Given a multiset of colors as the query and a list-colored graph, i.e., an undirected graph with a set of colors assigned to each of its vertices, in the NP-hard list-colored graph motif problem the goal is to find th...
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Given a multiset of colors as the query and a list-colored graph, i.e., an undirected graph with a set of colors assigned to each of its vertices, in the NP-hard list-colored graph motif problem the goal is to find the largest connected subgraph such that one can select a color from the set of colors assigned to each of its vertices to obtain a subset of the query. This problem was introduced to find functional motifs in biological networks. We present a branch-and-bound algorithm named RANGI for finding and enumerating list-colored graph motifs. As our experimental results show, RANGI's pruning methods and heuristics make it quite fast in practice compared to the algorithms presented in the literature. We also present a parallel version of RANGI that achieves acceptable scalability.
An efficient optimization algorithm for identifying the best least squares regression model under the condition of non-negative coefficients is proposed. The algorithm exposits an innovative solution via the unrestric...
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An efficient optimization algorithm for identifying the best least squares regression model under the condition of non-negative coefficients is proposed. The algorithm exposits an innovative solution via the unrestricted least squares and is based on the regression tree and branch-and-bound techniques for computing the best subset regression. The aim is to filling a gap in computationally tractable solutions to the non-negative least squares problem and model selection. The proposed method is illustrated with a real dataset. Experimental results on real and artificial random datasets confirm the computational efficacy of the new strategy and demonstrates its ability to solve large model selection problems that are subject to non-negativity constrains.
Solving exactly Combinatorial Optimization Problems (COPs) using a branch-and-bound (B&B) algorithm requires a huge amount of computational resources. Therefore, we recently investigated designing B&B algorith...
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ISBN:
(纸本)9780769547497
Solving exactly Combinatorial Optimization Problems (COPs) using a branch-and-bound (B&B) algorithm requires a huge amount of computational resources. Therefore, we recently investigated designing B&B algorithms on top of graphics processing units (GPUs) using a parallel bounding model. The proposed model assumes parallelizing the evaluation of the lower bounds on pools of sub-problems. The results demonstrated that the size of the evaluated pool has a significant impact on the performance of B&B and that it depends strongly on the problem instance being solved. In this paper, we design an adaptative parallel B&B algorithm for solving permutation-based combinatorial optimization problems such as FSP (Flow-shop Scheduling Problem) on GPU accelerators. To do so, we propose a dynamic heuristic for parameter auto-tuning at runtime. Another challenge of this pioneering work 1 is to exploit larger degrees of parallelism by using the combined computational power of multiple GPU devices. The approach has been applied to the permutation flow-shop problem. Extensive experiments have been carried out on well-known FSP benchmarks using an Nvidia Tesla S1070 Computing System equipped with two Tesla T10 GPUs. Compared to a CPU-based execution, accelerations up to x105 are achieved for large problem instances.
branch-and-bound (B&B) algorithms are time-intensive tree-based exploration methods for solving to optimality combinatorial optimization problems. In this paper, we investigate the use of GPU computing as a major ...
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ISBN:
(纸本)9781467324229
branch-and-bound (B&B) algorithms are time-intensive tree-based exploration methods for solving to optimality combinatorial optimization problems. In this paper, we investigate the use of GPU computing as a major complementary way to speed up those methods. The focus is put on the bounding mechanism of B&B algorithms, which is the most time consuming part of their exploration process. We propose a parallel B&B algorithm based on a GPU-accelerated bounding model. The proposed approach concentrate on optimizing data access management to further improve the performance of the bounding mechanism which uses large and intermediate data sets that do not completely fit in GPU memory. Extensive experiments of the contribution have been carried out on well-known FSP benchmarks using an Nvidia Tesla C2050 GPU card. We compared the obtained performances to a single and a multi-threaded CPU-based execution. Accelerations up to x100 are achieved for large problem instances.
This paper surveys the most effective mathematical models and exact algorithms proposed for finding the optimal solution of the well-known Asymmetric Traveling Salesman Problem (ATSP). The fundamental Integer Linear P...
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This paper surveys the most effective mathematical models and exact algorithms proposed for finding the optimal solution of the well-known Asymmetric Traveling Salesman Problem (ATSP). The fundamental Integer Linear Programming (ILP) model proposed by Dantzig, Fulkerson and Johnson is first presented, its classical (assignment, shortest spanning r-arborescence, linear programming) relaxations are derived, and the most effective branch-and-bound and branch-andcut algorithms are described. The polynomial ILP formulations proposed for the ATSP are then presented and analyzed. The considered algorithms and formulations are finally experimentally compared on a set of benchmark instances.
This paper proposes two new algorithms for inference in credal networks. These algorithms enable probability intervals to be obtained for the states of a given query variable. The first algorithm is approximate and us...
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This paper proposes two new algorithms for inference in credal networks. These algorithms enable probability intervals to be obtained for the states of a given query variable. The first algorithm is approximate and uses the hill-climbing technique in the Shenoy-Shafer architecture to propagate in join trees;the second is exact and is a modification of Rocha and Cozman's branch-and-bound algorithm, but applied to general directed acyclic graphs, (C) 2006 Elsevier Inc. All rights reserved.
Computing the 1-width of the incidence matrix of a Steiner Triple System gives rise to highly symmetric and computationally challenging set covering problems. The largest instance solved so far corresponds to a Steine...
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Computing the 1-width of the incidence matrix of a Steiner Triple System gives rise to highly symmetric and computationally challenging set covering problems. The largest instance solved so far corresponds to a Steiner Tripe System of order 81. We present optimal solutions for systems of orders 135 and 243. These are computed by a tailored implementation of constraint orbital branching, a method designed to exploit symmetry in integer programs. (c) 2011 Elsevier B.V. All rights reserved.
We introduce orbital branching, an effective branching method for integer programs containing a great deal of symmetry. The method is based on computing groups of variables that are equivalent with respect to the symm...
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We introduce orbital branching, an effective branching method for integer programs containing a great deal of symmetry. The method is based on computing groups of variables that are equivalent with respect to the symmetry remaining in the problem after branching, including symmetry that is not present at the root node. These groups of equivalent variables, called orbits, are used to create a valid partitioning of the feasible region that significantly reduces the effects of symmetry while still allowing a flexible branching rule. We also show how to exploit the symmetries present in the problem to fix variables throughout the branch-and-bound tree. Orbital branching can easily be incorporated into standard integer programming software. Through an empirical study on a test suite of symmetric integer programs, the question as to the most effective orbit on which to base the branching decision is investigated. The resulting method is shown to be quite competitive with a similar method known as isomorphism pruning and significantly better than a state-of-the-art commercial solver on symmetric integer programs.
We consider a parallel-machine scheduling problem with a learning effect and the makespan objective. The impact of the learning effect on job processing times is modelled by the general DeJong's learning curve. Fo...
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We consider a parallel-machine scheduling problem with a learning effect and the makespan objective. The impact of the learning effect on job processing times is modelled by the general DeJong's learning curve. For this NP-hard problem we propose two exact algorithms: a sequential branch-and-bound algorithm and a parallel branch-and-bound algorithm. We also present the results of experimental evaluation of these algorithms on a computational cluster. Finally, we use the exact algorithms to estimate the performance of two greedy heuristic scheduling algorithms for the problem. (c) 2010 Elsevier Ltd. All rights reserved.
Gene expression in eukaryotic cells is regulated by a complex network of interactions, in which transcription factors and their binding sites on the genomic DNA play a determining role. As transcription factors rarely...
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Gene expression in eukaryotic cells is regulated by a complex network of interactions, in which transcription factors and their binding sites on the genomic DNA play a determining role. As transcription factors rarely, if ever, act in isolation, binding sites of interacting factors are typically arranged in close proximity forming so-called cis-regulatory modules. Even when the individual binding sites are known, module discovery remains a hard combinatorial problem, which we formalize here as the Best Barbecue Problem. It asks for simultaneously stabbing a maximum number of differently colored intervals from K arrangements of colored intervals. This geometric problem turns out to be an elementary, yet previously unstudied combinatorial optimization problem of detecting common edges in a family of hypergraphs, a decision version of which we show here to be NP-complete. Due to its relevance in biological applications, we propose algorithmic variations that are suitable for the analysis of real data sets comprising either many sequences or many binding sites. Being based on set systems induced by interval arrangements, our problem setting generalizes to discovering patterns of co-localized itemsets in non-sequential objects that consist of corresponding arrangements or induce set systems of co-localized items. In fact, our optimization problem is a generalization of the popular concept of frequent itemset mining. (c) 2008 Elsevier B.V. All rights reserved.
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