Hydra mip automated algorithm configuration and selection for mixed integer programming
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Hydra-MIP: Automated Algorithm Configuration and Selection for Mixed Integer Programming. Lin Xu, Frank Hutter , Holger H. Hoos , and Kevin Leyton-Brown Department of Computer Science University of British Columbia. Solving MIP more effectively.

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

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Hydra mip automated algorithm configuration and selection for mixed integer programming

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

Lin Xu, Frank Hutter, Holger H. Hoos, and Kevin Leyton-Brown

Department of Computer Science

University of British Columbia


Solving mip more effectively

Solving MIP more effectively

Portfolio-based algorithm selection (SATzilla) [Xu et al., 2007;2008;2009]

Where are the solvers?

Parameter settings of a single solver (e.g. CPLEX)

How to find good settings?

Automated algorithm configuration tool[Hutter et al., 2007;2009]

How to find good candidates for algorithm selection?

Algorithm configuration with dynamic performance metric[Xu et al., 2010]

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Hydra

Hydra

  • Portfolio-based algorithm selection:

  • Automated algorithm configuration:

NEW MODELS

Some particularly related work: [Rice, 1976]; [Leyton-Brown, Nudelman & Shoham, 2003; 2009]; [Guerri & Milano, 2004]; [Nudelman, Leyton-Brown, Shoham & Hoos, 2004]

Better use

Some particularly related work: [Gratch & Dejong, 1992]; [Balaprakash, Birattari & Stuetzle, 2007]; [Hutter, Babic, Hoos & Hu, 2007]; [Hutter, Hoos, Stuetzle & Leyton-Brown, 2009]

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Outline

Outline

  • Improve algorithm selection

    • SATzilla

    • Drawback of SATzilla

    • New SATzilla with cost sensitive classification

    • Results

  • Reduce the construction cost

    • Hydra

    • The cost

    • Make full use of configuration

    • Results

  • Conclusion

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Hydra mip automated algorithm configuration and selection for mixed integer programming

SATzilla: Portfolio-Based Algorithm Selection

[Xu, Hutter, Hoos, Leyton-Brown, 2007; 2008]

NovelInstance

Metric

Portfolio Builder

  • Given:

    • training set of instances

    • performance metric

    • candidate solvers

    • portfolio builder (incl. instance features)

  • Training:

    • collect performance data

    • portfolio builder learns predictive models

  • At Runtime:

    • predict performance

    • select solver

Candidate Solvers

Training Set

SelectedSolver

Portfolio-BasedAlgorithm Selector

5

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Drawback of satzilla

Drawback of SATzilla

Algorithm selectionin SATzilla based on regression:

  • Predict each solver performance independently

  • Select best predicted solver

  • Classification based on regression

    Goal of regression:

    Accurately predict each solver’s performance

    Algorithm selection:

    Pick solvers on a per-instance basis in order to minimize some overall performance metric

    Better regression Better algorithm selection

Algorithm Selector

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Cost sensitive classification for satzilla

Cost sensitive classification for SATzilla

Loss function: the performance difference

  • Punish misclassifications in direct proportion to their impact on portfolio performance

  • No need for predicting runtime

    Implementation:

    Binary cost sensitive classifier: decision forest (DF)

  • Build DF for each pair of candidate solvers

  • one vote for the better solver

  • Most votes -> Best solver

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Satzilla df performance

SATzillaDF performance

LR: linear regression as used in previous SATzilla;

DF: cost sensitive decision forest

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Satzilla df performance1

SATzillaDF performance

LR: linear regression as used in previous SATzilla;

DF: cost sensitive decision forest

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Mipzilla df performance

MIPzillaDF performance

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Mipzilla df performance1

MIPzillaDF performance

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Hydra procedure iteration 1

Hydra Procedure: Iteration 1

Metric

PortfolioBuilder

Candidate Solver Set

Training Set

Algorithm Configurator

CandidateSolver

Portfolio-BasedAlgorithm Selector

ParameterizedAlgorithm

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Hydra procedure iteration 2

Hydra Procedure: Iteration 2

Metric

PortfolioBuilder

Candidate Solver Set

Training Set

Algorithm Configurator

CandidateSolver

Portfolio-BasedAlgorithm Selector

ParameterizedAlgorithm

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Hydra procedure iteration 3

Hydra Procedure: Iteration 3

Metric

PortfolioBuilder

Candidate Solver Set

Training Set

Algorithm Configurator

CandidateSolver

Portfolio-BasedAlgorithm Selector

ParameterizedAlgorithm

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Hydra procedure after termination

Hydra Procedure: After Termination

NovelInstance

Output:

SelectedSolver

Portfolio-BasedAlgorithm Selector

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


We are wasting configuration results

We are wasting configuration results!

Metric

Training Set

Algorithm Configurator

CandidateSolver

ParameterizedAlgorithm

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Make full use of configurations

Make full use of configurations

Metric

k Candidate Solvers

Training Set

Algorithm Configurator

ParameterizedAlgorithm

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Make full use of configurations1

Make full use of configurations

Advantage:

Add k solvers instead of 1 in each iteration (good for algorithm selection)

No need for validation step in configuration (SAVE time)

Disadvantage:

Need to collect runtime data for more solvers (COST time)

In our experiment, we found SAVE = COST(k=4)

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Experimental setup hydra s inputs

Experimental Setup: Hydra’s Inputs

Portfolio Builder:

MIPzillaLR (SATzilla for MIP) [Xu et al., 2008]

MIPzillaDF (MIPzilla using cost sensitive DF)

Parameterized Solver: CPLEX12.1

Algorithm Configurator:FocusedILS 2.4.3 [Hutter, Hoos, Leyton-Brown, 2009]

Performance Metric:

Penalized average runtime (PAR)

Instance Sets:

4 heterogeneous sets by combining homogeneous subsets [Hutter et al., 2010];[Kadioglu et al., 2010]; [Ahmadizadeh et al., 2010]

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Three versions of hydra for mip

Three versions of Hydra for MIP

HydraLR,1: Original Hydra for MIP [Xu et al., 2010]

HydraDF,1: Hydra for MIP with Improvement I

HydraDF,4: Hydra for MIP with Improvement I and II

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Mip hydra performance on mix

MIP-Hydra performance on MIX

  • HydraDF,* performs better than HydraLR,1

  • HydraDF,4 performs similar to HydraDF,1 , but converge faster

  • Performance close to Oracle and MIPzillaDF

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


Conclusion

Conclusion

Cost sensitive classification based SATzilla outperforms original SATzilla

New Hydra-MIP outperforms CPLEX default, algorithm configuration alone, and original Hydra on four heterogeneous MIP sets

Technical contributions:

Cost sensitive classification results better algorithm selection for SAT and MIP

Using multiple configurations speeds up the convergence of Hydra

Xu, Hutter, Hoos, and Leyton-Brown: Hydra-MIP


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