Early Estimates of the Size of Branch-and-Bound Trees

Cornujols, Grard; Karamanov, Miroslav; Li, Yanjun

doi:10.1287/ijoc.1040.0107

Cited by 33 publications

(16 citation statements)

References 13 publications

(13 reference statements)

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“…A more sophisticated approach, not investigated in the present paper, would be to determine N R on the fly, by using a (possibly rough) estimate of the remaining branching nodes, e.g., by using the early tree-node estimator proposed in [3].…”

Section: Computational Experimentsmentioning

confidence: 99%

Exploiting Erraticism in Search

Fischetti

Monaci

2014

Operations Research

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High-sensitivity to initial conditions is generally viewed as a drawback of tree search methods, as it leads to an erratic behavior to be mitigated somehow. In this paper we investigate the opposite viewpoint, and consider this behavior as an opportunity to exploit. Our working hypothesis is that erraticism is in fact just a consequence of the exponential nature of tree search, that acts as a chaotic amplifier, so it is largely unavoidable. We propose a bet-and-run approach to actually turn erraticism to one's advantage. The idea is to make a number of short sample runs with randomized initial conditions, to bet on the "most promising" run selected according to certain simple criteria, and to bring it to completion. Computational results on a large testbed of mixed-integer linear programs from the literature are presented, showing the potential of this approach even when embedded in a proof-of-concept implementation.

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Section: Computational Experimentsmentioning

confidence: 99%

Exploiting Erraticism in Search

Fischetti

Monaci

2014

Operations Research

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“…Still C, et al developed a sequential cutting plane method to solve convex mixed integer nonlinear programming problems [2]. Cornuejols G, et al did prediction on the size of branch and bound trees [3]. Morrison David R, et al made a survey of recent advances in searching, branching and pruning [4].…”

Section: Introductionmentioning

confidence: 99%

A Pre-estimate Approach to Find a Good Initial Point to Integer Linear Programming Problems

Kong¹,

Wei²

2017

Proceedings of the 2017 International Conference on Applied Mathematics, Modelling and Statistics Application (AMMSA 2017)

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Abstract-Integer Linear Programming problems are significant in many areas, and there exist many classic methods to deal with such problems. Based on the intuition that a proper pre-estimation of those problems may help find a good initial point that is relatively closed to the final solution, we constructed a framework to do such pre-estimate by introducing . We proposed two methods to estimate by trials and by direct estimation. In a case study our method reduces about 7% of computational expense compared to the Branch and Bound Algorithm.

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“…Unfortunately, it suffers from several drawbacks that arise frequently in practice: the times spent to solve subproblems are rarely well balanced and the communication of the objective value is not good when solving an optimization problem (the workers are independent). In order to equilibrate the subproblems that have to be solved some works have been done about the decomposition of the search tree based on its size [8,3,7]. However, the tree size is only approximated and is not strictly correlated with the resolution time.…”

Section: Introductionmentioning

confidence: 99%

Embarrassingly Parallel Search

Régin

Rezgui

Malapert

2013

Lecture Notes in Computer Science

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Abstract. We propose the Embarrassingly Parallel Search, a simple and efficient method for solving constraint programming problems in parallel. We split the initial problem into a huge number of independent subproblems and solve them with available workers (i.e., cores of machines). The decomposition into subproblems is computed by selecting a subset of variables and by enumerating the combinations of values of these variables that are not detected inconsistent by the propagation mechanism of a CP Solver. The experiments on satisfaction problems and on optimization problems suggest that generating between thirty and one hundred subproblems per worker leads to a good scalability. We show that our method is quite competitive with the work stealing approach and able to solve some classical problems at the maximum capacity of the multi-core machines. Thanks to it, a user can parallelize the resolution of its problem without modifying the solver or writing any parallel source code and can easily replay the resolution of a problem.

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Early Estimates of the Size of Branch-and-Bound Trees

Cited by 33 publications

References 13 publications

Exploiting Erraticism in Search

Exploiting Erraticism in Search

A Pre-estimate Approach to Find a Good Initial Point to Integer Linear Programming Problems

Embarrassingly Parallel Search

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