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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

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

Department of Computer Science

University of British Columbia

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

- 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

- 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

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

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

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

SATzillaDF performance

LR: linear regression as used in previous SATzilla;

DF: cost sensitive decision forest

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

SATzillaDF performance

LR: linear regression as used in previous SATzilla;

DF: cost sensitive decision forest

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

MIPzillaDF performance

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

MIPzillaDF performance

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

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

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

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

NovelInstance

Output:

SelectedSolver

Portfolio-BasedAlgorithm Selector

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

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

Metric

k Candidate Solvers

Training Set

Algorithm Configurator

ParameterizedAlgorithm

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

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

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

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

- 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

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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