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Click to edit Master title style MINLP with Combined Interior Point and Active Set Methods Jose L. Mojica Adam D. Lewis John D. Hedengren Brigham Young University INFORM 2013, Minneapolis, MN Presentation Overview NLP Benchmarking Hock-Schittkowski Dynamic optimization Biological models Combining Interior Point and Active Set MINLP Benchmarking MacMINLP MINLP Model Predictive Control Chiller Thermal Energy Storage Unmanned Aerial Systems Future Developments Oct 9, 2013 APMonitor.com APOPT.com Brigham Young University Overview of Benchmark Testing NLP Benchmark Testing 1 1 2 3 3 min J (x, y,u) APOPT , BPOPT , IPOPT , SNOPT , MINOS x Problem characteristics: s.t. 0 f , x, y,u t Hock Schittkowski, Dynamic Opt, SBML 0 g(x, y,u) Nonlinear Programming (NLP) Differential Algebraic Equations (DAEs) 0 h(x, y,u) n m APMonitor Modeling Language x, y u MINLP Benchmark Testing min J (x, y,u, z) 1 1 2 APOPT , BPOPT , BONMIN x s.t. 0 f , x, y,u, z Problem characteristics: t MacMINLP, Industrial Test Set 0 g(x, y,u, z) Mixed Integer Nonlinear Programming (MINLP) 0 h(x, y,u, z) Mixed Integer Differential Algebraic Equations (MIDAEs) x, y n u m z m APMonitor & AMPL Modeling Language 1–APS, LLC 2–EPL, 3–SBS, Inc. Oct 9, 2013 APMonitor.com APOPT.com Brigham Young University NLP Benchmark – Summary (494) 100 90 80 APOPT+BPOPT APOPT 70 1.0 BPOPT 1.0 60 IPOPT 3.10 IPOPT 50 2.3 SNOPT Percentage (%) 6.1 40 Benchmark Results MINOS 494 Problems 5.5 30 20 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Not worse than 2 times slower than -
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Click to edit Master title style APMonitor Modeling Language John Hedengren Brigham Young University Advanced Process Solutions, LLC http://apmonitor.com Overview of APM Software as a service accessible through: MATLAB, Python, Web-browser interface Linux / Windows / Mac OS / Android platforms Solvers 1 1 2 3 3 APOPT , BPOPT , IPOPT , SNOPT , MINOS Problem characteristics: min J (x, y,u, z) Large-scale x s.t. 0 f , x, y,u, z Nonlinear Programming (NLP) t Mixed Integer NLP (MINLP) 0 g(x, y,u, z) Multi-objective 0 h(x, y,u, z) n m m Real-time systems x, y u z Differential Algebraic Equations (DAEs) 1 – APS, LLC 2 – EPL 3 – SBS, Inc. Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Overview of APM Vector / matrix algebra with set notation Automatic Differentiation st nd Exact 1 and 2 Derivatives Large-scale, sparse systems of equations Object-oriented access Thermo-physical properties Database of preprogrammed models Parallel processing Optimization with uncertain parameters Custom solver or model connections Oct 14, 2012 APMonitor.com Advanced Process Solutions, LLC Unique Features of APM Initialization with nonlinear presolve minJ(x, y,u) x s.t. 0 f ,x, y,u min J (x, y,u) t 0 g(x, y,u) 0h(x, y,u) x minJ(x, y,u) x s.t. 0 f ,x, y,u s.t. 0 f , x, y,u t 0 g(x, y,u) t 0 h(x, y,u) minJ(x, y,u) x s.t. 0 f ,x, y,u t 0g(x, y,u) 0h(x, y,u) 0 g(x, y,u) minJ(x, y,u) x s.t. -
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. -
Treball (1.484Mb)
Treball Final de Màster MÀSTER EN ENGINYERIA INFORMÀTICA Escola Politècnica Superior Universitat de Lleida Mòdul d’Optimització per a Recursos del Transport Adrià Vall-llaura Salas Tutors: Antonio Llubes, Josep Lluís Lérida Data: Juny 2017 Pròleg Aquest projecte s’ha desenvolupat per donar solució a un problema de l’ordre del dia d’una empresa de transports. Es basa en el disseny i implementació d’un model matemàtic que ha de permetre optimitzar i automatitzar el sistema de planificació de viatges de l’empresa. Per tal de poder implementar l’algoritme s’han hagut de crear diversos mòduls que extreuen les dades del sistema ERP, les tracten, les envien a un servei web (REST) i aquest retorna un emparellament òptim entre els vehicles de l’empresa i les ordres dels clients. La primera fase del projecte, la teòrica, ha estat llarga en comparació amb les altres. En aquesta fase s’ha estudiat l’estat de l’art en la matèria i s’han repassat molts dels models més importants relacionats amb el transport per comprendre’n les seves particularitats. Amb els conceptes ben estudiats, s’ha procedit a desenvolupar un nou model matemàtic adaptat a les necessitats de la lògica de negoci de l’empresa de transports objecte d’aquest treball. Posteriorment s’ha passat a la fase d’implementació dels mòduls. En aquesta fase m’he trobat amb diferents limitacions tecnològiques degudes a l’antiguitat de l’ERP i a l’ús del sistema operatiu Windows. També han sorgit diferents problemes de rendiment que m’han fet redissenyar l’extracció de dades de l’ERP, el càlcul de distàncies i el mòdul d’optimització. -
GEKKO Documentation Release 1.0.1
GEKKO Documentation Release 1.0.1 Logan Beal, John Hedengren Aug 31, 2021 Contents 1 Overview 1 2 Installation 3 3 Project Support 5 4 Citing GEKKO 7 5 Contents 9 6 Overview of GEKKO 89 Index 91 i ii CHAPTER 1 Overview GEKKO is a Python package for machine learning and optimization of mixed-integer and differential algebraic equa- tions. It is coupled with large-scale solvers for linear, quadratic, nonlinear, and mixed integer programming (LP, QP, NLP, MILP, MINLP). Modes of operation include parameter regression, data reconciliation, real-time optimization, dynamic simulation, and nonlinear predictive control. GEKKO is an object-oriented Python library to facilitate local execution of APMonitor. More of the backend details are available at What does GEKKO do? and in the GEKKO Journal Article. Example applications are available to get started with GEKKO. 1 GEKKO Documentation, Release 1.0.1 2 Chapter 1. Overview CHAPTER 2 Installation A pip package is available: pip install gekko Use the —-user option to install if there is a permission error because Python is installed for all users and the account lacks administrative priviledge. The most recent version is 0.2. You can upgrade from the command line with the upgrade flag: pip install--upgrade gekko Another method is to install in a Jupyter notebook with !pip install gekko or with Python code, although this is not the preferred method: try: from pip import main as pipmain except: from pip._internal import main as pipmain pipmain(['install','gekko']) 3 GEKKO Documentation, Release 1.0.1 4 Chapter 2. Installation CHAPTER 3 Project Support There are GEKKO tutorials and documentation in: • GitHub Repository (examples folder) • Dynamic Optimization Course • APMonitor Documentation • GEKKO Documentation • 18 Example Applications with Videos For project specific help, search in the GEKKO topic tags on StackOverflow. -
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. -
MP-Opt-Model User's Manual, Version
MP-Opt-Model User's Manual Version 2.1 Ray D. Zimmerman August 25, 2020 © 2020 Power Systems Engineering Research Center (PSerc) All Rights Reserved Contents 1 Introduction6 1.1 Background................................6 1.2 License and Terms of Use........................7 1.3 Citing MP-Opt-Model..........................8 1.4 MP-Opt-Model Development.......................8 2 Getting Started9 2.1 System Requirements...........................9 2.2 Installation................................9 2.3 Sample Usage............................... 10 2.4 Documentation.............................. 14 3 MP-Opt-Model { Overview 15 4 Solver Interface Functions 16 4.1 LP/QP Solvers { qps master ...................... 16 4.1.1 QP Example............................ 19 4.2 MILP/MIQP Solvers { miqps master .................. 20 4.2.1 MILP Example.......................... 22 4.3 NLP Solvers { nlps master ....................... 22 4.3.1 NLP Example 1.......................... 25 4.3.2 NLP Example 2.......................... 26 4.4 Nonlinear Equation Solvers { nleqs master .............. 29 4.4.1 NLEQ Example 1......................... 31 4.4.2 NLEQ Example 2......................... 34 5 Optimization Model Class { opt model 38 5.1 Adding Variables............................. 38 5.1.1 Variable Subsets......................... 39 5.2 Adding Constraints............................ 40 5.2.1 Linear Constraints........................ 40 5.2.2 General Nonlinear Constraints.................. 41 5.3 Adding Costs............................... 42 5.3.1 Quadratic -
Component-Oriented Acausal Modeling of the Dynamical Systems in Python Language on the Example of the Model of the Sucker Rod String
Component-oriented acausal modeling of the dynamical systems in Python language on the example of the model of the sucker rod string Volodymyr B. Kopei, Oleh R. Onysko and Vitalii G. Panchuk Department of Computerized Mechanical Engineering, Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine ABSTRACT Typically, component-oriented acausal hybrid modeling of complex dynamic systems is implemented by specialized modeling languages. A well-known example is the Modelica language. The specialized nature, complexity of implementation and learning of such languages somewhat limits their development and wide use by developers who know only general-purpose languages. The paper suggests the principle of developing simple to understand and modify Modelica-like system based on the general-purpose programming language Python. The principle consists in: (1) Python classes are used to describe components and their systems, (2) declarative symbolic tools SymPy are used to describe components behavior by difference or differential equations, (3) the solution procedure uses a function initially created using the SymPy lambdify function and computes unknown values in the current step using known values from the previous step, (4) Python imperative constructs are used for simple events handling, (5) external solvers of differential-algebraic equations can optionally be applied via the Assimulo interface, (6) SymPy package allows to arbitrarily manipulate model equations, generate code and solve some equations symbolically. The basic set of mechanical components (1D translational “mass”, “spring-damper” and “force”) is developed. The models of a sucker rods string are developed and simulated using these components. The comparison of results of the sucker rod string simulations with practical dynamometer cards and Submitted 22 March 2019 Accepted 24 September 2019 Modelica results verify the adequacy of the models. -
Technical Program
TECHNICAL PROGRAM Wednesday, 9:00-10:30 Wednesday, 11:00-12:40 WA-01 WB-01 Wednesday, 9:00-10:30 - 1a. Europe a Wednesday, 11:00-12:40 - 1a. Europe a Opening session - Plenary I. Ljubic Planning and Operating Metropolitan Passenger Transport Networks Stream: Plenaries and Semi-Plenaries Invited session Stream: Traffic, Mobility and Passenger Transportation Chair: Bernard Fortz Invited session Chair: Oded Cats 1 - From Game Theory to Graph Theory: A Bilevel Jour- ney 1 - Frequency and Vehicle Capacity Determination using Ivana Ljubic a Dynamic Transit Assignment Model In bilevel optimization there are two decision makers, commonly de- Oded Cats noted as the leader and the follower, and decisions are made in a hier- The determination of frequencies and vehicle capacities is a crucial archical manner: the leader makes the first move, and then the follower tactical decision when planning public transport services. All meth- reacts optimally to the leader’s action. It is assumed that the leader can ods developed so far use static assignment approaches which assume anticipate the decisions of the follower, hence the leader optimization average and perfectly reliable supply conditions. The objective of this task is a nested optimization problem that takes into consideration the study is to determine frequency and vehicle capacity at the network- follower’s response. level while accounting for the impact of service variations on users In this talk we focus on new branch-and-cut (B&C) algorithms for and operator costs. To this end, we propose a simulation-based op- dealing with mixed-integer bilevel linear programs (MIBLPs). -
Quadratic Programming Models in Strategic Sourcing Optimization
IT 17 034 Examensarbete 15 hp Juni 2017 Quadratic Programming Models in Strategic Sourcing Optimization Daniel Ahlbom Institutionen för informationsteknologi Department of Information Technology Abstract Quadratic Programming Models in Strategic Sourcing Optimization Daniel Ahlbom Teknisk- naturvetenskaplig fakultet UTH-enheten Strategic sourcing allows for optimizing purchases on a large scale. Depending on the requirements of the client and the offers provided for Besöksadress: them, finding an optimal or even a near-optimal solution can become Ångströmlaboratoriet Lägerhyddsvägen 1 computationally hard. Mixed integer programming (MIP), where the Hus 4, Plan 0 problem is modeled as a set of linear expressions with an objective function for which an optimal solution results in a minimum objective Postadress: value, is particularly suitable for finding competitive results. Box 536 751 21 Uppsala However, given the research and improvements continually being made for quadratic programming (QP), which allows for objective functions with Telefon: quadratic expressions as well, comparing runtimes and objective values 018 – 471 30 03 for finding optimal and approximate solutions is advised: for hard Telefax: problems, applying the correct methods may decrease runtimes by several 018 – 471 30 00 orders of magnitude. In this report, comparisons between MIP and QP models used in four different problems with three different solvers Hemsida: were made, measuring both optimization and approximation performance in http://www.teknat.uu.se/student terms of runtimes and objective values. Experiments showed that while QP holds an advantage over MIP in some cases, it is not consistently efficient enough to provide a significant improvement in comparison with, for example, using a different solver. -
Nonlinear Modeling, Estimation and Predictive Control in Apmonitor
Brigham Young University BYU ScholarsArchive Faculty Publications 2014-11-05 Nonlinear Modeling, Estimation and Predictive Control in APMonitor John Hedengren Brigham Young University, [email protected] Reza Asgharzadeh Shishavan Brigham Young University Kody M. Powell University of Utah Thomas F. Edgar University of Texas at Austin Follow this and additional works at: https://scholarsarchive.byu.edu/facpub Part of the Chemical Engineering Commons BYU ScholarsArchive Citation Hedengren, John; Asgharzadeh Shishavan, Reza; Powell, Kody M.; and Edgar, Thomas F., "Nonlinear Modeling, Estimation and Predictive Control in APMonitor" (2014). Faculty Publications. 1667. https://scholarsarchive.byu.edu/facpub/1667 This Peer-Reviewed Article is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in Faculty Publications by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. Computers and Chemical Engineering 70 (2014) 133–148 Contents lists available at ScienceDirect Computers and Chemical Engineering j ournal homepage: www.elsevier.com/locate/compchemeng Nonlinear modeling, estimation and predictive control in APMonitor a,∗ a b b John D. Hedengren , Reza Asgharzadeh Shishavan , Kody M. Powell , Thomas F. Edgar a Department of Chemical Engineering, Brigham Young University, Provo, UT 84602, United States b The University of Texas at Austin, Austin, TX 78712, United States a r t i c l e i n f o a b s t r a c t Article history: This paper describes nonlinear methods in model building, dynamic data reconciliation, and dynamic Received 10 August 2013 optimization that are inspired by researchers and motivated by industrial applications. -
Datascientist Manual
DATASCIENTIST MANUAL . 2 « Approcherait le comportement de la réalité, celui qui aimerait s’epanouir dans l’holistique, l’intégratif et le multiniveaux, l’énactif, l’incarné et le situé, le probabiliste et le non linéaire, pris à la fois dans l’empirique, le théorique, le logique et le philosophique. » 4 (* = not yet mastered) THEORY OF La théorie des probabilités en mathématiques est l'étude des phénomènes caractérisés PROBABILITY par le hasard et l'incertitude. Elle consistue le socle des statistiques appliqué. Rubriques ↓ Back to top ↑_ Notations Formalisme de Kolmogorov Opération sur les ensembles Probabilités conditionnelles Espérences conditionnelles Densités & Fonctions de répartition Variables aleatoires Vecteurs aleatoires Lois de probabilités Convergences et théorèmes limites Divergences et dissimilarités entre les distributions Théorie générale de la mesure & Intégration ------------------------------------------------------------------------------------------------------------------------------------------ 6 Notations [pdf*] Formalisme de Kolmogorov Phé nomé né alé atoiré Expé riéncé alé atoiré L’univérs Ω Ré alisation éléméntairé (ω ∈ Ω) Evé némént Variablé aléatoiré → fonction dé l’univér Ω Opération sur les ensembles : Union / Intersection / Complémentaire …. Loi dé Augustus dé Morgan ? Independance & Probabilités conditionnelles (opération sur des ensembles) Espérences conditionnelles 8 Variables aleatoires (discret vs reel) … Vecteurs aleatoires : Multiplét dé variablés alé atoiré (discret vs reel) … Loi marginalés Loi