10th esicup meeting - bookletesicup/extern/esicup-10th... · 2013-04-18 · 10thesicupmeeting 5...

Organiza(on*

10th*ESICUP*Mee(ng*Lille,*France,*April*24@26,*2013*

10th ESICUP Meeting 3

Table of Contents

Welcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Information for Conference Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Program Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Scientific Program Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Social Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13

Abstracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

List of Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29

Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Lille Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Lille, France, April 24-26, 2013

4 10th ESICUP Meeting

Local Organizing Committee:

François Clautiaux, (chair) Université de Lille 1

Saïd Hanafi, Université de Valenciennes

Martin Bué, INRIA Lille Nord Europe

Matthieu Gérard, INRIA Lille Nord Europe

Aline Parreau, Université de Lille 1

Program Committee:

A. Miguel Gomes, (chair) University of Porto

Gerhard Wäscher, Otto-von-Guericke-Universität Magdeburg

Ramón Alvarez-Valdes, University of Valencia

Julia Bennell, University of Southampton

François Clautiaux, Université de Lille 1

José Fernando Oliveira, University of Porto

Organised by:

ESICUP – EURO Special Interest Group on Cutting and Packing

Lifl – Laboratoire d’Informatique Fondamentale de Lille (Computer Science Laboratory of Lille)

LAMIH – Laboratoire d’Automatique, de Mécanique et d’Informatique Industrielles et Humaines

IUT A de Lille – Institut Universitaire de Technologie A de Lille

We would like to thank the sponsors: ROADEF and INESC TEC



Welcome

A. Miguel Gomes François Clautiaux

Dear Friends,

Welcome to the 10th Meeting of ESICUP – EURO Special Interest Group on Cutting and Packing.Since its formal recognition as an EURO Working Group in 2003, ESICUP has run a series of annualmeetings that have joined researchers and practitioners in the field of cutting and packing. Wittenberg,Southampton, Porto, Tokyo, L’Aquila, Valencia, Buenos Aires, Copenhagen and La Laguna have hostedour past meetings and this 10th meeting is now held in Lille. The scientific program that has been puttogether guarantees that these will be rather fruitful days.

With 28 presentations organized in an unique stream, the 41 participants will be able to attend andenjoy all presentations, in a friendly and relaxed environment propitious to fruitful scientific discussions.Once more this meeting will be an instrument for the dissemination and the development of our field ofresearch.

Lille is the principal city of the Lille Métropole, the fourth-largest metropolitan area in France after thoseof Paris, Lyon and Marseille. Lille is situated on the Deûle River, near France’s border with Belgium.Lille Métropole has a population of 1,091,438. The eurodistrict of Lille-Kortrijk, which also includes theBelgian cities of Kortrijk, Tournai, Mouscron and Ypres, had 1,905,000 residents, ranking as one of themajor metropolitan areas of Europe.

Lille 1 University is a State University, founded in 1562 by the Spanish. It became French in 1667. LouisPASTEUR was the first Dean of the Science Faculty in 1854. In 2004, the University had more than20,000 full-time students plus 14,500 students in continuing education, 1,310 permanent faculty membersplus 1,200 staff and around 140 CNRS researchers in the 43 research labs. University Lille 1 is a memberof the European Doctoral College Lille-Nord-Pas de Calais, which produces 400 doctorate dissertationsevery year.

We would like to spend a word of gratitude to our colleagues, members of the Scientific and OrganizingCommittees, for the their important contribution for the existence and success of this meeting.

Our wish is that you may leave Lille looking forward to come back on holidays and for the 11th ESICUPMeeting, in 2014.

All the best.

A. Miguel Gomes François Clautiaux,University of Porto, FEUP / INESC-TEC Université de Lille 1

Program Chair Local Organizer



Information for Conference Participants

MEETING VENUEThe 10th ESICUP Meeting will be held at IUT A, Université de Lille 1. The institute is located inVilleneuve d’Ascq, 15 minutes by subway from the city center (a departure every minute at rush hour).

Address:IUT A Institut Universitaire Technologie de Lille 1,Avenue Paul Langevin,59650 Villeneuve-d’AscqFrance

ACCESS TO THE BUILDINGThe meeting is organized during the French holidays and the university buildings will be closed. We willlet the doors open at the beginning and ending of each session. A person will be there all day to openthe door to late people.

REGISTRATIONWednesday 24th of April, 16:00 to 18:00, and Thursday 25th April, 9:00 to 9:20 in the hall of IUT A,where the meeting takes place.

NOTES ON PRESENTATION• Equipment

The conference room is equipped with an overhead projector and with a video projector and acomputer. We suggest that you bring your own computer and/or transparencies as a backup.

• Length of Presentation22.5 minutes for each talk, including discussion. Please note that we are running on a very tightschedule. Therefore, it is essential that you limit your presentation to the time which has beenassigned to you. Session chairpersons are asked to ensure that speakers observe the time limits.



INTERNETTo use the wireless network, you should use Eduroam. We will also try to establish an open networkduring the conference.

GET-TOGETHERThe get-together takes place on Wednesday 24th March, 16:00 to 18:00, at the meeting venue, “IUT A,Université de Lille 1” (see details above). There will be coffee and pastries.After the Get-together, we are planning to have an informal dinner (on a pay-yourself basis) in Lille citycentre. Please inform us by email ([email protected]) if you are planning to join us. Further details willavailable later.

CONFERENCE DINNERThe gala dinner will be organized at “Restaurant La Terrasse des Remparts” from 19:30.

Address:Quartier du vieux Lille,Logis de la porte de Gand,Rue de Gand - 59000 LilleFranceTél. +33 (0) 3 20 06 74 74Fax +33 (0) 3 20 06 74 70.

CITY AND MOVING AROUNDLille is the largest city in the North of France. It is the principal city of the Lille Métropole, the fourth-largest metropolitan area in France after those of Paris, Lyon and Marseille. Lille is situated on the DeûleRiver, near France’s border with Belgium. The city of Lille had a population of 226,014 as recorded by the2006 census. However, Lille Métropole, which also includes Roubaix, Tourcoing and numerous suburbancommunities, had a population of 1,091,438. The eurodistrict of Lille-Kortrijk, which also includes theBelgian cities of Kortrijk, Tournai, Mouscron and Ypres, had 1,905,000 residents, ranking as one of themajor metropolitan areas of Europe.Lille has a very nice city centre, excellently suited for a city trip. Most of the sights (La vieille bourse,the Opera, the Chamber of Commerce, La Citadelle, le Vieux Lille) can be combined in a walking tour.



Program Overview



Scientific Program Schedule

Thursday Abril 25th9:20 – 9:30

Opening Session

Welcome Adress

9:30 – 10:30

Session 1 Chair: Andreas Bortfeldt

1.1 – The pickup and delivery problem with three-dimensional loading constraints: formulation, solution ap-proach and preliminary computational resultsDirk Männel, Andreas Bortfeldt

1.2 – Placing ships in locks: a decision support approach using exact and heuristic methodsJannes Verstichel, Patrick De Causmaecker, Greet Vanden Berghe

1.3 – Modeling and solving the placement problem of rectangles with variable metric characteristicsM. Novozhylova, I. Chub, M. Murin

11:00 – 12:30

Session 2 Chair: Joaquim Gromicho

2.1 – An algorithm for putting on pallets and loading products into trucksM. T. Alonso, R. Alvarez-Valdes, J. Gromicho, F. Parreño, G. Post, J.M. Tamarit

2.2 – Mixed case 3D pallet loading with optimized robotic loadingsTony Wauters, Jan Christiaens, Greet Vanden Berghe

2.3 – Placing pallets in containers under real life constraintsJ.A.S. Gromicho, J.J. van Hoorn, G.F. Post

2.4 – Container loading in international logistics platforms for the automotive industryAlain Nguyen, Jean-Philippe Brenaut

14:00 – 15:30

Session 3 Chair: Julia Bennell

3.1 – 3D Packing Problems with an Uniform Weight Distribution – A Case StudyMaria da Graça Costa, Maria Eugénia Captivo

3.2 – Development of a Cargo Loading Sequence Algorithm for the Container Loading ProblemAntónio Galrão Ramos, José Fernando Gonçalves, José F. Oliveira, Manuel P. Lopes

3.3 – Constructive Heuristic for the 3D Container Loading ProblemXiaozhou Zhao, Julia Bennell, Kathryn Dowsland, Tolga Bekta?

3.4 – A randomized constructive algorithm for the container loading problem with multi-drop constraintsDavid Álvarez Martínez, Francisco Parreño, Ramón Álvarez-Valdés

16:00 – 17:30

Session 4 Chair: Yuri Stoyan

4.1 – Models and algorithms for customizing shipping boxesF. Parreño, M. T. Alonso, R. Alvarez-Valdes, J.M. Tamarit

4.2 – A GRASP for circle packingJoão Pedro Pedroso, Sílvia Cunha, António Guedes de Oliveira, João Nuno Tavares



4.3 – Packing Cuboids and SpheresYu. Stoyan, A. Chugay

4.4 – Optimal Packing Circular Cylinders into a Cylindrical Container Taking into Account Behavior ConstraintsP. Stetsyuk, T. Romanova, A. Pankratov, A. Kovalenko

Friday April 26th9:00 – 10:30

Session 5 Chair: Ramón Álvarez-Valdés

5.1 – Optimal clustering of a pair of irregular objects bounded by arcs and line segmentsT. Romanova, J. Bennell, G. Scheithauer, Y. Stoyan, A. Pankratov

5.2 – Solving the bin packing problem with irregular pieces and guillotine cutsAntonio Martinez, Ramon Alvarez-Valdes, Julia Bennell, Jose Manuel Tamarit

5.3 – Exploring Non-Linear Models for Nesting ProblemsPedro Rocha, Rui Rodrigues, A. Miguel Gomes, Marina Andretta, Franklina M. B. Toledo

5.4 – A hybrid matheuristic algorithm for the nesting problemA. Martinez-Sykora, R. Alvarez-Valdes, M. A. Carravilla, A. M. Gomes, J. F. Oliveira, J. M. Tamarit

11:00 – 12:30

Session 6 Chair: Elsa Silva

6.1 – New Approximability Results for Two-Dimensional Bin PackingKlaus Jansen, Lars Prädel

6.2 – 2DCPackGen: A problem generator for two-dimensional rectangular cutting and packing problemsElsa Silva, José F. Oliveira, Gerhard Wäscher

6.3 – Construction Heuristic Algorithms for Soft Rectangle PackingShinji Imahori, Chao Wang

6.4 – A Hybrid Constructive Heuristic for the Rectilinear Area Minimization ProblemMarisa Oliveira, Eduarda Pinto Ferreira, A. Miguel Gomes

14:00 – 15:45

Session 7 Chair: François Clautiaux

7.1 – The Multi-Handler Knapsack Problem under Uncertainty: models and approximationsGuido Perboli, Roberto Tadei, Luca Gobbato

7.2 – Friendly Bin Packing Instances without Integer Round-up PropertyAlberto Caprara, Mauro Dell’Amico, José Carlos Diaz Diaz, Manuel Iori, Romeo Rizzi

7.3 – Biased Random Key Genetic Programming based Heuristics for the 1D Bin Packing ProblemJosé Fernando Gonçalves

7.4 – An exact/hybrid approach based on column generation for the bi-objective max-min knapsack problemRaïd Mansi, Cláudio Alves, Telmo Pinto, José Valério de Carvalho

7.5 – A chance-constrained strip packing problemFrançois Clautiaux, Saïd Hanafi, Ya Liu, Christophe Wilbaut

15:45 – 16:00

Closing Session

Closing Notes



Social Program

• Registration and Get-togetherApril 24th, from 16.00 to 18.00“IUT A Institut Universitaire Technologie de Lille 1”,Avenue Paul Langevin,59650 Villeneuve-d’Ascq,France

• Conference dinnerApril 25th, from 19:30“Restaurant La Terrasse des Remparts”,Quartier du vieux Lille, Logis de la porte de Gand,Rue de Gand - 59000 LilleFrance



Abstracts

1.1The pickup and delivery problem with three-dimensional loading constraints:

formulation, solution approach and preliminary computational resultsDirk Männel, Andreas Bortfeldt

Otto von Guericke University, Magdeburg, Germany

In the capacitated vehicle routing problem with pickup and delivery (VRPPD) a set of transportation requestshas to be satisfied by several vehicles such that the total travel distance is minimized. Each request is given by apickup point, a corresponding delivery point and a certain quantity of goods to be transported.In this talk, the VRPPD is extended to an integrated vehicle routing and loading problem, called VRPPD with3Dloading constraints (3L-VRPPD). The scalar quantities of goods are replaced by sets of 3D rectangular items thatare to be loaded in 3D loading spaces of the vehicles. Moreover, several packing constraints often occurring inreal-world settings, e.g. concerning stacking of goods, are also taken into account.First, we give a complete (verbal) formulation of the 3L-VRPPD and compare it to other integrated routing andloading problems. It will turn out that the 3L-VRPPD represents the highest difficulty level in this problem classthat has been found so far.Second, a hybrid algorithm for solving the 3L-VRPPD is outlined. It consists of a large neighborhood searchprocedure for routing (that has been adopted from the VRPPD literature) and a tree search procedure forpacking 3D items.Finally, we present preliminary results of computational experiments. In these experiments different routing pat-terns are applied that lead to different difficulty levels of the solution process.Keywords: vehicle routing, packing, pickup and delivery problem, large neighborhood search, tree search

1.2Placing ships in locks: a decision support approach using exact and heuristic

methodsJannes Verstichel∗, Patrick De Causmaecker†, Greet Vanden Berghe∗

∗CODeS, KU Leuven - KAHO Sint-Lieven, †CODeS, ITEC-iMinds, KU Leuven

Ships must often pass one or more locks when entering or leaving a tide independent port. So do barges travellingon a network of waterways. These locks control the flow and the level of inland waterways, or provide a constantwater level for ships while loading or unloading at the docks.We consider locks with a single chamber or several (possibly different) parallel chambers, that can transfer one ormore ships in a single operation. When transporting ships through such a lock, three problems need to be solved:selecting a chamber for each ship, placing ships inside the chamber, and scheduling the resulting lockages.The present contribution considers the ship placement problem, which constitutes a daily challenge for lockmasters. This problem is closely related to the 2D rectangular bin packing problem, and entails the positioning ofa set of ships (rectangles) into as few lockages (bins) as possible while satisfying a number of general and specificplacement constraints. These include mooring constraints for ship stability, ship dependent safety distances andcorridor constraints between sea ships that require tugboats.A decomposition model is presented that allows for computing optimal solutions. Experiments on simulatedand real-life instances show that the decomposition model generates optimal, real-life feasible solutions, whilemaintaining acceptable calculation times. Next, a constructive heuristic is introduced that obtains high-qualityresults in just a few milliseconds.Both solution methods are part of a decision support tool, which allows lock masters to compute and compareseveral solutions for a set of arriving and departing ships. Live tests have shown that the tool’s flexibility andhigh solution quality may help the lock masters in making quick and informed decisions.Keywords: ship placement, decomposition, decision support, lock scheduling



1.3Modeling and solving the placement problem of rectangles with variable

metric characteristicsM. Novozhylova∗, I. Chub†, M. Murin†

∗Kharkov National University of Civil Engineering and Architecture, Kharkov, Ukraine, †Kharkov NationalUniversity of Civil Defense of Ukraine, Kharkov, Ukraine

Most of placement problems considered in scientific literature concern placement of pieces having fixed metriccharacteristics (sizes) and spatial form. In general only placement area because its size is an objective function ofthe problem. However, some important resource-saving problems, as well as constructing industrial systems withsources of pollution emission allow the formulation in the terms of optimization placement problems where piecesbeing placed have variable metric characteristics and spatial form.We indicate two kinds of changing metric characteristics: a) metric characteristics are subject to functionalrelationships and b) metric characteristics of pieces can be changed independently of each other in a given range(interval analysis, fuzzy sets, soft computing). The result of changing metric characteristics with respect to spatialform of pieces may be different. A spatial form of piece could change under changing its metric characteristicsdown to loss of topological dimension of piece. In this communication we deal with the case a) when the metriccharacteristics of pieces vary so that the piece area remains unchanged.In so doing we consider a 2D placement problem where pieces are rectangles with variable metric characteristicsand placement area is a strip with a fixed width and variable length. The objective is to minimize the striplength. Based on approach proposed by Stoyan et al. [1] we construct continuous analytical representation ofmain problem geometric constraints: belonging pieces to placement area and non-overlapping pair of pieces.The set of problem constraint functions contains linear and hyperbolic ones. So, taking into account initialstatement we can formulate the problem being considered as a union of finite set of convex programming problems.On the other hand we treat hyperbolic functions of problem constraints as separable ones and propose effectivealgorithm for linear approximation the given functions with required precision set a priory.We study additional constructive properties of problem and propose on this base of a optimization methodsearching for local optimal solution of linearized problem using as the base the active set strategy approach.The proposed method has been applied for modeling resource constrained project scheduling and solving theresource leveling problem.Keywords: placement of rectangles, variable metric characteristics, separable functions

2.1An algorithm for putting on pallets and loading products into trucks

M. T. Alonso∗, R. Alvarez-Valdes†, J. Gromicho‡, F. Parreño∗, G. Post‡, J.M. Tamarit†∗University of Valencia, Department of Statistics and Operations Research, Burjassot, Valencia, Spain,

†University of Castilla-La Mancha. Department of Mathematics, Albacete, Spain, ‡ORTEC Logistics, Gouda,The Netherlands

In a large logistic company the inter-depot planning problem has to be solved every day. The products are placedon pallets and then the pallets loaded into trucks. The main objective is to send the fewest number of trucks,covering the demand of each depot and satisfying a number of constraints concerning the way in which pallets arebuilt and placed into the truck (priorities, stackability, total weight and volume, axle weight, center of gravity,. . . ).The problem can be solved in two phases, one for building the pallets and the other for loading the pallets intothe truck, but our proposal is to solve the problem in one phase building and placing pallets at the same time.For each place into the truck a pallet is built tailored for that the position according to the constraints (priority,axle weight, and so on). We have developed a metaheuristic in two phases, one for building a feasible solutionand the other for improving the solution trying to reduce the number of trucks that we have to send to the depot.Keywords: palletisation, truck loading, metaheuristics

2.2Mixed case 3D pallet loading with optimized robotic loadings

Tony Wauters, Jan Christiaens, Greet Vanden BergheCODeS, KU Leuven - KAHO Sint-Lieven, Gent, Belgium

The present paper considers the mixed case 3D pallet loading problem with optimized robotic loadings. Theproblem has been derived from a real-world pallet loading case. A number of rectangular shaped boxes of differentsizes have to be loaded onto one or multiple pallets, subject to various hard and soft constraints. In addition tothis complex three dimensional loading problem, the boxes have to be partitioned into layers. Each layer containsa set of boxes which can be loaded simultaneously by a robotic arm.



A set of n rectangular shaped boxes have to be loaded on one or multiple rectangular pallets. All pallets havea fixed length, width and height. Each box belongs to a particular box type with defined length, width, height,weight, weight class, order line and family. The boxes have a ‘this side up’ restriction, and can only be rotatedfor 0 or 90 degrees around the z-axis.The main objective is to place all given boxes onto a minimal number of pallets, while still respecting the followinghard and soft constraints. Hard constraints:

• Pallet dimensions: each box must be placed on a pallet such that it does not exceed the pallet boundaries.

• Overlap: each box must be placed on a pallet such that it does not overlap with other boxes.

• Support: each box must be supported by other boxes for a certain percentage of its surface. No floatingboxes are allowed.

• Weight class: a box can only be placed on boxes of the same or a lower weight class (heavy boxes havelower weight classes), or on the pallet surface.

Soft constraints:

• Number of loading steps: minimize the number of steps needed for loading all boxes using a robotic arm.The robotic arm can carry multiple boxes together, but has several properties that limit which boxes canbe carried together.

• Center of gravity: for each pallet minimize the absolute difference between the center of gravity and themiddle of the pallet.

• Order line grouping: put boxes belonging to the same order line close together.

• Family grouping: put boxes belonging to the same family close together. Some box families cannot beadjacent.

All hard constraints have to be respected at any time. The soft constraints can be added as extra terms to theobjective function. The hard constraints make it very hard to obtain a feasible solution for this problem, whilethe soft constraints are possibly conflicting with the main objective (minimize the number of required pallets).An example of such a conflict is that the positions of the boxes have a large effect on the number of loading steps.We present a heuristic approach to this complex pallet loading problem. This algorithm combines a new bestfit placement strategy for positioning the boxes, and a state-of-the-art graph colouring heuristic for partitioningthe boxes into layers. Good results are observed compared to current packing solutions on real-world probleminstances.Keywords: pallet loading, three-dimensional packing, heuristics, robotic loading

2.3Placing pallets in containers under real life constraints

J.A.S. Gromicho∗†, J.J. van Hoorn†, G.F. Post‡†∗VU University Amsterdam, †ORTEC, ‡University of Twente

We present an algorithm for placing loaded pallets in containers while obeying stackability and grouping con-straints. Other real life business requirements considered are a proper weight distribution over the vehicle axlesand a decreasing height of the stacked pallets from front to rear inside the container for stability reasons. Ouralgorithm amounts to one single construction based on local decisions taken optimally on the total set of palletssuch as the determination of pairs of pallets as solution of non-bipartite matching instances. A comparison withthe results obtained by a GRASP algorithm on an extensive set of real life instances shows promising results: weobtain solutions of similar quality in a much lower running time especially on larger instances.Keywords: container loading, weighted matching, deterministic construction heuristic

2.4Container loading in international logistics platforms for the automotive

industryAlain Nguyen, Jean-Philippe Brenaut

IT department / Optimization Team for Sales and Logistics, Renauit

European-based RENAULT’s international logistics platforms have to ship weekly several hundred containers tooverseas destinations. The minimization of the number of shipped containers is critical since a gain of one cubicmeter per container can generate annual savings worth hundreds of thousands of euros for a single platform.For every customer, all its weekly packages have to be shipped in a minimal number of containers under variedconstraints:



• a maximal weight per container,• stacking constraints : metallic packages cannot be mixed with wooden or cardboard packages in the same

stack,• resistance constraints on wooden and cardboard packages : heavy packages (> 500 kg) must be layered on

the ground while small and light packages (< 100 kg) must be put on top of the stacks,• stability constraints : thin packages must be positioned in twin stacks,• orientation constraints on packages : due to the minimal distance between the forks of forklift trucks, thin

packages have to be loaded by the longest side (and not by the shortest side).A customer can have as many as 1200 packages a week to be loaded into 50 containers. Packages dimensions(length/width/height) can vary widely from small packages (300x200x125 mm) to very large ones (1950x1300x1250mm).The loading process consists in building stacks of packages and then loading these stacks into the container. Wedesigned a two-phase algorithm to cope with this process:

1. pre-computation of all the theoretical packages stacks configurations based on the dimensions and materialof packages.

2. 2D placement of the packages simultaneously into all the not yet full containers, using the most relevanttheoretical stacks configurations.

Two algorithms were implemented for the 2D placement. The first algorithm is heuristics driven: each stack isoriented along its shortest side, and placed so as to minimize the length of the used floor space, simultaneouslyon the left, right and middle sides of the container. The second algorithm applies the same heuristics, but witha look-ahead of length N (usually 5): for the placement of a stack, the algorithm evaluates all the combinationsfor the placement of the current stack and the N following stacks, and selects the placement of the current stackwhich generates the best solution for the N+1 stacks. The best solution is the one which minimizes both thelength of the used floor space and the lost space between the stacks.We obtain satisfactory filling rates for the business (> 75%), but response times remain a challenge to be addressed.For a medium-sized logistics platform, our algorithm takes 1h30 to load 16000 packages into 220 containers (onan Intel Xeon 2.4 Ghz PC). We need to make breakthroughs in terms of response times in order to deal withlarge-sized logistics platforms, which handle as many as 50000 packages.Keywords: container loading, bin packing, automotive industry

3.13D Packing Problems with an Uniform Weight Distribution – A Case Study

Maria da Graça Costa∗‡, Maria Eugénia Captivo†‡∗Escola Superior de Ciências Empresariais, Instituto Politécnico de Setúbal, Campus do IPS, Estefanilha,

2914-503 Setúbal, Portugal, †Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Bloco C6 - Piso 4,1749-016, Lisboa, Portugal, ‡ Centro de Investigação Operacional da Faculdade de Ciências da Universidade de

Lisboa

This work addresses a real world problem proposed to us by a Portuguese automotive company. Every day thiscompany needs to establish a plan to pack a set of boxes onto a truck. Since the transport is made directlyfrom the suppliers to the factory, we don’t need to consider the problem of establishing a route or to worry withmulti-drop situations. So, we will only address the operations for packing the boxes.The cargo consists of rectangular boxes with different sizes and weight, and the vehicle is a single truck. There aredifferent types of boxes that are divided into two major groups: group A consists of small boxes with no lid that,before being placed inside the truck, need to be combined onto a pallet; group B consists of bigger, completelyformed, boxes that are packed individually in the truck.We can divide our problem into two successive phases: the construction of pallets (a manufacturer’s pallet loadingproblem) and the loading of the cargo into the truck (a single container loading problem). These two phasesshould not be solved independently, since the final dimensions of the pallets will have an impact on the finalpacking plan of the whole cargo. According to Wascher et. al. (2007) typology, this problem can be classified asa Three- Dimensional Rectangular Single Large Object Placement Problem.Since this is a real application, some practical constraints cannot be overlooked, like load stability and boxorientation constraints, weight limit of the truck and uniform distribution of weight inside the truck.To solve this problem, we propose a constructive heuristic based on a layer arrangement approach, with a starstrategy and with a weighted average measure for the boxes. For each layer, the main idea is to spread theheaviest boxes along the container in a star form, from the sides to the centre of the container. This heuristic isbased on a corner selection that, instead of finding the appropriate corner for the current selected box, finds theappropriate box for the current corner.When we are left with a small number of boxes that weren’t placed in the current layer, or when there isn’t asufficient number of boxes of the same height to build a complete layer, we will have to do some local changes



in order to try to obtain a feasible solution. The application of this constructive heuristic to the company’s dataand the corresponding results will be presented and discussed.Keywords: container loading, weight distribution, heuristics

3.2Development of a Cargo Loading Sequence Algorithm for the Container

Loading ProblemAntónio Galrão Ramos∗†, José Fernando Gonçalves‡, José F. Oliveira∗, Manuel P. Lopes†

∗INESC-TEC, Faculty of Engineering, University of Porto, †School of Engineering, Polytechnic Institute ofPorto, ‡LIAAD, INESC-TEC, Faculty of Economics, University of Porto

The role that cargo transportation plays as the basis for worldwide trade places enormous challenges to transportmanagers, demanding for a continuous quest to increase rationality in the usage of transportation.The container loading problem, a NP-hard, real-world driven, combinatorial optimization problem, addresses theoptimization of the spatial arrangement of cargo inside transportation vehicles or containers, maximizing thecontainers space utilization.Many Container Loading Problem approaches, found in the literature, are still of limited applicability in practicalsituations because they do not effectively address real-world problems requests, like the existence of a physicallystable packing sequence or cargo stability during transportation.The physical packing sequence is the sequence by which each box is placed inside the container in a specificlocation determined by the algorithm. It is considered that some determined arrangements of boxes can’t beloaded, as it does not exist a sequence to load them into those positions, namely because there are obstructionsand some of the arrangements aren’t stable during the loading operations.This article presents an algorithm that, given a loading plan, proposes a cargo loading sequence that maximizesstability during these operations.Keywords: physical packing sequence, container loading, 3d packing, static stabilitySupported by Fundação para a Ciência e Tecnologia (FCT) project PTDC/EGE-GES/117692/2010.

3.3Constructive Heuristic for the 3D Container Loading Problem

Xiaozhou Zhao∗, Julia Bennell∗, Kathryn Dowsland†, Tolga Bektaş̧∗∗School of Management, CORMSIS, University of Southampton, UK, †Gower Optimal Algorithms Ltd., UK

The paper arises from an ongoing research project with Gower Optimal Algorithms Ltd (GOAL), focusing on theircontainer packing problem. The overall aim is to develop effective heuristics for 3D regular packing problem wherethere are multiple identical or non-identical large items. The project is in its early stages. In this presentationwe investigate problems with weakly heterogeneous small items and one or more identical large item. Specificallywe consider the Single Large Object Placement Problem, with the aim of output maximisation, and the SingleStock Size Cutting Stock Problem, with the aim of input minimisation. GOAL’s core algorithm utilises a numberof heuristic strategies for determining the placement of boxes, which can be used individually or combined as auser defined subset. Since the output must be usable in practice, placements must obey all additional practicalconstraints such as orientation, stability, weight limits, weight distribution, stacking and bearing strength. Prior-ities can be assigned to boxes according to customer requirements. Our research focuses on the impact of priorityorders. Different existing box sorting strategies in the literature are combined into sets with a third-tier tie breakerand tested on benchmark data. Results under different sorting rules when the rule is strictly adhered to and whenit can be relaxed if the next item can not put into the open container are compared with the literature. In asimilar manner, we test different sets of heuristics for their impact on the various problem instances. Finally wedevise problem instances that simulate the requirements of the vehicle routing problem where deliveries involvemultiple commodities and unnecessary unloading and reloading is to be avoided. Extensive numerical results onbenchmark problem instances will be presented.Keywords: container loading, sequencing, heuristics



3.4A randomized constructive algorithm for the container loading problem with

multi-drop constraintsDavid Álvarez Martínez∗, Francisco Parreño†, Ramón Álvarez-Valdés‡

∗Department of Electrical Engineering, São Paulo State University, Campus 3, Ilha Solteira, Brazil, †Universityof Castilla-La Mancha. Department of Mathematics, Albacete, Spain, ‡University of Valencia, Department of

Statistics and Operations Research, Burjassot, Valencia, Spain

The container loading problem is a classic problem in operation research and has a big importance and applica-tion in the industry, despite that it is not common to find studies including all the characteristics that representpractical constraints for this problem, such as: box rotations, load-bearing strength, weight limits, full supportand multi-drop constraints. In this paper, we consider the container loading problem with all the constraintspreviously mentioned. Formally, this problem is known as three-dimensional multi-drop Single Large ObjectPlacement Problem (3DSLOPP) or Single Knapsack Problem (3DSKP). The aim is maximize the loading value,but guaranteeing that all the constraints are satisfied. Specifically, the multi-drop constraint refers to the factthat subsets of item go to different costumers and the position of these subsets inside the container has to allow tounload the items of a costumer without moving the items of other costumers. We have developed a randomizedconstructive algorithm based on maximal-spaces, which builds totally feasible solutions. We have also developeda local search phase with several improvement moves. These two phases have been put together in a GRASPmetaheuristic scheme. A computational study using all the instances and real-world problems taken from theliterature is presented and discussed.Keywords: container loading, constraints, heuristics

4.1Models and algorithms for customizing shipping boxes

F. Parreño∗, M. T. Alonso∗, R. Alvarez-Valdes†, J.M. Tamarit†∗University of Castilla-La Mancha. Department of Mathematics, Albacete, Spain, †University of Valencia,

Department of Statistics and Operations Research, Burjassot, Valencia, Spain

A distribution company in Spain has to send products, packed into shipper boxes, from the store to the retailshops. The problem is to decide the sizes of the shipper boxes to be kept at the store so as to minimize the cost ofpacking all the forecasted demands along the planning horizon. The number of different sizes is fixed beforehand,looking for a balance between transportation costs and stock and procurement costs.In this work we describe two integer linear programming formulations for the problem. The first one uses asvariables the possible packing patterns and the other is based on the p-median problem, adapted to the charac-teristics of this case. The first one is used to obtain lower bounds and the second one in order to obtain feasiblesolutions. As the number of possible boxes is very large and consequently the models may have a huge number ofvariables, we have designed several heuristics to reduce the set of possible boxes. We only use feasible and efficientpartitions. In order to avoid symmetrical solutions, due to the rotation of the products, we only consider shipperboxes whose length is lower or equal to their width. If we have orders with the same quantities of products, theorder is repeated and we can remove one of these orders of the formulation, doubling its cost in the objectivefunction.Even with these reductions, the integer problems are usually too large to be solved in reasonable times, but solvingthe first formulation over some subsets of packing patterns gives us good feasible solutions while some relaxationsof the second one can be used in order to obtain lower bounds.With the aim of improving the solutions obtained with the previous methods, we have also used a metaheuristicalgorithm in order to improve the packing of products in the shipper boxes. Other alternative consists of usingthe models in a reduced problem. A computational study conducted on real instances provided by the companyis presented and discussed.Keywords: integer formulations, metaheuristics, packing patterns



4.2A GRASP for circle packing

João Pedro Pedroso∗, Sílvia Cunha†, António Guedes de Oliveira†, João Nuno Tavares††INESC TEC and Faculdade de Ciências, Universidade do Porto, †CMUP and Faculdade de Ciências,

Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal

We address a problem of packing tubes in a container, consisting of two steps:

1. packing tubes inside other tubes (telescoping);

2. packing these tube modules in a container.

Given that tubes are cut with the length of the container, the problem reverts to circle packing in circles and inrectangles, respectively, with an additional constraint limiting the total weight in each container.There may be two objectives, depending on the order/customer:

1. Packing all the items of a given order in the minimum number of containers;

2. Packing as many items of a given size as possible in a container (as long as weight is not constraining).

The approach used for solving this problem is based on a greedy heuristics, where tubes are inserted one at a timefrom the bottom up, thicker tubes being inserted first. From the possible positions for a tube touching two othertubes (or container walls), the one at the lowest height is chosen (if there are several possibilities, the leftmost ischosen).This greedy heuristics is combined with a random component which determines several possible candidates (tubesand their positions) and chooses one among them. Follows a local search, where tubes are moved into lowerpositions, if possible.Preliminary results indicate that the solutions are appropriate for practical implementation.Keywords: circle packing, container loading, grasp, local search

4.3Packing Cuboids and Spheres

Yu. Stoyan, A. ChugayInstitute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkov,

Ukraine

This talk presents a packing optimization problem of different spheres and cuboids into a larger cuboid of theminimal height. Translations and continuous rotations of cuboids are allowed. In order to derive a mathematicalmodel of the optimization problem we offer special functions (Phi -functions) describing how translations androtations can be dealt with. These functions permit to build the mathematical model as a classical mathematicalprogramming problem. Basic characteristics of the mathematical model are investigated. The characteristics allowto apply a number of original and state-of-the-art efficient methods of local and global optimization when solvingthe optimization problem. On the ground of a jump algorithm ensuring a smooth transition from a local extremalpoint to one another, a technique of non-exhaustive search of local extrema to calculate a good approximation toa global extrema is worked out. Numerical examples of packings from 20 to 300 geometric objects are given.Keywords: optimization, packing, sphere, cuboid, translatioin, rotationYu. Stoyan acknowledges the support of the Science and Technology Center in Ukraine and the National Academy ofSciences of Ukraine, grant 5710.

4.4Optimal Packing Circular Cylinders into a Cylindrical Container Taking into

Account Behavior ConstraintsP. Stetsyuk∗, T. Romanova†, A. Pankratov†, A. Kovalenko†

∗Institute of Cybernetics of the National Academy of Sciences of Ukraine, Kiev, Ukraine, †Institute forMechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkov, Ukraine

The paper considers packing problem of parallel circular cylinders into a cylindrical container of the minimalradius taking into account the system behavior mechanical constraints (dynamic balance, inertia moments andstability). We provide a mathematical model on the basis of the phi-function technique. Mathematical modelis presented as a constrained non-linear optimisation problem with linear objective. The number of variables is3N+1, where N is the number of objects and each object has tree variables of placement parameters (x,y,z), as wellas radius R of the container base is a variable. We consider the following restrictions: (a) N quadratic non-convexinequalities for containment constraints; (b) N*(N+1)/2 quadratic non-convex inequalities for non-overlappingconstraints; (c) six linear inequalities for stability constraints; (d) six quadratic fractional inequalities for inertia



moments constraints; (e) six quadratic fractional inequalities for dynamic balance constraints. We offer two solu-tion algorithms: based on the Shor r-algorithm and IPOPT. Computational of test experiences are given.Keywords: circular packing, system behavior mechanical constraints, mathematical model, phi-functions,approximate methodsP. Stetsyuk, T. Romanova, and A. Pankratov acknowledge the support of the Science and Technology Center in Ukraineand the National Academy of Sciences of Ukraine, grant 5710.

5.1Optimal clustering of a pair of irregular objects bounded by arcs and line

segmentsT. Romanova∗, J. Bennell†, G. Scheithauer‡, Y. Stoyan∗, A. Pankratov∗

∗Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkov,Ukraine, † Southampton Management School, United Kingdom, ‡Technische Universität Dresden, Germany

Cutting and packing problems arise in many fields of applications and theory. When dealing with irregular ob-jects, an important subproblem is the identification of the optimal clustering of two objects. Within this paperwe consider a container (a rectangle or a circle or a convex polygon) of variable sizes and two irregular objectsbounded by circular arcs and/or line segments, that can be continuously translated and rotated. In additionminimal allowable distances between objects as well as between each object and the frontier of a container maybe given. The objects should be arranged within container such that a given objective will reach its minimalvalue. As the objective we consider a polynomial function which depends on variable parameters both of objectsand container. We propose a solution strategy which is based on the concept of phi-functions and provide someexamples of containment or enclosing problems with finding minimal area, perimeter, homotetic coefficient of agiven container as well as finding the convex polygonal hull (or its approximation) of a pair of objects.Keywords: contaiment, irregular shapes, continuous rotations, enclosing rectangle, enclosing circle, en-closing covex polygon, convex polygonal hull, distance constraints, mathematical modeling, optimizationT. Romanova, Yu. Stoyan and A. Pankratov acknowledge the support of the Science and Technology Center in Ukraineand the National Academy of Sciences of Ukraine, grant 5710.

5.2Solving the bin packing problem with irregular pieces and guillotine cuts

Antonio Martinez∗, Ramon Alvarez-Valdes∗, Julia Bennell†, Jose Manuel Tamarit∗∗University of Valencia, Department of Statistics and Operations Research, Burjassot, Valencia, Spain, †School

of Management, CORMSIS, University of Southampton, UK

The two-dimensional irregular-shape bin packing problem with guillotine cuts arises in the glass cutting industry,when a given set of convex non-rectangular pieces has to be cut from the minimum number of glass sheets. Theglass cutting process imposes guillotine cuts, cuts that divide a given piece of glass into two different parts.Most of the algorithms that can be found in the literature on two-dimensional irregular shape packing problemsminimize the length of strip required to accommodate the pieces and do not force a guillotine cut structure.On the other hand, most of the algorithms including guillotine cuts deal with rectangles, so the guillotine cutsare orthogonal with the edges of the stock sheet. The problem considered in this paper combines three difficultcomponents: the non-overlapping of the irregular pieces that can be freely rotated, the bin packing problem wherepieces are associated to stock sheets, and guillotine constraints that guarantee that the solution can be producedby a set of freely rotating guillotine cuts.e propose a constructive algorithm which inserts the pieces one at a time. A predefined order determines the nextpiece and mathematical programming determines its position using two different guillotine cut structures. Whena bin is full, we call an improvement procedure with the aim of increasing the utilization of the bin by changingthe rotation and the order of the pieces, before the bin is closed.The computational results on a set of available instances shows that the proposed algorithm outperforms aprevious algorithm designed for this problem. We have also applied the procedure to the bin packing problem withrectangular pieces and guillotine cuts and the results obtained are competitive with the best know constructivealgorithms for this problem.Keywords: irregular pieces, bin packing, guillotine cuts



5.3Exploring Non-Linear Models for Nesting Problems

Pedro Rocha∗, Rui Rodrigues∗, A. Miguel Gomes∗, Marina Andretta†, Franklina M. B. Toledo†∗INESC-TEC, Faculty of Engineering, University of Porto, †Instituto de Ciências Matemáticas e de

Computação, Universidade de São Paulo

Nesting problems are a variant of Cutting and Packing problems where irregular shaped pieces need to be packedinto a given region without overlap, while minimizing the waste. In this work we tackle a variant of the Nestingproblem where the pieces can rotate freely. The proposed approach is based on a Circle Covering representationof the pieces together with a Non-Linear Programming (NLP) model.Circle Covering uses circles to represent irregular pieces, which are simple to rotate, and can compute overlapswithout much computational cost. The overlapping constraints, used to represent overlap and structural integrityof each piece, are described by non-linear equations, leading to a NLP model. The mathematical model is solvedby a non-linear solver, which starts with an initial solution and converges to a local minimum. Due to insufficientcomputational performance to solve large instances, we propose to explore several improvement approaches.Experimentation included reducing the number of constraints and variables, and also restricting movement androtations of pieces. Changes to the objective function also show positive influence on the solver performance.The potential improvement in allowing free-rotations in Nesting problems can bring significant increases in effi-ciency (waste and cost reduction), which will impact many industrial applications. Preliminary computationalexperiments showed promising results.Keywords: non-linear programming, circle covering,irregular packing problemSupported by Fundação para a Ciência e Tecnologia (FCT) project PTDC/EME-GIN/105163/2008.

5.4A hybrid matheuristic algorithm for the nesting problem

A. Martinez-Sykora∗, R. Alvarez-Valdes∗, M. A. Carravilla†, A. M. Gomes†, J. F. Oliveira†, J. M.Tamarit∗

∗University of Valencia, Department of Statistics and Operations Research, Burjassot, Valencia, Spain,†INESC-TEC, Faculty of Engineering, University of Porto

Two-dimensional strip packing problems with non-rectangular pieces, known as Nesting problems, arise in awide variety of industries like garment, sheet metal cutting, furniture making and shoe manufacturing. Theproblem is very difficult to solve by exact methods and good quality solutions are difficult to obtain even by usingsophisticated metaheuristic procedures.We have designed an Iterated Greedy Algorithm, which combines three components:

– a dynamic constructive algorithm, that is, a constructive algorithm based on the insertion of the pieces oneat a time.

For each insertion a Mixed Integer Programming (MIP) model has to be solved. Some parameters controllingthe procedure change dynamically along the process depending on whether the insertion of the new pieceis proved to be optimal or not.

– a destructive phase in which part of the current solution is removed and built again by using the constructivealgorithm

– a local search phase to improve the rebuilt solution, based on the removal and reinsertion of individual orpairs of pieces.

The parameters which define the neighborhood also change dynamically according to the computationaltime needed to solve the corresponding model.

Computational results on a set of well-known instances show that the IGA is competitive and in several instancesit founds the best known solution.Keywords: nesting problems, matheuristics, iterated greedy algorithm, integer programming

6.1New Approximability Results for Two-Dimensional Bin Packing

Klaus Jansen, Lars PrädelUniversity Kiel, Germany

We study the two-dimensional bin packing problem: Given a list of n rectangles the objective is to find a feasible,i.e. axis-parallel and non-overlapping, packing of all rectangles into the minimum number of unit sized squares,also called bins. Our problem consists of two versions; in the first version it is not allowed to rotate the rectangleswhile in the other it is allowed to rotate the rectangles by 90◦, i.e. to exchange the widths and the heights.



Two-dimensional bin packing is a generalization of its one-dimensional counterpart and is therefore strongly NP -hard. Furthermore Bansal et al. showed that even an APTAS is ruled out for this problem, unless P = NP .This lower bound of asymptotic approximability was improved by Chlebík & Chlebíková to values 1+1/3792 and1 + 1/2196 for the version with and without rotations, respectively. On the positive side there is an asymptotic1.69.. approximation by Caprara without rotations and an asymptotic 1.52 . . . approximation by Bansal et al. forboth versions.We give a new asymptotic upper bound for both versions of the problem: for any fixed ε and any instance Ithat fits optimally into OPT (I) bins, our algorithm computes a packing into (1.5 + ε) · OPT (I) + 69 bins withpolynomial running time in the input length.Keywords: scheduling and resource allocation problems, bin packing, rectangle packing, approximationalgorithms

6.22DCPackGen: A problem generator for two-dimensional rectangular cutting

and packing problemsElsa Silva∗, José F. Oliveira∗, Gerhard Wäscher†

∗INESC-TEC, Faculty of Engineering, University of Porto, †Otto-von-Guericke-Universität Magdeburg

Cutting and packing problems have been extensively studied in the literature in the last decades, mainly due toits computational complexity (almost all NP-hard) and due to its numerous real-world applications.Different variants and objectives may be considered depending on the applications where the problem appeared.However, all the problems have in common the existence of a geometric sub-problem, originated by the naturalitem non-overlapping constraints.In order to provide an organization in categories of the cutting and packing problems and of the literature onthis topic, a relevant recent contribute was given by Wäscher (2007) with an improved typology on cutting andpacking problems. In addition to the unification of definitions and notations, the recent typology facilitated alsothe access to the relevant literature to each cutting and packing problem category.Nevertheless, a limitation is felt by researchers in cutting and packing problems field, the absence of appro-priate test problems and problem generators which are widely and commonly used by all researchers in theircomputational experiments.Regarding the one-dimensional problems, a problem generator is available in the literature. However, for thetwo-dimensional problem the computational experiments are conducted over classical sets, usually without anycritical analysis of their nowadays difficulty, adding a few of self-generated instances.Computational experiments are used to demonstrate the superiority of an algorithm regarding the quality of thesolutions, the computational times and the identification of its limits and behaviour. Therefore, when the rightinstances are not used to test the algorithms, the published foundations for the superiority of an algorithm overothers may be rather weak.The lack of appropriate test problems for each type of cutting and packing problem, led also to the adaptation ofexisting instances to solve problems for which they were not designed.To overcome the drawback of the lack of general two-dimensional cutting and packing problem generators, thiswork proposes a problem generator for each type of 2D rectangular cutting and packing problem (2DCPackGen).The problem generator will strongly contribute for the quality of the computational experiments run with cuttingand packing problems and will allow the generation of a large number of problems instances under controlledconditions with specific desired properties, which provides the ground for systematic testing and variation ofproblem parameters.The 2DCPackGen is not build on sampling uniform distributions and will contribute for a faster access to theproblem tests, for every type of two-dimensional rectangular cutting and packing problems.Keywords: two-dimensional rectangular problems, problem generator and benchmarksSupported by Fundação para a Ciência e Tecnologia (FCT) project PTDC/EIA-CCO/115878/2009.

6.3Construction Heuristic Algorithms for Soft Rectangle Packing

Shinji Imahori, Chao WangDepartment of Computational Science and Engineering, Nagoya University, Japan

A problem of packing a set of soft rectangles into a larger rectangular container is studied. A set of n softrectangular items are given, where each item i has its area a(i), lower bound of width wL(i) and upper bound ofwidth wU (i). Each rectangular item i can be deformed under the above constraints; that is, width w(i) shouldbe in the range [wL(i), wU (i)] and height h(i) = a(i)/w(i) holds. If item i can be rotated, its width w(i) shouldbe in the ranges [wL(i), wU (i)] or[a(i)/wU (i), a(i)/wL(i)] (these two ranges may have overlap). Also given is arectangular container with fixed width W and unrestricted height H. The task is to pack all of the soft rectangular



items orthogonally without overlap into the container, so as to maximize the occupation rate (equivalent to theminimization of height H of the container).This problem is relevant for many applications in VLSI design, and practical algorithms are necessary. Thisproblem is, however, known to be NP-hard, and heuristic or metaheuristic algorithms are important for tacklinglarge-scale instances. Young et al. (2001) and Ibaraki and Nakamura (2006) proposed metaheuristic algorithmswith mathematical programming techniques. Their algorithms were effective but need much computation timefor large-scale instances.In this study, we propose two construction heuristic algorithms for the problem. Our algorithms are based onthe best-fit algorithm for rectangle packing. The best-fit algorithm was proposed by Burke et al. (2004) andits efficient implementation, which runs in O(nlogn) time, was proposed by Imahori and Yagiura (2010). Ouralgorithms for the soft rectangle packing problem run in O(nlogn) or O(n2) time, and it is possible to apply ouralgorithms to large-scale instances.We implement the algorithms and perform computational experiments. The computational results show that ouralgorithms run fast; they place thousands of soft rectangular items within one second. One of our algorithmsoutputs layouts whose occupation rate are around 99% for instances with hundreds or thousands of items.Keywords: soft rectangle packing, construction heuristics, best-fit algorithm

6.4A Hybrid Constructive Heuristic for the Rectilinear Area Minimization

ProblemMarisa Oliveira∗, Eduarda Pinto Ferreira∗, A. Miguel Gomes†

∗Instituto Superior de Engenharia do Porto, Instituto Politécnico do Porto, †INESC-TEC, Faculdade deEngenharia, Universidade do Porto

In this work we intend to solve large rectilinear packing (RP) problems in a reasonable computational time. In theRP problems small pieces have rectilinear shapes (pieces with 90 or 270 degrees interior angles) and the objectiveis to minimize the area of the enclosing rectangle which contains, without overlap, all the pieces.The pieces must be placed orthogonally (i.e., with sides parallel to the horizontal and vertical axes, through 0,90, 180 or 270 degrees rotations) and their dimensions are fixed. This problem arises in a wide range of activities,such as in the placement of circuit modules in Very Large Scale Integration (VLSI) circuits and in the designof facility layouts. For example, in VLSI circuits rectilinear shaped pieces appeared to reduce the circuits’ areawhile improving the connectivity between pieces and increasing the circuit performance.To tackle this problem we propose a hybrid approach that combines mathematical models with heuristic ap-proaches. Combining ideas from mathematical models and heuristics can provide a more efficient behavior andhigher flexibility when dealing with real-world and large scale problems. With this approach the objective is totackle large instances and getting better heuristic solutions in shorter time.The proposed approach uses heuristic rules to decompose large and complex RP problems in smaller ones. Math-ematical models are used to solve iteratively the smaller problems to ensure good quality solutions. In eachiteration, to decrease the model complexity the relative positions between some pairs of pieces are fixed and/orrelaxed. The complete solutions are built by an iterative procedure. At each iteration mathematical models areused to place a small set of pieces. Each small set is obtained by heuristic rules based on the pieces sizes. Ineach iteration, the relative positions between pairs of pieces placed in previous iterations are kept fixed, whilethe new pieces to place have free relative positions. The idea is to start by placing the bigger pieces to find agood arrangement between them and use the small ones to fill the gaps between the bigger ones. The iterativeprocedure stops when there are no pieces available to place.The computational results show that the proposed approaches are able to solve large instances in a reasonablecomputational time. They also show that these approaches are effective dealing with rectilinear shaped pieces.Keywords: area minimization, rectilinear packing, hibridizationSupported by Fundação para a Ciência e Tecnologia (FCT) project PTDC/EME-GIN/105163/2008.

7.1Friendly Bin Packing Instances without Integer Round-up PropertyAlberto Caprara∗, Mauro Dell’Amico†, José Carlos Diaz Diaz†, Manuel Iori†, Romeo Rizzi‡

∗ Department of Electrical, Electronic and Information Engineering Guglielmo Marconi (DEI), University ofBologna, Italy, † Department of Science and Methods for Engineering (DISMI), University of Modena and

Reggio Emilia, Italy, ‡ Department of Computer Science (DI), University of Verona, Italy

It is well known that the gap between the optimal values of bin packing and fractional bin packing, if the latter isrounded up to the closest integer, is almost always null. Known counterexamples to this for integer input valuesinvolve fairly large numbers. Specifically, the first one was derived in 1986 and involved a bin capacity of theorder of a billion. Later in 1998 a counterexample with a bin capacity of the order of a million was found. In



this paper we show a large number of counterexamples with bin capacity of the order of a hundred, showing thatthe gap may be positive even for numbers which arise in customary applications. The associated instances areconstructed starting from the Petersen graph and using the fact that it is fractionally, but not integrally, 3-edgecolorable.Keywords: bin packing problem, integer round-up property, petersen graph

7.2Biased Random Key Genetic Programming based Heuristics for the 1D Bin

Packing ProblemJosé Fernando Gonçalves

LIAAD, INESC-TEC, Faculdade de Economia, Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-464Porto, Portugal

This paper addresses the one-dimensional bin packing problem. The heuristics are generated automatically by aGenetic Programming algorithm which combines intelligently base components and uses a biased random key forthe evolutionary process. The analysis of the heuristics generated is based on an average-case performance. Thecomputational experiments demonstrate that the approach performs well on several types of inputs distributionsand is competitive when compared with human designed heuristics.Keywords: cutting and packing, metaheuristics, bin packingSupported by Fundação para a Ciência e Tecnologia (FCT) project PTDC/EGE-GES/117692/2010.

7.3An exact/hybrid approach based on column generation for the bi-objective

max-min knapsack problemRaïd Mansi, Cláudio Alves, Telmo Pinto, José Valério de Carvalho

Centro de Investigação Algoritmi da Universidade do Minho, Escola de Engenharia, Universidade do Minho,4710-057 Braga, Portugal

In this work, we address the max-min knapsack problem (MNK), which is an extension of the standard knapsackproblem where the profit of the items changes according to the scenario (each scenario is characterized by aspecific objective function). The objective of the MNK is to achieve the best solution in the worst possible casewithout exceeding the capacity of the knapsack, i.e. it consists in maximizing the worst total profit of the selecteditems. Since it is an extension of the standard knapsack problem, the MNK is NP-hard for a limited number ofscenarios, and strongly NP-hard when the number of scenarios is unbounded.We propose an original approach based on column generation to compute strong lower and upper bounds for theMNK. We describe the details of the underlying Dantzig-Wolfe decomposition, and present the associated columngeneration algorithm. The method was implemented and tested on large scale instances of the MNK. The resultsachieved with the method attest the performance of the approach.Keywords: column generation, bi-objective optimization, max-min knapsack problem

7.4The Multi-Handler Knapsack Problem under Uncertainty: models and

approximationsGuido Perboli, Roberto Tadei, Luca Gobbato

DAUIN - Politecnico di Torino, Turin, Italy

The Multi-Handler Knapsack Problem under Uncertainty is a new stochastic knapsack problem where, given a setof items, characterized by volume and random profit, and a set of potential handlers, we want to find a subset ofitems which maximizes the expected total profit. The item profit is given by the sum of a deterministic profit plusa stochastic profit due to the random handling costs of the handlers. On the contrary of other stochastic problemsin the literature, the probability distribution of the stochastic profit is unknown. By using the asymptotic theoryof extreme values, a deterministic approximation for the stochastic problem is derived. The accuracy of sucha deterministic approximation is tested against the two-stage with fixed recourse formulation of the problem.Extensive computational results are presented in order to show the tightness of the deterministic approximation.Keywords: knapsack problem, stochastic profit, multiple handlers, deterministic approximation



7.5A chance-constrained strip packing problem

François Clautiaux∗, Saïd Hanafi†, Ya Liu‡, Christophe Wilbaut†∗Université de Lille 1, LIFL UMR CNRS 8022, INRIA Lille Nord Europe, †Université de Valenciennes et duHainaut Cambrésis, LAMIH UMR CNRS 8201, Le Mont Houy, F-59313 Valenciennes, France, ‡School of

Management, Xi’an Jiaotong University, China

In the strip-packing problem, a set of rectangles have to be packed in a strip of a given width by minimizing the totalheight. In this paper, we focus on the level (or two-stage) case where items are packed into levels that are parallelto the bottom of the strip. The levels are packed on above the others. In the typology of [Waescher et al., 2006], thetwo dimensional strip-packing problem (2D-SPP) belongs to the class of two-dimensional open-dimension packingproblems. Many works have been devoted to this problem, among which exact and metaheuristic algorithms.All these works consider that the sizes of the items are fixed and known in advance. In some cases, the solutionsare so tight (i.e., there is no free space in the pattern) that any small modification (error) in the size of one singleitem may make the solution practically unfeasible. Such uncertainty on the data is quite common in industry andhas to be take into account. A first solution would be to disregard completely the possible error. This would leadto non feasible solutions. On the opposite, an over-conservative solution would consider an additional margin inthe size of each item, leading to possibly bad solutions in term of height.Therefore, in this paper, we deal with a new version of the strip-packing problem, denoted by CC-2DSPP, whereonly an estimation of each item size is known. The objective is to build a packing pattern with the minimumexpected height in such a way that the probability of the pattern to be feasible is no less than a given tolerance,denoted by α.The talk will be organized as follows. First we will introduce some notations and we deal with mathematicalformulations of the problem. Then heuristics will be proposed. Finally, we will report computational results.Keywords: strip packing, chance constrained



List of ParticipantsAlonso Martinez, Maria TeresaCastilla-La mancha [email protected]

Álvarez Martínez, DavidDepartment of Electrical Engineering, São Paulo [email protected]

Alvarez-Valdes, RamonUniversity Of [email protected]

Bennell, JuliaUniversity of [email protected]

Bortfeldt, AndreasOtto von Guericke University [email protected]

Brenaut, Jean-PhilippeRENAULT [email protected]

Bué, MartinUniversité de Lille [email protected]

Clautiaux, FrançoisUniversité de Lille [email protected]

Côté, Jean-FrançoisUniversity of [email protected]

Gérard, MatthieuUniversité de Lille [email protected]

Gomes, A. MiguelINESC-TEC, Faculdade de Engenharia, Universidadedo [email protected]

Gonçalves, José FernandoFaculdade de Economia do [email protected]

Gromicho, Joaquim A. S.VU University & [email protected]

Hanafi, SaïdUniversité de [email protected]

Imahori, ShinjiNagoya [email protected]

Iori, ManuelDepartment of Science and Methods for Engineering(DISMI), University of Modena and Reggio [email protected]

Jansen, KlausUniversity of [email protected]

Lopes, Isabel CristinaESEIG - Polytechnic Institute of [email protected]

Macedo, RitaUniversidade do [email protected]

Martinez Sykora, AntonioUniversity of [email protected]

Nguyen, [email protected]

Novozhylova, MarynaKharkov National University of Civil Engineering [email protected]

Oliveira, MarisaSchool of Engineering - Polytechnic Institute of [email protected]

Parreau, AlineUniversité de Lille [email protected]



Parreño, FranciscoUniversidad de Castilla-La [email protected]

Pedroso, João PedroUniversidade do Porto – Faculdade de [email protected]

Perboli, GuidoDAUIN - Politecnico di [email protected]

Post, Gerhard F.University of Twente & [email protected]

Prädel, LarsUniversity of [email protected]

Ramos, AntónioINESC-TEC - Polytechnic Institute of [email protected]

Rocha, [email protected]

Rodrigues Gomes da Costa, Maria da GraçaEscola Superior de Ciências Empresariais do InstitutoPolitécnico de Setú[email protected]

Romanova, TetyanaInstitute for Mechanical Engineering Problems of theNational Academy of Sciences of [email protected]

Silva, [email protected]

Stetsyuk, PetroInstitute of Cybernetics of the National Academy ofSciences of UkraineUkraine

Stoyan, YuriInstitute for Mechanical Engineering Problems of theNational Academy of Sciences of UkraineUkraine

Valério de Carvalho, J.Universidade do [email protected]

van Hoorn, Jelke [email protected]

Verstichel, JannesCODeS, KU Leuven – KAHO [email protected]

Wauters, TonyCODeS, KAHO [email protected]

Zhao, Xiaozhou (Joe)University of [email protected]



Notes


Lille Map

Montde Terre

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StationOxygène

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N.-D. dela Treille

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Monnoyer

Liberté

RenoirPlace A. Tacq

Isly

Bd. deMetz

PiscineDormoy

Catinat

UniversitéCatholique

Desmazières

JardinVauban

Solférino

Colbert

Leclerc

Les Bateliers

ConservatoireVoltaire

Danel

Palais de Justice

Lion d’Or

Carnot

SacréCœur J. Giélée

Nationale

R. duPort


Arago

Pl. aux Bleuets

Dieu deMarcq

StMaurice

Dupleix

GassendiBallon

LycéePasteur

GrimonprezJooris

H. Regnault Legrand

Casino

Colpin

Champde Mars

Esplanade Magasin

Rue deWazemmes

J. F.Kennedy

Mairiede Lille

ArtoisJeanned’Arc

Rue deToul

Mont de Terre

Lebon

Citadelle

Thionville

Churchill

Painlevé

Gare Ruede Tournai

Fulton

Chasseursde Driant

Diderot

Guesde

R. de l’Oise

Fg. d’Arras

Verne

Simons

Courbet

Cimetièredu Sud

Cavell

Tilmant

Mont de Terre

Édition 06/2011

Pt. deTournai

Frères Lumière

Le BoisHabité

Painlevé

Zénith

Parvis deRotterdam

Casino

G. Lyon

Bd. del’Usine

Ferrer

Legrand

Rue deCambrai

Condé

Meunier

DouaiArrasRue de

Wazemmes Bas Jardin

MolinelParis

Tanneurs

Monnoyer

Gare Ruede Tournai

Liberté

J. F.Kennedy

Mairiede Lille

RenoirPlace A. Tacq

Isly

Bd. deMetz

PiscineDormoy

Catinat Rue deToul

UniversitéCatholique

Desmazières

JardinVauban

Solférino

Colbert

Leclerc

Les Bateliers

Thionville

Churchill

ConservatoireVoltaire

Danel

Citadelle

Palais de Justice

Liond’Or

Carnot

SacréCœur J. Giélée

Nationale

R. duPort


Lebon

ArtoisJeanned’Arc

Arago

Pl. aux Bleuets

Dieu deMarcq

StMaurice

Dupleix

Jacquet

GassendiBallon

LycéePasteur

GrimonprezJooris

H. Regnault

Colpin

Champde Mars

Esplanade Magasin TR

TR

TR

15 min4 min

LILLE CENTREVieux Lille

VaubanEsquermes

Wazemmes

Centre

Moulins

Fives

Fives

St MauricePellevoisin

Faubourg deBéthune

Lille Sud

10th esicup meeting - bookletesicup/extern/esicup-10th... · 2013-04-18 · 10thesicupmeeting 5...

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