Welcome [mip2014.engineering.osu.edu]€¦ · Tuesday, July 22 09:30a - 10:00a Juliane Dunkel Mixed-integer programming for real-time railway control 10:00a - 10:30a Co↵ee Break

Welcome

We are happy to be welcome you to Mixed Integer Programming (MIP) 2014, hosted by theDepartment of Integrated Systems Engineering at the Ohio State University. The Mixed IntegerProgramming workshop series is designed to bring together the integer programming research com-munity in an annual meeting and is organized by volunteer members of the community. MIP 2014will be the eleventh workshop in the series.

We are thankful for the help of our volunteer sta↵ members and students from the Departmentof Integrated Systems Engineering, The Ohio Union and The O�ce of University Housing. Inparticular, we are immensely grateful towards Nick Stefanik, Candi McCain, Judith Flickinger,Mike Zazon, Matt Gaul and Cedric Sze from our administrative sta↵ for handling many logisticalmatters. We would also like to give a shout-out to the student volunteers from the INFORMS OSUStudent Chapter for their invaluable help: Hamed Rahimian, Xiao Liu, Sayak Roychowdhury andJangho Park.

We look forward to a dynamic and successful workshop and hope that you enjoy your time inColumbus.

MIP 2014 Program Committee MIP 2014 Local Organization CommitteeTobias Achterberg, Gurobi Optimization, ZIB Simge KüçükyavuzAmitabh Basu, Johns Hopkins U. Ramteen SioshansiJon Lee, U. Michigan, Ann ArborSusan Margulies, U.S. Naval AcademyJim Ostrowski, U. Tennessee, Knoxville

Venue

The conference venue, is the Ohio Union at the Ohio State University located at 1739 N. HighStreet, at the corner of 12th Avenue and High Street. The meetings will take place in the CartoonRoom on the third floor of the Ohio Union. The poster reception will take place in the Great Hallon the first floor of the Ohio Union. Maps of the first and third floors are provided in this program.

WiFi Connection

The guest wifi network is called: WiFi@OSU. To log on, guests just need to go to a browser, select“guest” and agree to terms.

Workshop Dinner

The workshop dinner will take place from 6-9pm on July 22 in the Ohio State Faculty Club. Therewill be a bu↵et available (including vegetarian options), as well as a cash bar. The per personcharge for attending the banquet is $35. So that we have an accurate count of the number ofpeople who will be attending the dinner, payments were requested (and your guests meal if any)by July 16. A small number of last-minute dinner tickets may be available – please contact SimgeKucukyavuz ([email protected]) if you have not paid for the dinner but wish to attend.

A map with directions from the Ohio Union to the Faculty Club is provided in this program.

Sponsors for MIP 2014 We would like to thank our sponsors for their generous support of MIP 2014.

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Program for MIP 2014

Monday, July 21

09:00a - 09:45a Registration09:45a - 10:00a Opening Statements10:00a - 10:30a Simge Küçükyavuz Cut Generation in Optimization Problems with

Multivariate Risk Constraints

10:30a - 11:00a Co↵ee Break

11:00a - 11:30a François Margot Solving Quadratic Chance Constrained Problemswith Random Technology Matrix

11:30a - 12:00p Giacomo Nannicini An algorithm for nonlinear chance-constrainedproblems with applications to hydro scheduling

12:00p - 02:00p Lunch (on your own)

02:00p - 02:45p Daniel Bienstock Solving QCQPs02:45p - 03:15p Poster Teasers, Part I

03:15p - 03:45p Co↵ee Break

03:45p - 04:15p Stefan Vigerske Analyzing the computational impact of individualMINLP solver components

04:15p - 05:00p Andreas Wächter Hot starting NLP solvers05:00p - 05:30p Poster Teasers, Part II05:30p - 08:00p Poster Session and Reception at Great Hall in the Union

Tuesday, July 22

09:30a - 10:00a Juliane Dunkel Mixed-integer programming for real-timerailway control


10:30a - 11:15a Karen Aardal GMI/Split cuts based on lattice information11:15a - 12:00p Sanjeeb Dash On two-branch split cuts


02:00p - 02:30p Marco Molinaro How Good Are Sparse Cutting-Planes?02:30p - 03:00p Minjiao Zhang On Knapsack-Constrained Continuous Mixing Set


03:30p - 04:00p Pierre Bonami Cut generation through binarization04:00p - 04:45p Alper Atamtürk Network design with uncertain capacities04:45p - 05:15p Business Meeting

06:00p - 09:00p Workshop Dinner at the OSU Faculty Club

Wednesday, July

23

09:30a - 10:15a Sebastian Pokutta The information-theoretic method in optimization


10:45a - 11:15a Laurent Poirrier Permutations in the factorization of simplex bases11:15a - 12:00p Zonghao Gu Solving LP and MIP Models with Piecewise Linear

Objective Functions


02:00p - 02:45p Andrea Lodi Indicator Constraints in Mixed-IntegerProgramming

02:45p - 03:15p Timo Berthold Cloud branching: How to exploit dual degeneracyin global search


03:45p - 04:15p Michele Monaci Proximity Search for 0-1 Mixed-Integer ConvexProgramming

04:15p - 04:45p Je↵ Linderoth Orbital Conflict-When Worlds Collide04:45p - 05:15p Domenico Salvagnin Detecting and exploiting permutation structures

in MIPs

Thursday, July 24

09:30a - 10:00a Raymond Hemmecke Augmentation Algorithms for Linear and IntegerLinear Programming


10:30a - 11:00a Robert Hildebrand Convex Set Operators and Polynomial IntegerMinimization in Fixed Dimension

11:00a - 11:45a Warren Adams Modeling Polynomial Functions of Two DiscreteVariables

11:45a - 12:15p Best Poster Prize Ceremony

Posters

The poster session will be held on the first evening of the workshop (July 21) from 5:30-8pm in theGreat Hall at the Union.

Accepted Posters (Poster Presenters are printed in bold)

• N. Adalgren, P. Belotti, A. Gupte, Enhancing fathoming rules in branch-and-bound forbiobjective mixed-integer programming.

• A. M. Alvarez, Q. Louveaux, L. Wehenkel, A Machine Learning based approximation ofstrong branching.

• S. Anvari, M. C. Arslan, M. Türkay, Development and Analysis of Sustainable FacilityLocation and Demand Allocation Problem.

• M. Bodur, S. Dash, O. Günlük, J. Luedtke, Strengthened Bender’s Cuts for StochasticInteger programs with continuous recourse.

• A. Bulut, T. Ralphs, On the complexity of inverse MILP.

• A. Atamtürk, C. Chen, S. Oren, Spatial branch-and-bound for spatial ACOPF.

• A. Danandeh, B. Zeng, A cutting plane approach to robust mixed-integer programming.

• Y. Deng, J. Lee, S. Shen, Dual Decomposition Algorithms for Solving Chance-ConstrainedBinary Programs.

• C. Fast, I. Hicks, On branch decompositions of linear relaxations for integer programming.

• U. Friedrich, R. Munnich, S. de Vries, M. Wagner, Optimal Sample Size Allocation for theGerman Census.

• G. Gamrath, Improving Strong Branching by Domain Propagation.

• A. Atamtürk, A. Gomez , S. Küçükyavuz, Three partition inequalities for equal capacityfixed-charge networks.

• M. Hamzeei, J. Luedtke, MILP approaches to a class of mixed-integer bilevel programs.

• S. Ahmed, Q. He, S. Li, G. Nemhauser, Minimum Concave cost flows in capacitated gridnetworks.

• S. Dey, J. Huchette, J. P. Vielma, New MIP and SDP approaches to the floor layoutproblem.

• E. Balas, A. Kazachkov, F. Margot, S. Nadarajah, Obtaining deeper intersection cuts forgeneralized intersection cuts.

• S. Küçükyavuz, X. Liu, J. Luedtke, Decomposition Algorithms for Two-Stage Chance-Constrained Programs.

• I. Dunning, J. Huchette, M. Lubin, JuMP: open-source algebraic modeling in Julia.

• S. Dey, S. Modaresi, J. P. Vielma, The Power of a Negative Eigenvalue: Aggregation Cutsfor Nonlinear Integer Programming.

• G. Chandra Mouli, V. Narayanan, On the Chvatal-Gomory Rank of a Class of Convex Sets.

• L. Rademacher, A. Toriello, J. P. Vielma, On blocking and anti-blocking polyhedra ininfinite dimensions.

• P. Bendotti, C. D’Ambrosio, G. Doukopoulos, A. Lenoir, L. Liberti, Y. Sahraoui, MILPmodel for a real-world short-term hydro-power unit-commitment problem.

• W. Cao, S. Chopra, S. Shim, A few strong knapsack facets.

• R. Fukasawa, L. Poirrier, A. Xavier, Facet defining inequalities for the bound relaxed two-integer knapsack.

• E. Boros, E. Yamangil, Generating multi-row simplex cuts on higher dimensional spaces.

• G. Cornuéjols, F. Kılınç-Karzan, S. Yıldız, Two-term disjunctions on the second order cone.

Local Restaurants(* = Recommended)

On-campus restaurants

• Union Market (Ohio Union): Salads, deli sandwiches, grab & go

• Woody’s (Ohio Union): Pizza and beer

• Sloopy’s (Ohio Union): Diner

• Heirloom Café (Wexner Center for the Arts): Soups, salads and sandwiches*

• Bistro 2110 (Blackwell Inn): Bistro

• Berry Café (Thompson Library): Salads, deli sandwiches, grab & go

Adjacent to campus, on High Street

• Potbelly’s (10 E. 11th Ave): Sandwiches

• Eddie George’s (1636 N. High St.): Sports bar

• Five Guys (1603 N. High St.): Burgers

• Panera Bread (1619 N. High St.): Soups, salads and sandwiches

• Chipotle (1726 N High St): Mexican

• Diaspora (2118 N High St): Korean

• Pera (1980 N. High St): Turkish

• Buckeye Donuts (1998 N High St): Donuts & Greek food

• Moy’s (1994 N High St): Chinese

• Starbucks (1784 N High St.): Co↵ee

RESTAURANTS, BARS & CAFES

Close to Olentangy South Hotels

• Bravo! Cucina Italiana (1803 Olentangy River Rd): American-Italian food

• Champs Americana (1827 Olentangy River Rd): Sports bar

• Columbus Fish Market (1245 Olentangy River Rd): Fresh fish and seafood

• Cap City Fine Diner (1299 Olentangy River Rd): Upscale diner

• Brazenhead (1027 W 5th Ave): Irish pub

• Zauber Brewing Co. (909 W 5th Ave): Craft brews, food truck

Grandview Heights

• Figlio (1369 Grandview Ave): Pasta, wood-fired pizza, wine bar

• Spagio (1295 Grandview Ave): European and Pacific Rim cuisine

• Aab India (1470 Grandview Ave): Indian*

• Third & Hollywood (1433 W 3rd Ave): Contemporary American*

• Jeni’s (1281 Grandview Ave): Creative, locally-sourced ice creams*

• Stauf’s Co↵ee Roasters (1277 Grandview Ave)

Short North

• Basi Italia (811 Highland St): Italian, patio*

• Marcella’s (615 N. High St): Italian

• Hyde Park (569 N. High St): Steakhouse

• Northstar Café (951 N. High St): Locally grown & organic American*

• The Pearl (641 N. High St): Gastropub

• Jeni’s (714 N High St): Creative, locally-sourced ice creams*

• Nida’s (976 N High St): Thai

• Bakersfield (733 N High St): Tacos, bar

• Philco (747 N High St): Modern diner

• Mouton (954 N High St): Cocktail bar, no food*

• Short North Pint House (780 N High St): Beer garden

• North High (1288 N High St): Craft brews

• Seventh Son Brewing Co. (1101 N 4th St): Craft brews, patio, food truck*

• Mission Co↵ee (11 Price Ave): Co↵ee, espresso drinks*

• Bodega (1044 N High St): Beer and pub food

• One Line Co↵ee (745 N High St): Co↵ee, espresso drinks*

Arena District/Downtown

• Barley’s Brewing Company (467 N. High St): Brews, pub food, best wings*

• Martini Modern Italian (445 N. High St): Italian

• Rodizio Grill (125 W. Nationwide Blvd): Brazilian steakhouse

• Gordon Biersch Brewery (401 Front St): Brewery and pub food

• Elevator Brewery (161 N High St): Brews and gastropub

German Village

• G. Michael’s (595 S. Third St): Contemporary American*

• Lindey’s (169 E. Beck St): Contemporary American*

• Harvest (491 S 4th St): Wood-fired pizzas*

• Curio (491 S 4th St): Cocktail bar*

• Pistacia Vera (541 S 3rd St): French pastries*

• The Sycamore (262 E Sycamore St): Contemporary American*

Local TransportationIn addition to the shuttles provided by some hotels, the following options for transportation areavailable:

CABS shuttle: The Campus Area Bus Service (CABS) is a free transit service provided by TheOhio State University. The summer hours are 7am-7pm. From the Olentangy North Hotels (HiltonGarden Inn, Holiday Inn Express, Fairfield Inn), you can take the Buckeye Village bus from theOlentangy and Ackerman station and get o↵ at the College and 17th station. The Buckeye Villageroute map is at http://ttm.osu.edu/sites/default/files/maps/BVMap_2.pdf.

COTA Bus: The Central Ohio Transit Authority (COTA) buses are $2/ride, or $4.5/day pass.You can use the Trip Planner on the COTA website (http://www.cota.com/) or Google Maps tofind the best route based on your departure time.

• From the Olentangy North Hotels (Hilton Garden Inn, Holiday Inn Express, Fairfield Inn):you can take either Bus #7 (Schedule & Map: http://www.cota.com/assets/Riding-Cota/Schedules/Current/007N.pdf) or Bus #18 (Schedule &Map: http://www.cota.com/assets/Riding-Cota/Schedules/Current/018.pdf) from the closest Olentangy River Rd stop go-ing south. Get o↵ at the College Rd & 12th Ave stop if riding Bus #7, and the High & 12thAve stop if riding Bus #18.

• From the Olentangy South hotels (Springhill Suites, Varsity Inn South): Take Bus #82(Schedule & Map: http://www.cota.com/assets/Riding-Cota/Schedules/Current/082.pdf) from King Ave & Olentangy River and get o↵ at the 12th Ave & High. You can take#82 in the other direction to go to the Grandview Heights neighborhood, which has severalrestaurants, cafes and bars.

• To Short North/Downtown/German Village: You can take Bus #2 (Schedule & Map: http://www.cota.com/assets/Riding-Cota/Schedules/Current/002H.pdf) from any stop onHigh Street towards south, to go to Short North and Downtown, where many of the hiprestaurants and bars are. You can also ride CBUS, which is a free bus that runs from ShortNorth to German Village and Brewery District.

Car2Go: Point-to-point carsharing service with convenient locations at OSU. See http://columbus.car2go.com/ for details.

Uber: Request a car ride via mobile app. See https://www.uber.com/cities/columbus fordetails.

Taxis:

• Yellow Cab: (614) 444-4444

• Orange Cab: (614) 414-0000

• Blue Cab: (614) 333-3333

http://ttm.osu.edu/sites/default/files/maps/BVMap_2.pdf.http://www.cota.com/assets/Riding-Cota/Schedules/Current/007N.pdfhttp://www.cota.com/assets/Riding-Cota/Schedules/Current/007N.pdfhttp://www.cota.com/assets/Riding-Cota/Schedules/Current/018.pdfhttp://www.cota.com/assets/Riding-Cota/Schedules/Current/018.pdfhttp://www.cota.com/assets/Riding-Cota/Schedules/Current/082.pdfhttp://www.cota.com/assets/Riding-Cota/Schedules/Current/082.pdfhttp://www.cota.com/assets/Riding-Cota/Schedules/Current/002H.pdfhttp://www.cota.com/assets/Riding-Cota/Schedules/Current/002H.pdfhttp://columbus.car2go.com/http://columbus.car2go.com/https://www.uber.com/cities/columbus

Maps of 1st and 3rd floors of Ohio Union

Directions to Workshop Dinner at the Faculty Club

!Directions from the Hotels to the Ohio Union You can download the Ohio State mobile app for maps, directions and bus information:

http://www.osu.edu/downloads/apps/osu-mobile.html !From Blackwell: !!

From Olentangy South Hotels (Springhill Suites, Varsity Inn South): !

!!From Olentangy North Hotels (Hilton Garden Inn, Holiday Inn Express, Fairfield): !!!!!!!!!!!!!!!!!!!!!

2014 Workshop on Mixed Integer Programming (MIP 2014) Abstracts

!MONDAY, JULY 21: !10:00a-10:30a: Simge Küçükyavuz, Ohio State University, USA Title: Cut Generation in Optimization Problems with Multivariate Risk Constraints Abstract: We consider a class of multicriteria stochastic optimization problems that feature benchmarking constraints based on conditional value-at-risk and second-order stochastic dominance. We develop alternative mixed-integer programming formulations and solution methods for cut generation problems arising in optimization under such multivariate risk constraints. We give the complete linear description of two non-convex substructures common in these cut generation problems. We present computational results that show the effectiveness of our proposed models and methods. Joint work with Nilay Noyan. !11:00a-11:30a: François Margot, Carnegie Mellon University, USA Title: Solving Quadratic Chance Constrained Problems with Random Technology Matrix Abstract: Two broad classes of Stochastic Programming (SP) models are SPs with recourse (where decisions taken prior to realization of the stochastic events can be corrected) and chance constrained programming (CCP) (where no recourse is possible). Most of the solution approaches for CCP models deal with the case where random variables only appear in the right-hand side of the constraints and are unable to tackle problems having random variables impacting constraint coefficients (a.k.a. "random technology matrix"). !We develop methods to solve CCP problems with a multi-row random technology matrix, using an exact Boolean reformulation method based on the binarization of probability distributions. For linear stochastic constraints, the method derives an equivalent mixed-integer linear programming reformulation. We extend the method to problems with bilinear stochastic constraints, deriving deterministic reformulations with trilinear terms. Such problems appear naturally in many different fields, including response model to propagation of epidemics, facility location problem with random demand, and pooling systems with uncertain quality of reservoirs and flows. !

We report on experiments with Couenne (a COIN-OR software project) to solve the resulting trilinear deterministic problems. We discuss practical issues with several mathematically equivalent formulations for some propagation of epidemic and facility location problems. Joint work with M. Lejeune. !11:30a-12:00p: Giacomo Nannicini, SUTD, Singapore Title: An algorithm for nonlinear chance-constrained problems with applications to hydro scheduling Abstract: In the spirit of MIP, I will present very recent work on midterm hydro scheduling, which is the problem of optimizing the performance of a hydro network over a period of a few months. This decision problem is affected by uncertainty on energy prices, demands and rainfall, and we model it as a nonlinear chance-constrained mathematical program. !Akin to this problem, the talk is affected by uncertainty at the present stage. There is a probability bounded away from zero that I will discuss a Branch-and-Cut algorithm based on the approach recently proposed by Jim Luedtke, which uses Benders-type cuts. However, in our case the feasible region induced by each scenario is a general convex set instead of a polyhedron. I will almost surely present a separation algorithm for the corresponding scenario subproblems that exploits projection and KKT conditions, and has some clear advantages over generalized Benders decomposition. With unknown probability I will provide a preliminary computational evaluation of the proposed method for the scheduling of a hydro network in Greece. Finally, with probability one I will apologize for giving a talk that does not correspond to this abstract. Joint work with Andrea Lodi, Enrico Malaguti and Dimitri Thomopulos. !2:00p-2:45p: Daniel Bienstock, Columbia University, USA Title: Solving QCQPs Abstract: Quadratically constrained quadratic programs, or QCQPs are a natural generalization of linear programs and, in recent years, have received growing interest, motivated by both fundamental reasons and also by many applications in science and engineering. Typically QCQPs are continuous, but the similarity with linear programming ends there, because QCQPs are usually nonconvex, and even in simple cases, are NP-hard. In fact, QCQPs are quite general, because any polynomial optimization problem can be reduced to an equivalent (and polynomially larger) QCQPs. In this talk we will review classical results and describe recent results, including (hopefully) some applications of linear mixed integer programming ideas. Joint work with Gonzalo Munoz and Irene Lo. !

2:45p-3:15p: Poster Teasers, Part I !3:45p-4:15p: Stefan Vigerske, GAMS, Germany Title: Analyzing the computational impact of individual MINLP solver components Abstract: General-purpose solvers that address large and heterogeneous problem classes like mixed-integer nonlinear programming (MINLP) necessarily combine a variety of algorithmic techniques in their solution process. In this talk, we present recent advances in the constraint integer programming-based MINLP solver SCIP with a special focus on analyzing the computational impact of individual solver components such as branching strategies, separation routines, bound tightening techniques, and primal heuristics. Joint work with Ambros Gleixner. !4:15p-5:00p: Andreas Wächter, Northwestern University, USA Title: Hot starting NLP solvers Abstract: One reason for the efficiency of the branch-and-bound method for MILP is that LP nodes can often be solved very quickly, especially when only a small number of variables bounds are changed during strong-branching or diving. The crucial observation here is that the factorization of the basis matrix from a previously solved LP can be reused and updated in the dual Simplex method for the new LP. NLP algorithms (such as sequential quadratic programming) also require the factorization of matrices that involve parts of the constraint Jacobian during the step computation with an active-set QP solver. However, due to the nonlinearity of the constraints, these matrices change with every iterate, so that the factorization from a previously solved NLP is not the one required for the step computations during the solution of a new NLP. !In this talk, we present one approach that attempts to "hot-start" the solution of a new NLP by reusing the matrix factorization available from a previously solved NLP. In this way, the work of factorizing the new constraint matrix from scratch is avoided, at the cost of multiple refinement iterations that compensate for the error. Numerical results will be presented. !5:00p-5:30p: Poster Teasers, Part II !5:30p-8:00p: Poster Session and Reception !!!!

TUESDAY, JULY 22: !9:30a-10:00a: Juliane Dunkel, IBM Research, Zurich, Switzerland Title: Mixed-integer programming for real-time railway control Abstract: Railway networks are operated more and more at their capacity limits, disturbances and delays propagate quickly and affect the service level experienced by customers. As a consequence, railway traffic management and, in particular, real-time railway control has become an increasingly challenging task. Revised schedules have to be computed within a few seconds, making the need of computer-aided systems to support dispatchers more and more evident. !However, due to the combinatorial complexity of the underlying optimization problems and the immense sizes of instances, this problem is difficult to solve in acceptable time. Macroscopic models generally neglect important technical details as train dynamics and safety regulations, and microscopic models that incorporate many technical aspects become practically infeasible. We suggest a mixed-integer programming formulation for the problem of computing revised schedules that combines macroscopic and microscopic aspects. The formulation allows us to model bottleneck areas of a network up to microscopic detail, while uncritical areas can be considered with only macroscopic granularity. Hence, the model produces practically workable solutions. We enhance our formulation with several variable fixing procedures and show how very large instances can be solved efficiently via a rolling-horizon approach. !10:30a-11:15a: Karen Aardal, TU Delft, Netherlands Title: GMI/Split cuts based on lattice information Abstract: Cutting planes incorporated in a branch-and-bound framework is the most dominant solution approach for (mixed)-integer optimization problems. One important family of cutting planes is the family of split cuts. A computational study by Balas and Saxena indicates that the first closure associated with the family of split inequalities is a very good approximation of the convex hull of feasible solution. It is, however, NP-hard to optimize a linear function over the split closure, so achieving these results is computationally expensive. A special case of the split cuts, which can trivially be generated, is the family of GMI-inequalities that can be obtained from optimal basic feasible solutions. The computational effectiveness of these inequalities is however much more modest (Bixby, Gu, Rothberg, and Wunderling). The discrepancy between the potential effectiveness of GMI/split inequalities indicated by the study of Balas and Saxena, and the results that so far can be realized by generating such inequalities from optimal basic solutions, led

Cornuejols to suggest that one should look for deep split cuts that can be separated efficiently. !In our work we suggest a heuristic way of generating GMI/split inequalities that is based on information from the structure of the underlying lattice. We present examples and some computational indications. This talk is based on joint work with Frederik von Heymann, Andrea Lodi, Andrea Tramontani, and Laurence Wolsey. !11:15a-12:00p: Sanjeeb Dash, IBM Research, New York, USA Title: On two-branch split cuts Abstract: In this talk we present some properties of two-branch split cuts, which generalize the split cuts of Cook, Kannan and Schrijver, and were studied by Li and Richard (2008). In particular, we show that the closure of a polyhedral set with respect to two-branch split cuts is a polyhedron. Furthermore, we use this result to show that the quadrilateral closure of the two-row continuous group relaxation — the set of points satisfying all cutting planes obtained from maximal lattice-free quadrilaterals — is a polyhedron. We also discuss computational results with split cuts and two-branch split cuts in a few different settings. Joint work with Oktay Gunluk and Diego Moran. !2:00p-2:30p: Marco Molinaro, Georgia Institute of Technology, USA Title: How Good Are Sparse Cutting-Planes? Abstract: Sparse cutting-planes are often the ones used in mixed-integer programing (MIP) solvers, since they help in solving the linear programs encountered during branch-&-bound more efficiently. However, how well can we approximate the integer hull by just using sparse cutting-planes? In order to understand this question better, given a polyope P (e.g. the integer hull of a MIP), let P^k be its best approximation using cuts with at most k non-zero coefficients. We consider d(P, P^k) = max_{x in P^k} (min_{y in P} |x - y|) as a measure of the quality of sparse cuts. In our first result, we present general upper bounds on d(P, P^k) which depend on the number of vertices in the polytope and exhibits three phases as k increases. Our bounds imply that if P has polynomially many vertices, using half sparsity already approximates it very well. Second, we present a lower bound on d(P, P^k) for random polytopes that show that the upper bounds are quite tight. Third, we show that for a class of hard packing IPs, sparse cutting-planes do not approximate the integer hull well. Finally, we show that using sparse cutting-planes in extended formulations is at least as good as using them in the original polyhedron, and give an example where the former is actually much better. Joint work with Santanu Dey and Qianyi Wang. !

2:30p-3:00p: Minjiao Zhang, University of Alabama, USA Title: On Knapsack-Constrained Continuous Mixing Set Abstract: We study the knapsack-constrained continuous mixing set, which arises in the joint chance-constrained program. We characterize the extreme points and rays of the convex hull of the knapsack-constrained continuous mixing set, and develop two extended formulations and linear descriptions. In addition, for the cardinality-constrained continuous mixing set, which is a special case of the knapsack-constrained continuous mixing set, we propose the sufficient and necessary conditions for the valid inequalities, and present a set of valid inequalities in an explicit form. In particular, we show that the proposed valid inequalities are enough to describe a particular case of the cardinality-constrained continuous mixing set. !3:30p-4:00p: Pierre Bonami, IBM CPLEX, Spain Title: Cut generation through binarization Abstract: For a mixed integer linear program with bounded general integer variables, we study the combination of a reformulation introduced by Roy that maps general integer variables to a collection of binary variables and simple split cuts. We show that a pure integer problem with two bounded integer variables is solved by doing this reformulation and computing the rank-2 simple split closure. We show that this result does not generalize to problems in higher dimensions. We compare in particular rank-2 simple split cuts from the reformulated problem to intersection cuts from two dimensional lattice free sets. Finally, we present an algorithm to approximate the rank-2 simple split cut closure and report empirical results on 22 benchmark instances. We show that the bounds obtained compare favorably with those obtained with other approximate methods to compute the split closure or lattice-free cut closure. Joint work with François Margot. !4:00p-4:45p: Alper Atamtürk, UC Berkeley, USA Title: Network design with uncertain capacities Abstract: We consider a network design problem with uncertain edge capacities, which, under various assumptions, can be modeled using conic quadratic constraints on binary variables. Conic quadratic constraints on binary variables lead to supermodular or submodular knapsack problems. We will discuss cover and pack inequalities, their extensions, reductions, lifting and separation for uncorrelated and correlated cases. Joint work with Avinash Bhardwaj and Vishnu Narayanan. !4:45p-5:15p: Business meeting !

!WEDNESDAY, JULY 23: !9:30a-10:15a: Sebastian Pokutta, Georgia Institute of Technology, USA Title: The information-theoretic method in optimization Abstract: Recently problems in extended formulations, convex black-box optimization, and compressed sensing have been shown to be especially tractable via an information-theoretic approach. We provide an overview of the information-theoretic method, the underlying paradigms, and present three applications demonstrating the power of the method, both for obtaining lower bounds as well as upper bounds. !10:45a-11:15a: Laurent Poirrier, University of Waterloo, Canada Title: Permutations in the factorization of simplex bases Abstract: The basis matrices corresponding to consecutive iterations of the simplex method only differ in a single column. This fact is commonly exploited in current LP solvers to avoid the computation of a fresh factorization at every iteration. Instead, a previous factorization is updated to reflect the modified column. We present a variant of this process for the special case where the update can be performed purely by permuting rows and columns of the factors. Joint work with Ricardo Fukasawa. !11:15a-12:00p: Zonghao Gu, Gurobi, USA Title: Solving LP and MIP Models with Piecewise Linear Objective Functions Abstract: LP and MIP models often contain piecewise linear structure; this structure may capture a true piecewise linear function, or it may be used to approximate a non-linear function. Current solvers use one optimization variable for each piece of the piecewise function, which can dramatically increase the model size. This talk will discuss extensions of the simplex and MIP B&B algorithms that allow them to solve piecewise linear models without requiring additional variables. !2:00p-2:45p: Andrea Lodi, University of Bologna, Italy Title: Indicator Constraints in Mixed-Integer Programming Abstract: Mixed Integer Linear Programming (MILP) models are commonly used to model indicator constraints, which either hold or are relaxed depending on the value of a binary variable. Classification problems with Ramp Loss functions are an important application of such models. Mixed Integer Nonlinar Programming (MINLP) models are usually dismissed because they cannot be solved as efficiently. However, we show here that a subset of classification problems can be solved much more efficiently by a MINLP model with nonconvex constraints. This calls for a

reconsideration of the modeling of these indicator constraints, and we present several new results and interpretations obtained by digging into the relationship between MILP and MINLP. !2:45p-3:15p: Timo Berthold, FICO Xpress Optimization, Germany Title: Cloud branching: How to exploit dual degeneracy in global search Abstract: Branch-and-bound methods for MIP are traditionally based on solving an LP relaxation and branching on a variable which takes a fractional value in the (single) computed relaxation optimum. We study branching strategies for mixed-integer programs that exploit the knowledge of *multiple* alternative optimal solutions (a cloud) of the current LP relaxation. These strategies naturally extend state-of-the-art methods like strong branching, pseudocost branching, and their hybrids. !We show that by exploiting dual degeneracy, and thus multiple alternative optimal solutions, it is possible to enhance traditional methods. We present preliminary computational results, applying the newly proposed strategy to full strong branching, which is known to be the MIP branching rule leading to the fewest number of search nodes, and pseudo cost branching, which is the basis of most state-of-the-art branching algorithms. Experiments are carried out in the state-of-the-art MIP solvers SCIP and FICO Xpress Optimizer. Joint work with Domenico Salvagnin and Gerald Gamrath. !3:45p-4:15p: Michele Monaci, University of Padova, Italy Title: Proximity Search for 0-1 Mixed-Integer Convex Programming Abstract: In this talk we investigate the effects of replacing the objective function of a 0-1 Mixed-Integer Convex Program with a ``proximity'' one, with the aim of enhancing the heuristic behavior of a black-box solver. The relationship of this approach with primal integer methods is also addressed. Promising computational results on different proof-of-concept implementations are presented, suggesting that proximity search can be very effective in quickly improving the incumbent in the early part of the search. This is particularly true when a sequence of similar MIPs has to be solved as, e.g., in a column-generation setting, or for problems that can be easily decomposed, e.g., according to a Benders' scheme. Joint work with Matteo Fischetti. !4:15p-4:45p: Jeff Linderoth, University of Wisconsin-Madison, USA Title: Orbital Conflict-When Worlds Collide Abstract: In this talk, we smash together ideas that have proven to be effective at exploiting symmetry with strong cutting planes for mixed integer programs. We

hope that the computational results will be earth-shattering. Joint work with Jim Ostrowski, University of Tennessee and Fabrizio Rossi and Stefano Smriglio, Universita di L’Aquila. !4:45p-5:15p: Domenico Salvagnin, University of Padova, Italy Title: Detecting and exploiting permutation structures in MIPs Abstract: Many combinatorial optimization problems can be formulated as the search for the best possible permutation of a given set of objects, according to a given objective function. The corresponding MIP formulation is thus typically made of an assignment substructure, plus additional constraints and variables (as needed) to express the objective function. Unfortunately, the permutation structure is generally lost when the model is flattened out as a mixed integer program, and state-of-the-art MIP solvers do not take full advantage of it. In the present paper we propose a heuristic procedure to detect permutation problems from their MIP formulation, and show how we can take advantage of this knowledge to speedup the solution process. Computational results on quadratic assignment and single machine scheduling problems show that the technique, when embedded in a state-of-the-art MIP solver, can indeed improve performance. !!THURSDAY, JULY 24: !9:30a-10:00a: Raymond Hemmecke, TU Munich, Germany Title: Augmentation Algorithms for Linear and Integer Linear Programming Abstract: Separable convex IPs can be solved via polynomially many augmentation steps if best augmenting steps along Graver basis directions are performed. Using instead augmentation along directions with best ratio of cost improvement/unit length, we show that for linear objectives the number of augmentation steps is bounded by the number of elements in the Graver basis of the problem matrix, giving strongly polynomial-time algorithms for the solution of N-fold LPs and ILPs. !10:30a-11:00a: Robert Hildebrand, ETH Zurich, Switzerland Title: Convex Set Operators and Polynomial Integer Minimization in Fixed Dimension Abstract: We propose a new approach to minimizing a polynomial over the integer points in a polyhedron based on a convex set operator. This problem is known to be NP-Hard in dimension two even when the feasible region is bounded and the objective is a polynomial of degree four. We solve the feasibility problem by dividing the plane into regions where a sub-level set is convex or its complement

is convex. The operator then applies to solving the feasibility problem on convex sets or polyhedra after removing a convex set. We use this approach to show that cubic and homogeneous polynomials can be minimized over a polytope in dimension two in polynomial time. In particular, this completes a complexity classification by degree of the minimization problem in dimension two. !11:00a-11:45a: Warren Adams, Clemson University, USA Title: Modeling Polynomial Functions of Two Discrete Variables Abstract: Given two discrete variables x and y, the challenge is to construct efficient polyhedral representations of a general polynomial function of these variables. To obtain such representations, we recast the function in an extended-variable space by defining a new continuous variable for each distinct nonlinear term. Then we construct, in an encompassing space, a polytope that possesses two key properties. The first property is a one-to-one correspondence between the extreme points and the number of possible pairwise-realizations of x and y. Second, at every extreme point, each variable x and y realizes one of its permissible values, and each auxiliary variable equals to its intended product. In this manner, optimization of any such polynomial function reduces to a linear program. The methodology uses Lagrange Interpolating Polynomials, as in the reformulation-linearization-technique for general discrete variables, to compute the extended spaces, and a projection operation to re-express the polytopes in more tractable lower-dimensional regions. Complete characterizations of the projections are explicitly available when one of the discrete variables is binary, extending the classic Fortet - McCormick inequalities for two binary variables. Joint work with Stephen M. Henry.

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Welcome [mip2014.engineering.osu.edu]€¦ · Tuesday, July 22 09:30a - 10:00a Juliane Dunkel Mixed-integer programming for real-time railway control 10:00a - 10:30a Co↵ee Break