nonlinear continuous and mixed-integer nonlinear programming · joseph-sommer-straße 34, 41812...

GOR-Arbeitsgruppe: Praxis der

Mathematischen Optimierung

Prof. Dr. Josef Kallrath,

Am Mahlstein 8

D-67273 Weisenheim am Berg

Tel: +49 172 747-0689

Fax: +49 621 60-6678297

Joseph-Sommer-Straße 34, 41812 Erkelenz, Tel.: 02431 9026710, Fax: 02431 9026711

Herewith, we invite you to the 97th meeting of the GOR working group “Real World Mathematical Optimization” in the Physikzentrum Bad Honnef (Hauptstr. 5, 53604 Bad Honnef, http://www.pbh.de). This meeting is hold as a symposium with the topic

Nonlinear Continuous and Mixed-Integer Nonlinear Programming

The two day workshop will be held on November, 24th and 25th in 2016. The working language will be preferably English, since some speakers or participants are expected from abroad. Please note that the participation in a GOR-AG-Workshop for non-members is subject to a registration fee, unless you are a speaker or a host. Please register yourself online using https://www.redseat.de/pmo97/ as soon as possible, but ideally not later than Nov 21st, 2016. The latest information on the meeting is available on the homepage of the GOR (https://gor.uni-paderborn.de/index.php?id=54).

Yours sincerely, Josef Kallrath & Steffen Rebennack (GOR AG) (Colorado School of Mines) Vorstand: Bürozeiten: Bankverbindung: Prof. Dr. B. Werners (Vorsitz) Dienstag bis Freitag von 10 bis 13 Uhr Sparkasse Bochum Dr. Ralph Grothmann (Finanzen) E-mail: Konto-Nr. 1 465 160 Prof. Dr. Stefan Nickel (Tagungen) [email protected] BLZ 430 500 01 Prof. Dr. Lena Suhl (Arbeitsgruppen) URL: http://www.gor-online.de

Nonlinear Continuous and Mixed-Integer Nonlinear Programming

This symposium is about real world optimization problems leading to NLP or MINLP formulations. This two-day event attempts to give an overview of the current state-of-the-art of mathematical optimization techniques to treat such nonlinear optimization problems. Please contact Steffen Rebennack ([email protected]) or myself if you are interested to contribute a talk or a presentation. In talks, each approx. 15+5, 25+5, or 40+5 minutes, experts from practice, research institutions or software companies, will present selected problems and the corresponding solutions. The following presentations have been confirmed (in alphabetic order): Radu Baltean-Lugojan (Imperial College London, London, UK) A Parametric Approach to Solving the Pooling Problem Prof. Dr. Josef Kallrath (GOR Working Group, Weisenheim am Berg, Germany) Nonlinear, Con-convex Cutting Stock and Packing Problems Prof. Dr. Oliver Kolb (University of Mannheim, Mannheim, Germany) Modeling, Simulation and Optimization on Networks Sascha Kuhnke, M.Sc. (RWTH Aachen University, Aachen, Germany) An Adaptive Discretization Algorithm for the Waste Water Network Design and Operation Problem Dr. Thomas Lehmann (Siemens AG, Erlangen, Germany) Mixed Integer Quadratically Constrained Optimization Problems in Energy Management Applications for Electro-Thermal Networks Dipl.-Math. Ralf Lenz (Zuse Institute Berlin, Berlin, Germany) Applications of MINLP to Gas Network Optimization Benjamin Müller (Zuse Institute Berlin, Berlin, Germany) A Branch-and-Price Algorithm for the Recursive Circle Packing Problem Prof. Dr. Klaus Schittkowski (Eckersdorf, Germany) A Trust-Region-SQP Algorithm for Mixed-Integer Nonlinear Programming


97. Meeting of the GOR Working Group

„Real World Mathematical Optimization“

Nonlinear Continuous and

Mixed-Integer Nonlinear Programming

Physikzentrum, Bad Honnef, November 24 & 25, 2016

Thursday, Nov 24 - 2016: 10:00 – 22:00

10:00-10:15 Opening and Welcome Session (J. Kallrath)

10:15-11:05 Prof. Dr. Klaus Klaus Schittkowski (Eckersdorf, Germany) A Trust-Region-SQP Algorithm for Mixed-Integer Nonlinear Programming

11:05-11:25 ------------------------------ Coffee Break -----------------------------------

11:25-12:15 Dr. Thomas Lehmann (Siemens AG, Erlangen, Germany) Mixed Integer Quadratically Constrained Optimization Problems in Energy Management Applications for Electro-Thermal Networks

12:15-13:55 ------------------------------ Lunch Break ----------------------------------- 14:00-14:50 Prof. Dr. Josef Kallrath (GOR Working Group, Weisenheim am Berg,

Germany) Nonlinear, Con-convex Cutting Stock and Packing Problems

14:50-15:40 Benjamin Müller (Zuse Institute Berlin, Berlin, Germany)

A Branch-and-Price Algorithm for the Recursive Circle Packing Problem

15:40-16:00 ------------------------------ Coffee Break -----------------------------------

16:00-16:50 ---------------- Extended Break for Discussions --------------------- 16:50-17:30 N.N.

tbA

17:30-17:50 Internal Meeting of the Working Group 18:00 - Conference Dinner – Buffet; get-together in the wine-cellar

Celebrating the 97th meeting of our GOR Working Group


Friday, Nov 25 - 2016: 09:30 – 16:30 09:30-10:20 Dipl.-Math. Ralf Lenz (Zuse Institute Berlin, Berlin, Germany) Applications of MINLP to Gas Network Optimization 10:20-10:50 ------------------------------ Coffee Break ---------------------------------

10:50-11:40 Sascha Kuhnke, M.Sc. (RWTH Aachen University, Aachen, Germany)

An Adaptive Discretization Algorithm for the Waste Water Network Design and Operation Problem

11:40-12:30 Prof. Dr. Oliver Kolb (University of Mannheim, Mannheim, Germany)

Modeling, Simulation and Optimization on Networks 12:30-13:45 ------------------------------ Lunch Break ----------------------------------

13:45-14:35 Radu Baltean-Lugojan (Imperial College London, London, UK) A Parametric Approach to Solving the Pooling Problem

14:35-14:50 ------------------------------ Coffee Break ---------------------------------

14:50-15:40 N.N.

tBA

16:00 Final Discussion – End of the Workshop – Coffee Break

The Speakers

Radu Baltean-Lugojan is a Ph.D. student at Imperial College London, UK, under the su-pervision of Prof. Dr. Ruth Misener. Previously, he has worked in quantitative and tradingroles within J.P. Morgan and Intercontinental Exchange (systematic strategies, exotic deriva-tives pricing and trading). His research interests involve large-scale global optimization usingproblem structure, appearing in topological (optimization on networks) or model-based forms.

Josef Kallrath obtained his PhD in astrophysics from Bonn University (Germany) in 1989.He is professor at the University of (Gainesville, FL, www.astro.ufl.edu/∼kallrath), and solvesreal-world problems in industry using a broad spectrum of methods in scientific computing,from modeling physical systems to supporting decisions processes by mathematical optimiza-tion. He has written review articles on the subject, about 70 research papers in astronomyand applied mathematics, and several books on mixed integer optimization, as well as oneon eclipsing binary stars.

He leads the Real World Optimization Working Group of the German Operations ResearchSociety. His current research interests are polylithic modeling and solution approaches to solvelarge-scale or difficult optimization problems, for instance, by decomposition techniques suchas column generation, or hybrid methods.

Oliver Kolb is assistant professor for Applied Mathematics at the University of Mannheim.He holds a diploma in Mathematics and a PhD from Technical University of Darmstadt.His research interests include numerical schemes for partial differential equations, nonlinearand mixed integer linear programming, and uncertainty quantification. In particular, he isworking on simulation and optimization software for a variety of problems on networks -especially the daily operation of gas and water supply networks.

Sascha Kuhnke is a scientific employee and Ph.D. student at RWTH Aachen University,Germany, supervised by Prof. Dr. Arie Koster. He received his master’s degree in mathemat-ics in 2016 from University of Cologne, Germany. His current research interests are in mixedinteger nonlinear programming (MINLP), particularly with applications in water allocationproblems.

Ralf Lenz is a scientific employee and PhD Student at the Zuse Institute Berlin. Currentlyhe is involved with the research project GasLab in cooperation with the German gas trans-mission operator Open Grid Europe GmbH within the research organisation “MathematicalOptimization and Data Analysis Laboratories”. He is also a co-author of the book “Evaluat-ing Gas Network Capacities”, which appears in the MOS-SIAM Series on Optimization. Hismain research interest focuses are on MINLP and large scale problems occuring in real worldapplications.

Benjamin Muller is a Ph.D. student at the Zuse Institute Berlin, Germany. He is a maindeveloper of the constraint integer programming and branch-cut-and-price framework SCIPand the linear programming solver SoPlex. His research interests include separation andpropagation techniques for general mixed integer nonlinear programming, and packing appli-cations in tube industry.

Klaus Schittkowki is retired professor of the University of Bayreuth, Germany, Departmentof Computer Science. His main research area is nonlinear optimization, especially SQPmethods for continuous and, since about 10 years, also mixed-integer optimization. Mainfocus has always been the development and numerical tests of efficient and reliable codes foracademic and industrial use.

A Parametric Approach to Solving the Pooling Problem

Radu Baltean-LugojanImperial College London

South Kensington Campus, London SW7 2AZ

e-mail: [email protected]

Standard pooling is an NP-hard, non-convex blending problem that arises in process networksapplications such as crude oil scheduling and more widely as a general problem pattern[Ceccon et al., AIChE J, 2016]. Unfortunately, state-of-the-art general solvers do not scalewell to large-scale instances of the problem which are commercially-relevant.

In this talk we introduce an algorithm that solves specialized pooling problem instances toglobal optimality and integrate it within a Branch and Bound framework for more genericinstances. The approach parameterizes the optimization problem with respect to the poolconcentration variables and uncovers embedded sparsity and polyhedral/topological proper-ties for a variety of instances. We generalize and extend recent work analyzing the compu-tational complexity of the pooling problem [Haugland, J Glob Optim, 2016; Boland et al.,J Glob Optim, 2016; Haugland and Hendrix, J Optim Theory Appl, 2016]. Our analysisalso integrates source-to-output streams and both upper and lower bounds on the networkparameters. This talk is based on joint work with Prof. Dr. Ruth Misener.

Nonlinear, Con-convex Cutting Stock and Packing Problems

Josef KallrathGOR Arbeitsgruppe

Praxis der mathematischen Optimierung

Am Mahlstein 8, 67273 Weisenheim am Berg, Germany


Cutting problems occur in in the paper and metalls industry, packing problems in transportlogistics. The pulp and paper industry plays an important role worldwide. There are inthe order of 3000 paper mills, which produced a total of 394 million tons of paper andpaperboard, in 2010. Europe (including Russia) has approximately 900 paper mills, whileGermany has about 180. The largest producer in the world is the Finnish UPM group with anannual tonnage of 12.7 million tonnes, followed by Stora Enso with 11.8 million tons and byInternational Paper with 9.7 million tonnes per year. In Portugal the pulp and paper industrycontributes over 4% of the GDP and 5% of the active employees. As it is subject of bothlocal and global environmental discussions, effective planning and cutting stock techniqueslies at the very heart of the operational performance of its manufacturing organizations.

Exact solution approaches and heuristics have been used for decades to support cutting stockdecisions in the paper industry. In the standard cutting stock problem, the input data consistof a set of item sizes and demands, and of a set of master rolls of given widths; the simplestcase consists of only one type of master rolls. The task is to decide on how many master rollsare cut to a certain pattern in order to minimize the total number of master rolls used. ThisMINLP problem is usually solved by column generation.

We present various examples related to 1D-role or 2D-format production solved by exactmethods such as column generation or wider polylithic modeling and solution approaches.

As an example from the metals industry we present the following example. A set of circles,rectangles, and convex polygons are to be cut from rectangular design plates to be producedor from a set of stocked rectangles of known geometric dimensions. The objective is tominimize the area of the design rectangles subject to lower and upper bounds of their widthsand lengths. The objects are free of any orientation restrictions.

If all nested objects fit into one design or stocked plate the problem is formulated and solvedas a nonconvex nonlinear programming problem. If the number of objects cannot be cut fromone plate, additional integer variables are needed to represent the allocation problem leadingto a nonconvex mixed integer nonlinear optimization problem.

As a natural extention of this problem, is to cut a set of given ellipses from minimal arearectangles. The 2D problem with ellipses find its natural extension in packing 3D ellipsoidsfor which, in 2015 we were the first to find a closed NLP formulation.

Keywords: Global Optimization, mixed integer programming, cutting stock, packing, shapeconstraints, non-overlap constraints, design problem, assignment packing ellipsoids.

Modeling, simulation and optimization on networks

Oliver KolbUniversity of Mannheim

Department of Mathematics


In this talk we consider several applications on networks within a unified simulation andoptimization framework, in particular the daily operation of gas and water supply networksand road traffic. Based on the underlying macroscopic models, we first apply appropriatediscretization schemes to each problem. To solve optimization tasks, we use an SQP solver andcompute gradient information with a first-discretize adjoint approach. The latter informationcan additionally be exploited for error estimation and an adaptive simulation/optimizationalgorithm. Finally, various numerical results are shown to demonstrate the applicability ofthe presented framework.

An Adaptive Discretization Algorithm for the Waste Water

Network Design and Operation Problem

Sascha KuhnkeRWTH Aachen University

Lehrstuhl II fur Mathematik


The Waste Water Network Design and Operation Problem deals with a flow network wherewater is polluted by different contaminants. The objective is to install and operate watertreatment units to remove contaminants from the water at minimum costs. These regen-eration facilities have to ensure that certain industrial processing units receive water thatis clean enough and that environmental regulations for effluent streams are met. Due tomany bilinear terms, this water allocation problem is a non-convex MINLP and, therefore,nonlinear solvers have difficulties to even find feasible solutions for larger instances.

In this talk, we present an adaptive discretization algorithm for this problem, which approx-imates a solution by iteratively solving discretized MILPs and finally computes a feasiblesolution for the original nonlinear problem. The discretization grid in the MILPs is adaptedafter each iteration based on the previous calculated solution, thus allowing us to generate asuitable superstructure of the network. Afterwards, by fixing all previously calculated designdecisions, the original non-convex program is solved. In many cases where general nonlinearsolvers failed, this approach leads to feasible solutions with good solution quality in shortrunning time.

Applications of MINLP to Gas Network Optimization

Ralf LenzZuse Institute Berlin

Takustr. 7, 14195 Berlin, Germany


In this talk we present selected gas network optimization problems that can be formulatedas MINLP models. A major difficulty in modeling are the nonlinear and nonconvex pressureloss constraints, while the mixed-integer part is due to the active elements.

At first, we present the “nomination validation problem”. Here, we focus on stationarymodels. We thus consider a fixed and balanced demand situation, called nomination. It isa pure feasibility problem without any cost function, where the gas transmission companyis faced with the task to transport specified amounts of flow from sources to sinks whileaccounting for physical and technical requirements.

In case that a given nomination is found to be infeasible, the gas transmission system opera-tors need to extend their networks in a cost minimal way in order to increase the transporta-tion capacity and hence enable feasible operations, called “network expansion problem”.

The structure of the MINLP model for the nomination validation problem enables to extendit to the “network expansion problem”. This is due to the fact that the purchase decisionsand the related costs can be mapped to the potential network expansions. Since expansioncosts are very high, we solve the model to global optimality, using outer approximation andspatial branching. We further strengthen our formulation by computing the convex envelopeof the nonlinearities directly.

A Branch-and-Price Algorithm for the Recursive Circle Packing

Problem

Benjamin MullerZuse Institute Berlin

Takustr. 7, 14195 Berlin, Germany


A large fraction of the total costs in tube industry arise from the delivery of tubes insiderectangular-shaped containers. The problem of minimizing the number of containers to trans-port a set of different tubes can be modeled as the recursive circle packing problem (RCPP),which is a non-convex MINLP. This class of packing problems is practically unsolvable forany state-of-the-art MINLP solver.

We present a reformulation of the RCPP based on an enumeration scheme for all possiblepackings of tubes inside other tubes on a 1-level recursion. The reformulation is solved by abranch-and-price algorithm implemented inside the MINLP-solver SCIP. Our computationalresults show that this approach solves small-sized instances to optimality and produces bettersolutions than the best known heuristic.

A Trust-Region-SQP Algorithm for Mixed-Integer Nonlinear

Programming

Klaus Schittkowski

Siedlerstr. 3, 95488 Eckersdorf, Germany


Mixed-integer optimization problems are everywhere in operations research and engineering,for instance, when optimizing both the number of bolts and the diameter of the bolts inan assembly. In this particular case, the integer variable ’number of bolts’ cannot get re-laxed. Based on the success of sequential quadratic programming (SQP) methods especiallyin industrial optimization, the idea to add integer variables lead to a straigthforward exten-sion towards a new mixed-integer nonlinear programming (MINLP) algorithm. The maindesign goal is to minimize the total number of function evaluations, i.e., executions of theunderlying simulation software. The resulting code is called MISQP and and was developedby Schittkowski and co-workers at the Unversity of Bayreuth over a period of 10 years. Amixed-integer quadratic subproblem is solved in each step by a branch-and-bound methodexploiting dual information. The algorithm is stabilized by a trust region correction whichgoes back to Yuan (1995). The Hessian of the Lagrangian function is approximated by BFGSupdates subject to the continuous and integer variables. We outline the mathematical struc-ture of the algorithm and present some numerical results based on a set of 200 academic testexamples. The development of MISQP has been sponsored by Shell Global Solutions.

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