Topic
Branching factor
About: Branching factor is a research topic. Over the lifetime, 101 publications have been published within this topic receiving 1684 citations.
Papers published on a yearly basis
Papers
Proceedings Article•
12 Feb 2016TL;DR: This work proposes a machine learning (ML) framework for variable branching in MIP, and observes the decisions made by Strong Branching, a time-consuming strategy that produces small search trees, collecting features that characterize the candidate branching variables at each node of the tree.
Abstract: The design of strategies for branching in Mixed Integer Programming (MIP) is guided by cycles of parameter tuning and offline experimentation on an extremely heterogeneous testbed, using the average performance. Once devised, these strategies (and their parameter settings) are essentially input-agnostic. To address these issues, we propose a machine learning (ML) framework for variable branching in MIP. Our method observes the decisions made by Strong Branching (SB), a time-consuming strategy that produces small search trees, collecting features that characterize the candidate branching variables at each node of the tree. Based on the collected data, we learn an easy-to-evaluate surrogate function that mimics the SB strategy, by means of solving a learning-to-rank problem, common in ML. The learned ranking function is then used for branching. The learning is instance-specific, and is performed on-the-fly while executing a branch-and-bound search to solve the instance. Experiments on benchmark instances indicate that our method produces significantly smaller search trees than existing heuristics, and is competitive with a state-of-the-art commercial solver.
400 citations
TL;DR: The generalization of minimax search with alpha-beta pruning to non-cooperative, perfect-information games with more than two players is considered and it is shown that it is an optimal directional algorithm for two players.
66 citations
1 Oct 2005
TL;DR: A natural branching strategy with which backtracking with 2-way branching finds refutations of these instances in time O(d2n2) is given, and exponential separations between C-RES and NG-RES, as well as between the tree-like and unrestricted versions of each system are shown.
Abstract: Most CSP algorithms are based on refinements and extensions of backtracking, and employ one of two simple "branching schemes": 2-way branching or d-way branching, for domain size d. The schemes are not equivalent, but little is known about their relative power. Here we compare them in terms of how efficiently they can refute an unsatisfiable instance with optimal branching choices, by studying two variants of the resolution proof system, denoted C-RES and NG-RES, which model the reasoning of CSP algorithms. The tree-like restrictions, tree-C-RES and tree-NG-RES, exactly capture the power of backtracking with 2-way branching and d-way branching, respectively. We give a family instances which require exponential sized search trees for backtracking with d-way branching, but have size O(d2n) search trees for backtracking with 2-way branching. We also give a natural branching strategy with which backtracking with 2-way branching finds refutations of these instances in time O(d2n2). The unrestricted variants of C-RES and NG-RES can simulate the reasoning of algorithms which incorporate learning and k-consistency enforcement. We show exponential separations between C-RES and NG-RES, as well as between the tree-like and unrestricted versions of each system. All separations given are nearly optimal.
51 citations
1 Jan 1992
TL;DR: In this paper, the authors examined the combinatoric and probabilistic properties of the branching process associated with the class of trees having a finite number of kinds of nodes, with each node having a limited number of ways in which it produces offspring.
Abstract: HIS PAPER examines the combinatoric and probabilistic properties of the branching processes associated with the class of trees having a finite number of kinds of nodes, with each node having a finite number of ways in which it produces offspring. The probabilistic structure assumed requires that the branching proceed in a manner so that each node at any level in the tree generates subtrees independent
39 citations
1 Jan 1988
TL;DR: A new and very powerful technique that is termed ‘razoring’ is described, which cannot guarantee finding the optimum solution but it will always find a good solution in a much shorter time.
Abstract: This paper first discusses the now standard tree searching techniques of mini-max and alpha-beta and the recent improvements to alpha-beta, in particular the killer heuristic. It then describes a new and very powerful technique that we have termed ‘razoring’. Unlike the alpha-beta technique, razoring cannot guarantee finding the optimum solution but it will, however, always find a good solution in a much shorter time. Typically a four-ply tree with a branching factor of 33 can be searched an order of magnitude faster than with alpha-beta. We also discuss ‘forward marginal pruning’ — a technique similar to razoring.
32 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 3 |
| 2020 | 2 |
| 2019 | 3 |
| 2018 | 5 |
| 2017 | 4 |
| 2016 | 1 |