# Predicting the Solution Time of Branch-and-Bound Algorithms for Mixed-Integer Programs

@article{zaltn2011PredictingTS, title={Predicting the Solution Time of Branch-and-Bound Algorithms for Mixed-Integer Programs}, author={Osman Y. {\"O}zaltın and Brady Hunsaker and Andrew J. Schaefer}, journal={INFORMS J. Comput.}, year={2011}, volume={23}, pages={392-403} }

The most widely used progress measure for branch-and-bound (B&B) algorithms when solving mixed-integer programs (MIPs) is the MIP gap. We introduce a new progress measure that is often much smoother than the MIP gap. We propose a double exponential smoothing technique to predict the solution time of B&B algorithms and evaluate the prediction method using three MIP solvers. Our computational experiments show that accurate predictions of the solution time are possible, even in the early stages of…

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## References

SHOWING 1-10 OF 21 REFERENCES

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

- Mathematics, Computer ScienceINFORMS J. Comput.
- 2006

The time needed to solve mixed-integer-programming problems by branch and bound can be roughly predicted early in the solution process, based on analyzing the partial tree resulting from running the algorithm for a short period of time and predicting the shape of the whole tree.

Heuristic Sampling: A Method for Predicting the Performance of Tree Searching Programs

- Mathematics, Computer ScienceSIAM J. Comput.
- 1992

A new method based on a stratified sampling approach, which is called heuristic sampling, is a generalization of Knuth’s original algorithm for estimating the efficiency of backtrack programs and can produce significantly more accurate cost estimates for commonly used tree search algorithms.

Estimating the efficiency of backtrack programs.

- Mathematics
- 1974

One of the chief difficulties associated with the so-called backtracking technique for combinatorial problems has been our inability to predict the efficiency of a given algorithm, or to compare the…

Miplib 2003

- Computer ScienceOper. Res. Lett.
- 2006

This paper reports on the fourth version of the Mixed Integer Programming Library, and presents an overview of the 27 new problems and statistical data for all 60 instances that became too easy.

Estimating Search Tree Size

- Computer ScienceAAAI
- 2006

This work proposes two new online methods for estimating the size of a backtracking search tree based on a weighted sample of the branches visited by chronological backtracking and compares them against an old method due to Knuth based on random probing.

Tree Size by Partial Backtracking

- Mathematics, Computer ScienceSIAM J. Comput.
- 1978

The efficiency of Knuth's method can be greatly improved by occasionally following more than one path from a node, which results in an improvement which increases exponentially with the height of the tree.

Forecasting for Inventory Control with Exponential Smoothing

- Economics
- 2002

Exponential smoothing, often used for sales forecasting in inventory control, has always been rationalized in terms of statistical models that possess errors with constant variances. It is shown in…

FORECASTING WITH EXPONENTIAL SMOOTHING: SOME GUIDELINES FOR MODEL SELECTION

- Economics
- 1980

Despite the general acceptance of exponential smoothing, the choice of a specific smoothing model is often a difficult problem. Previous research involving smoothing-model comparisons and the…

Double Exponential Smoothing: An Alternative to Kalman Filter-Based Predictive Tracking

- Computer ScienceIPT/EGVE
- 2003

Novel algorithms for predictive tracking of user position and orientation based on double exponential smoothing are presented, which are faster, easier to implement, and perform equivalently to the Kalman and extended Kalman filtering predictors.

An introduction to Kalman filter

- 2003

3 A deterministic construction of the Kalman filter 7 3.1 The quadratic criterion to be minimized in the absence of process control noise and the corresponding solution . . . . . . . . . . . . . . .…