Binary Decision Diagrams for Bin Packing with Minimum Color Fragmentation

Bergman, David; Cardonha, Carlos; Mehrani, Saharnaz

doi:10.1007/978-3-030-19212-9_4

Cited by 5 publications

(4 citation statements)

References 34 publications

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“…A purely combinatorial version of floor planning is the well-known Bin Packing problem, where items of different sizes must be packed into bins, each of a fixed capacity, in a way that minimizes the number of bins used. Bergman et al [5] consider a variant called Bin Packing with Minimum Color Fragmentation, where each item is associated with a color. Then the goal is to find a bin packing where items of a common color are placed in the fewest number of bins possible.…”

Section: Related Workmentioning

confidence: 99%

Algorithms for Floor Planning with Proximity Requirements

Klawitter¹,

Klesen²,

Wolff³

2021

Preprint

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Floor planning is an important and difficult task in architecture. When planning office buildings, rooms that belong to the same organisational unit should be placed close to each other. This leads to the following NP-hard mathematical optimization problem. Given the outline of each floor, a list of room sizes, and, for each room, the unit to which it belongs, the aim is to compute floor plans such that each room is placed on some floor and the total distance of the rooms within each unit is minimized. The problem can be formulated as an integer linear program (ILP). Commercial ILP solvers exist, but due to the difficulty of the problem, only small to medium instances can be solved to (near-) optimality. For solving larger instances, we propose to split the problem into two subproblems; floor assignment and planning single floors. We formulate both subproblems as ILPs and solve realistic problem instances. Our experimental study shows that splitting the problem helps to reduce the computation time considerably. Where we were able to compute the global optimum, the solution cost of the combined approach increased very little.

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Section: Related Workmentioning

confidence: 99%

Algorithms for Floor Planning with Proximity Requirements

Klawitter¹,

Klesen²,

Wolff³

2021

Preprint

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“…Considerations on limiting communications lead use to include additional constraints on the feasible packings, with a limit on the number of processors alloted to a given row or column. This can be seen as a generalization of some related literature on bin packing: bin packing with class constraints [28,38], in which there is a limit to the number of classes allowed in a bin, and bin packing with minimum color fragmentation [15], in which the number of bins containing a given class is limited. Since we consider both rows and columns, our case is a two-dimensional version of these problems, however the techniques developed in these papers can not be generalized to our context.…”

Section: Bin Packing Problemsmentioning

confidence: 99%

2D Static Resource Allocation for Compressed Linear Algebra and Communication Constraints

Beaumont

Eyraud-Dubois

Vérité

2020

2020 IEEE 27th International Conference on High Performance Computing, Data, and Analytics (HiPC)

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This paper adresses static resource allocation problems for irregular distributed parallel applications. More precisely, we focus on two classical tiled linear algebra kernels: the Matrix Multiplication and the LU decomposition algorithms on large linear systems. In the context of parallel distributed platforms, data exchanges can dramatically degrade the performance of linear algebra kernels and in this context, compression techniques such as Block Low Rank (BLR) are good candidates both for limiting data storage on each node and data exchanges between nodes. On the other hand, the use of BLR representation makes the static allocation problem of tiles to nodes more complex. Indeed, the workload associated to each tile depends on its compression factor, which induces an heterogeneous load balancing problem. In turn, solving this load balancing problem optimally might lead to complex allocation schemes, where the tiles allocated to a given node are scattered over the whole matrix. This in turn causes communication complexity problems, since matrix multiplication and LU decompositions heavily rely on broadcasting operations along rows and columns of processors, so that the communication volume is minimized when the number of different nodes on each row and column is minimized. In the fully homogeneous case, 2D Block cyclic allocation solves both load balancing and communication minimization issues simultaneously, but it might lead to bad load balancing in the heterogeneous case. Our goal in this paper is to propose data allocation schemes dedicated to BLR format and to prove that it is possible to obtain good performance on makespan when simultaneously balancing the load and minimizing the maximal number of different resources in any row or column.

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“…Such a model is potentially orders of magnitude smaller than an explicit representation of X as it identifies and merges equivalent partial solutions. Several BDD encodings have already been investigated for linear and non-linear problems [13,14,40] and are used to exploit submodularity [15] or more general combinatorial structure [17].…”

Section: Introductionmentioning

confidence: 99%

“…Lastly, §7 and §8 present the empirical evaluation and final remarks, respectively. encodings for vehicle routing [23,49,36], scheduling [26,20,21,33], and other combinatorial optimization problems [14,16,24,17]. Within the context of this work, Becker et al (2005) [12] presented the first BDD cut generation procedure based on an iterative subgradient algorithm that relies on a longest-path problem over the BDD.…”

Section: Introductionmentioning

confidence: 99%

A Combinatorial Cut-and-Lift Procedure with an Application to 0-1 Second-Order Conic Programming

Castro,

Cire,

Beck

2020

Preprint

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Cut generation and lifting are key components for the performance of state-of-the-art mathematical programming solvers. This work proposes a new general cut-and-lift procedure that exploits the combinatorial structure of 0-1 problems via a binary decision diagram (BDD) encoding of their constraints. We present a general framework that can be applied to a large range of binary optimization problems and show its applicability for normally distributed chance constraints. We identify conditions for which our lifted inequalities are facet-defining and derive a new BDD-based cut generation linear program. Such a model serves as a basis for a max-cut combinatorial algorithm over the BDD that can be applied to derive valid cuts more efficiently. Our numerical results show encouraging performance when incorporated into a state-of-the-art mathematical programming solver, significantly reducing the root node gap, increasing the number of problems solved, and reducing the run-time by a factor of three on average.

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Binary Decision Diagrams for Bin Packing with Minimum Color Fragmentation

Cited by 5 publications

References 34 publications

Algorithms for Floor Planning with Proximity Requirements

Algorithms for Floor Planning with Proximity Requirements

2D Static Resource Allocation for Compressed Linear Algebra and Communication Constraints

A Combinatorial Cut-and-Lift Procedure with an Application to 0-1 Second-Order Conic Programming

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