulation (ms) R (GillespieSSA) 894.25 R (handcoded) 1087.94 Rcpp (handcoded) 1.31 Julia (Gillespie.jl) 3.99 Julia (Gillespie.jl, passing object) 1.78 Julia (handcoded) 1.2 Those who convert ideas to products fastest will win Computer Quants develop Scientists prepare algorithms The last 25 years for production (Python, R, SAS, DEPLOY (C++, C#, Java) Matlab) Quants and Computer Compress the Scientists DEPLOY innovation cycle collaborate on one platform - JULIA with Julia Julia offers competitive advantages to its users Julia is poised to become one of the Thank you for Julia. Yo u ' v e k i n d l ed leading tools deployed by developers serious excitement. -
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. -
Arxiv:1804.07332V1 [Math.OC] 19 Apr 2018
Juniper: An Open-Source Nonlinear Branch-and-Bound Solver in Julia Ole Kr¨oger,Carleton Coffrin, Hassan Hijazi, Harsha Nagarajan Los Alamos National Laboratory, Los Alamos, New Mexico, USA Abstract. Nonconvex mixed-integer nonlinear programs (MINLPs) rep- resent a challenging class of optimization problems that often arise in engineering and scientific applications. Because of nonconvexities, these programs are typically solved with global optimization algorithms, which have limited scalability. However, nonlinear branch-and-bound has re- cently been shown to be an effective heuristic for quickly finding high- quality solutions to large-scale nonconvex MINLPs, such as those arising in infrastructure network optimization. This work proposes Juniper, a Julia-based open-source solver for nonlinear branch-and-bound. Leverag- ing the high-level Julia programming language makes it easy to modify Juniper's algorithm and explore extensions, such as branching heuris- tics, feasibility pumps, and parallelization. Detailed numerical experi- ments demonstrate that the initial release of Juniper is comparable with other nonlinear branch-and-bound solvers, such as Bonmin, Minotaur, and Knitro, illustrating that Juniper provides a strong foundation for further exploration in utilizing nonlinear branch-and-bound algorithms as heuristics for nonconvex MINLPs. 1 Introduction Many of the optimization problems arising in engineering and scientific disci- plines combine both nonlinear equations and discrete decision variables. Notable examples include the blending/pooling problem [1,2] and the design and opera- tion of power networks [3,4,5] and natural gas networks [6]. All of these problems fall into the class of mixed-integer nonlinear programs (MINLPs), namely, minimize: f(x; y) s.t.