## Hydra-MIP: Automated Algorithm Configuration and Selection for Mixed Integer Programming

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Citations: | 4 - 3 self |

### BibTeX

@MISC{Xu_hydra-mip:automated,

author = {Lin Xu and Frank Hutter and Holger H. Hoos and Kevin Leyton-brown},

title = {Hydra-MIP: Automated Algorithm Configuration and Selection for Mixed Integer Programming},

year = {}

}

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### Abstract

Abstract. State-of-the-art mixed integer programming (MIP) solvers are highly parameterized. For heterogeneous and a priori unknown instance distributions, no single parameter configuration generally achieves consistently strong performance, and hence it is useful to select from a portfolio of different configurations. HYDRA is a recent method for using automated algorithm configuration to derive multiple configurations of a single parameterized algorithm for use with portfolio-based selection. This paper shows that, leveraging two key innovations, HYDRA can achieve strong performance for MIP. First, we describe a new algorithm selection approach based on classification with a non-uniform loss function, which significantly improves the performance of algorithm selection for MIP (and SAT). Second, by modifying HYDRA’s method for selecting candidate configurations, we obtain better performance as a function of training time. 1

### Citations

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Citation Context ...n contrast to clustering methods, DFs take runtime into account when determining that partitioning. We constructed cost-sensitive DFs as collections of T cost-sensitive decision trees [27]. Following =-=[4]-=-, given n training data points with k features each, for each tree we construct a bootstrap sample of n training data points sampled uniformly at random with repetitions; during tree construction, we ... |

462 |
N.: An extensible SAT-solver
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Citation Context ... findings suggest that there is merit in constructing such highly parameterized solvers for SAT and other NP-hard problems. 2 The closest to a SAT equivalent of what CPLEX is for MIP would be MiniSAT =-=[5]-=-, but it does not expose many parameters and does not perform well for random instances. The highly parameterized SATenstein solver [18] cannot be expected to perform well across the board for SAT; in... |

138 | Towards a universal test suite for combinatorial auction algorithms
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Citation Context ...encoded instances of the winner determination problem in combinatorial auctions. We generated 500 training and 500 test instances using the regions generator from the Combinatorial Auction Test Suite =-=[22]-=-, with the number of bids selected uniformly at random from between 750 and 1250, and a fixed bids/goods ratio of 3.91 (following [21]). CL∪REG∪RCW is the union of CL∪REG and another set of MILP-encod... |

91 | Satzilla: Portfolio-based algorithm selection for sat
- Xu, Hutter, et al.
(Show Context)
Citation Context ...en optimizing performance on homogeneous sets of benchmark instances, it is no panacea. In fact, it is characteristic of NP-hard problems that no single solver performs well on all inputs (see, e.g., =-=[30]-=-); a procedure that performs well on one part of an instance distribution often performs poorly on another. An alternative approach is to choose a portfolio of different algorithms (or parameter confi... |

87 | Paramils: An automatic algorithm configuration framework
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(Show Context)
Citation Context ...n evaluated each of our improvements to HydraLR,1. 4.1 Experimental setup For algorithm configuration we used PARAMILS version 2.3.4 with its default instantiation of FOCUSEDILS with adaptive capping =-=[14]-=-. We always executed 25 parallel configuration runs with different random seeds with a 2-day cutoff. (Running times were always measured using CPU time.) During configuration, the captime for each CPL... |

86 |
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Citation Context ...n another. An alternative approach is to choose a portfolio of different algorithms (or parameter configurations), and to select between them on a per-instance basis. This algorithm selection problem =-=[24]-=- can be solved by gathering cheaply computable features from the problem instance and then evaluating a learned model to select the best algorithm [20, 9, 6]. The well-known SATZILLA [30] method uses ... |

63 | A Bayesian approach to tackling hard computational problems
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Citation Context ..., and the full new method as HydraDF,k. 32.1 Decision forests for algorithm selection There are many existing techniques for algorithm selection, based on either regression [30, 26] or classification=-=[10, 9, 25, 23]-=-. SATZILLA [30] uses linear basis function regression to predict the runtime of each of a set of K algorithms, and picks the one with the best predicted performance. Although this approach has led to ... |

59 | Automatic algorithm configuration based on local search
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Citation Context ...includes a self-tuning tool that takes this approach. A variety of problem-independent algorithm configuration procedures have also been proposed in the AI community, including I/F-Race [3], ParamILS =-=[15, 14]-=-, and GGA [2]. Of these, only PARAMILS has been demonstrated to be able to effectively configure CPLEX on a variety of MIP benchmarks, with speedups up to several orders of magnitude, and overall perf... |

44 | A gender-based genetic algorithm for the automatic configuration of solvers
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(Show Context)
Citation Context ...ning tool that takes this approach. A variety of problem-independent algorithm configuration procedures have also been proposed in the AI community, including I/F-Race [3], ParamILS [15, 14], and GGA =-=[2]-=-. Of these, only PARAMILS has been demonstrated to be able to effectively configure CPLEX on a variety of MIP benchmarks, with speedups up to several orders of magnitude, and overall performance subst... |

38 | A portfolio approach to algorithm selection
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(Show Context)
Citation Context ...instance basis. This algorithm selection problem [24] can be solved by gathering cheaply computable features from the problem instance and then evaluating a learned model to select the best algorithm =-=[20, 9, 6]-=-. The well-known SATZILLA [30] method uses a regression model to predict the runtime of each algorithm and selects the algorithm predicted to perform best. Its performance in recent SAT competitions i... |

37 | Using case-based reasoning in an algorithm portfolio for constraint solving
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Citation Context ..., and the full new method as HydraDF,k. 32.1 Decision forests for algorithm selection There are many existing techniques for algorithm selection, based on either regression [30, 26] or classification=-=[10, 9, 25, 23]-=-. SATZILLA [30] uses linear basis function regression to predict the runtime of each of a set of K algorithms, and picks the one with the best predicted performance. Although this approach has led to ... |

37 |
An instance-weighting method to induce cost-sensitive trees
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(Show Context)
Citation Context ...fferent parts. In contrast to clustering methods, DFs take runtime into account when determining that partitioning. We constructed cost-sensitive DFs as collections of T cost-sensitive decision trees =-=[27]-=-. Following [4], given n training data points with k features each, for each tree we construct a bootstrap sample of n training data points sampled uniformly at random with repetitions; during tree co... |

35 | The winner determination problem
- Lehmann, Müller, et al.
- 2006
(Show Context)
Citation Context ..., it is widely used both in academia and industry. MIP used to be studied mainly in operations research, but has recently become an important tool in AI, with applications ranging from auction theory =-=[19]-=- to computational sustainability [8]. Furthermore, several recent advances in MIP solving have been achieved with AI techniques [7, 13]. One key advantage of the MIP representation is that highly opti... |

32 | SATenstein: Automatically building local search SAT solvers from components
- KhudaBukhsh, Xu, et al.
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(Show Context)
Citation Context ...st to a SAT equivalent of what CPLEX is for MIP would be MiniSAT [5], but it does not expose many parameters and does not perform well for random instances. The highly parameterized SATenstein solver =-=[18]-=- cannot be expected to perform well across the board for SAT; in particular, local search is not the best method for highly structured instances. 10DataSet Solver Train (cross valid.) Test Time PAR (... |

31 |
Learning techniques for automatic algorithm portfolio selection
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(Show Context)
Citation Context ...instance basis. This algorithm selection problem [24] can be solved by gathering cheaply computable features from the problem instance and then evaluating a learned model to select the best algorithm =-=[20, 9, 6]-=-. The well-known SATZILLA [30] method uses a regression model to predict the runtime of each algorithm and selects the algorithm predicted to perform best. Its performance in recent SAT competitions i... |

26 | Automated configuration of mixed integer programming solvers
- Hutter, Hoos, et al.
- 2010
(Show Context)
Citation Context ...important tool in AI, with applications ranging from auction theory [19] to computational sustainability [8]. Furthermore, several recent advances in MIP solving have been achieved with AI techniques =-=[7, 13]-=-. One key advantage of the MIP representation is that highly optimized solvers can be developed in a problem-independent way. IBM ILOG’s CPLEX solver 1 is particularly well known for achieving strong ... |

19 | Using cbr to select solution strategies in constraint programming
- Gebruers, Hnich, et al.
- 2005
(Show Context)
Citation Context ...instance basis. This algorithm selection problem [24] can be solved by gathering cheaply computable features from the problem instance and then evaluating a learned model to select the best algorithm =-=[20, 9, 6]-=-. The well-known SATZILLA [30] method uses a regression model to predict the runtime of each algorithm and selects the algorithm predicted to perform best. Its performance in recent SAT competitions i... |

18 | Empirical hardness models: Methodology and a case study on combinatorial auctions
- Brown, Nudelman, et al.
(Show Context)
Citation Context ...he CPLEX parameters we configured, and the data sets upon which we evaluated our methods. 3.1 Features of MIP Instances We constructed a large set of 139 MIP features, drawing on 97 existing features =-=[21, 11, 17]-=- and also including 42 new probing features. Specifically, existing work used features based on problem size, graph representations, proportion of different variable types (e.g., discrete vs continuou... |

17 |
Learning To Solve QBF
- Samulowitz, Memisevic
- 2007
(Show Context)
Citation Context ..., and the full new method as HydraDF,k. 32.1 Decision forests for algorithm selection There are many existing techniques for algorithm selection, based on either regression [30, 26] or classification=-=[10, 9, 25, 23]-=-. SATZILLA [30] uses linear basis function regression to predict the runtime of each of a set of K algorithms, and picks the one with the best predicted performance. Although this approach has led to ... |

14 | Automated Configuration of Algorithms for Solving Hard Computational Problems
- Hutter
- 2009
(Show Context)
Citation Context ...he CPLEX parameters we configured, and the data sets upon which we evaluated our methods. 3.1 Features of MIP Instances We constructed a large set of 139 MIP features, drawing on 97 existing features =-=[21, 11, 17]-=- and also including 42 new probing features. Specifically, existing work used features based on problem size, graph representations, proportion of different variable types (e.g., discrete vs continuou... |

14 | Hydra: Automatically configuring algorithms for portfolio-based selection
- Xu, Hoos, et al.
- 2010
(Show Context)
Citation Context ... to yield automatic portfolio construction methods applicable to domains in which only a single, highly-parameterized algorithm exists. Two such approaches have been proposed in the literature. HYDRA =-=[28]-=- is an iterative procedure. It begins by identifying a single configuration with the best overall performance, and then iteratively adds algorithms to the portfolio by applying an algorithm configurat... |

13 | SATzilla2009: an automatic algorithm portfolio for SAT
- Xu, Hutter, et al.
- 2009
(Show Context)
Citation Context ...e the effectiveness of SATZILLA based on our new cost-sensitive decision forests, compared to the original version using linear regression models. We used the same data used for building SATzilla2009 =-=[29]-=-. The number of training/test instances were 1211/806 (RAND category with 17 candidate solvers), 672/447 (HAND category with 13 candidate solvers) and 570/379 (INDU category with 10 candidate solvers)... |

12 | Information-Theoretic Approaches to Branching in Search
- Gilpin, Sandholm
- 2007
(Show Context)
Citation Context ...important tool in AI, with applications ranging from auction theory [19] to computational sustainability [8]. Furthermore, several recent advances in MIP solving have been achieved with AI techniques =-=[7, 13]-=-. One key advantage of the MIP representation is that highly optimized solvers can be developed in a problem-independent way. IBM ILOG’s CPLEX solver 1 is particularly well known for achieving strong ... |

8 | Connections in networks: A hybrid approach
- Gomes, Hoeve, et al.
- 2008
(Show Context)
Citation Context ...and industry. MIP used to be studied mainly in operations research, but has recently become an important tool in AI, with applications ranging from auction theory [19] to computational sustainability =-=[8]-=-. Furthermore, several recent advances in MIP solving have been achieved with AI techniques [7, 13]. One key advantage of the MIP representation is that highly optimized solvers can be developed in a ... |

6 | A.: Collaborative Expert Portfolio Management
- Stern, Herbrich, et al.
- 2010
(Show Context)
Citation Context ...ands for decision forests), and the full new method as HydraDF,k. 32.1 Decision forests for algorithm selection There are many existing techniques for algorithm selection, based on either regression =-=[30, 26]-=- or classification[10, 9, 25, 23]. SATZILLA [30] uses linear basis function regression to predict the runtime of each of a set of K algorithms, and picks the one with the best predicted performance. A... |

4 | An empirical study of optimization for maximizing diffusion in networks
- Ahmadizadeh, Dilkina, et al.
- 2010
(Show Context)
Citation Context ... conditional on decisions about certain parcels of land to be protected. We generated 990 RCW instances (10 random instances for each 7combination of 9 maps and 11 budgets), using the generator from =-=[1]-=- with the same parameter setting, except a smaller sample size of 5. We split these instances 50:50 into training and test sets. ISAC(new) is a subset of the MIP data set from [17]; we could not use t... |

4 |
Empirical Methods for the Analysis of Optimization Algorithms, chapter F-race and iterated F-race: An overview
- Birattari, Yuan, et al.
- 2010
(Show Context)
Citation Context ... CPLEX itself includes a self-tuning tool that takes this approach. A variety of problem-independent algorithm configuration procedures have also been proposed in the AI community, including I/F-Race =-=[3]-=-, ParamILS [15, 14], and GGA [2]. Of these, only PARAMILS has been demonstrated to be able to effectively configure CPLEX on a variety of MIP benchmarks, with speedups up to several orders of magnitud... |

2 |
Sac - instance specific algorithm configuration
- Kadioglu, Malitsky, et al.
- 2010
(Show Context)
Citation Context ...ively adds algorithms to the portfolio by applying an algorithm configurator with a customized, dynamic performance metric. At runtime, algorithms are selected from the portfolio as in SATZILLA. ISAC =-=[17]-=- first divides instance sets into 2clusters based on instance features using the G-means clustering algorithm, then applies an algorithm configurator to find a good configuration for each cluster. At... |