Automatic Fine-tuning Xpress-MP to Solve MIP

© 2008 Fair Isaac Corporation.
Automatic Fine-tuning Xpress-MP to Solve MIP
by Gabriel Tavares
Horia Tipi
Alkis Vazacopoulos
INFORMS Annual Meeting
Washington, DC, October, 2008

2 © 2007 Fair Isaac Corporation.© 2008 Fair Isaac Corporation.
Agenda
 Heuristics in Xpress-MP
 Xpress-Tuner
New Features
Process
Creating Specialized Tuning Strategies
 Conclusions

Classes of Heuristics in Xpress-MP
 Branch-&-Bound Heuristics (Integral Nodes)
 Feasibility Pump Heuristics
 Diving Heuristics
 Local Search Heuristics
Node BestSoln BestBound Sols Active Depth Gap GInf Time
11500 56138.00000 55821.97518 11 29 48 0.56% 0 29
+ 11516 56138.00000 55828.26120 12 12 5 0.55% 0 29
+ 11516 56138.00000 55828.26120 13 12 5 0.55% 0 29
+ 11516 56137.00000 55828.26120 14 12 5 0.55% 0 29
* 11572 56137.00000 55852.82171 15 33 29 0.51% 0 40
11600 56137.00000 55932.33767 15 32 8 0.36% 253 43
* 11636 56137.00000 56137.00000 16 20 29 7.3e-12 0 45
The * Xpress Heuristics
The + Xpress Heuristics

CORAL Benchmark for MIP
 Publicly available from
http://coral.ie.lehigh.edu/mip-instances/
 Consists of 372 MIPs from various sources (mostly from NEOS)
4 instances are infeasible
 On an average problem, Xpress 2008A out-of-the-box found:
4.1 (+) heuristics at the root node
2.5 (+) heuristics during B&B
1.6 (*) heuristics

Xpress 2008A Serial vs 2008A 2-Threads
on CORAL Set
 The Xpress parallel search is now deterministic (by default)
2008A
2 Threads
Speedup
Total Time to Find the Optimal
Solutions found by Both Solvers
7 h 57 m 5 h 9 m 1.54x
Within 30 Minutes:
2008A
Serial
2008A
2 Threads
Number of Optimal Solutions 218 220
Deterministic
Algorithm

Number of Improved Solutions Xpress
2008A Serial vs 2008A 2-Threads
Number of Improved
Solutions by
2008A
2008A
2 Threads
(+) heuristics at root node 4.1 4.1
(+) heuristics during B&B 2.5 2.7
(*) heuristics 1.6 1.4

Using another Local Search (LS)
Heuristic Families on CORAL Set
 Set controls
HEURSEARCHROOTSELECT=5
HEURSEARCHTREESELECT=5
HEURSEARCHEFFORT=1.0
 Xpress 2 Threads + LS is better in about 1/3 of the cases
Number of Improved
Solutions by
2008A
2 Threads
2008A 2
Threads + LS

Fine-Tuning Threads in Xpress-MP
 Each Individual Thread of the
Parallel Search can be Specialized:
To improve the Best Objective by
Applying local search Heuristics
Applying diving Heuristics
Using Depth-First-Search etc. OR
To improve the Best Bound by
Using Best-First-Search (BFS)
Increasing the effort on strong branching
Applying in-Tree Cuts, etc.

Multiple Worker Paradigm
Many Workers
Same Tasks
Few Specialized
Workers

Using a Specialized Local Search
(LS) Heuristic Thread on CORAL Set
 Set control MIPTHREADSELECT=2
Activates other Local Search Heuristics to be run on 1 Thread
 1 Thread + 1 LS Thread is better in 38% of the cases
Number of Improved
Solutions by
2008A
2 Threads
2008A 1 Thread
+ 1 LS Thread

The MIPLIB 2003 Experience
Problem
Old Best Known Obj.
Value (*)
Xpress Improved Obj.
Value (**)
GAIN
(|1-(**)/(*)|)
atlanta-ip 95.009549704 90.00987861 5.3%
msc98-ip 20980991.006 19839497.006 5.4%
protfold -30 -31 3.3%
rd-rplusc-21 171182 165395.2753 3.4%
sp97ar 664565103.76 660705646.5 0.6%
stp3d unknown 500.736 N/A
ds 283.4425 116.59 58.9%
momentum3 370177.036 236426.335 36.1%
t1717 193221 170195 11.9%
liu 1172 1102 5.9%
dano3mip 691.2 687.733333 0.5%
OptimalUnsolved
Solving Hard Mixed Integer Programming Problems with Xpress-MP:
A MIPLIB 2003 Case Study, Informs Journal on Computing, to appear
by Richard Laundy, Michael Perregaard, Gabriel Tavares, Horia Tipi, and Alkis Vazacopoulos

Node BestSoln BestBound Sols Active Depth Gap GInf Time
100000 1098.000000 560.000000 1 64916 79 49.00% 207 15576
100500 1098.000000 560.000000 1 65228 70 49.00% 229 15659
101000 1098.000000 560.000000 1 65581 56 49.00% 267 15734
101500 1098.000000 560.000000 1 65918 102 49.00% 147 15808
+ 101653 1090.000000 560.000000 2 66033 23 48.62% 0 15834
liu
 Is a MIPLIB 2003 model that involves the floor plan and placement
problem in the physical design of VLSI circuits
The best known solution is 1102
 Consider the algorithm:
1 standard Thread
1 specialized Thread (Breadth-First Search and heavy 2 LS Heuristics)
NODESELECTION=2
HEURSEARCHROOTSELECT=5
HEURSEARCHTREESELECT=5
HEURSEARCHFREQ=1
HEURSEARCHEFFORT=10000
liu’s best solution is now 1090

Improved Branching & Heuristics in
2008A
Computing Time to the N-th Solution
(Geometric Mean )
0 sec
5 sec
10 sec
15 sec
20 sec
25 sec
30 sec
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
Solution Number
2008A
2007B
2008A 2 threads

Improving Out-of-the-Box
Performance using the Xpress-Tuner
 Xpress-Tuner allows the user to automatically find a set of control
parameters and their values that can improve the solve time of
the default settings for a single or a group of problems
 Xpress-Tuner 2008A New Features:
Tuning Process is Parallelized
Allows to Warm Start a Problem with a Known Solution
Improved Tuning Methods
Cloning of Tuning Methods
 Xpress-Tuner usually finds settings that can improve the
computing times by a factor between 2x and 10x

Xpress-Tuner: How to Tune
(Automatically) an Optimization Problem?

Xpress-Tuner in Action
 Mittelmann Benchmark for MIP
 Advertising Up-Front Market Sales Plan Generation
 Planogram Optimization
 Set Covering

Mittelmann results
 Considered subset of 9 MIPs from Mittelmann for which the best
reported solve time was larger than 2 minutes (as of 6/4/08)
 Computer used in Mittelmann tests
2.667 GHz Intel Core 2 (4GB, Linux, 64 bit)
 Computer used in Xpress tests
2 GHz Intel Core 2 (2GB, Windows, 32 bit)

Mittelmann Tuning Results
MIP
Fastest Time in
Mittelmann’s
Website
Xpress-MP
Defaults
Xpress-MP
Tuned
Speedup
to Best
neos5 188 s 4142 s 1218 s 0.2x
seymour1 165 s 676 s 193 s 0.8x
dano3_5 214 s 212 s 161 s 1.3x
neos9 180 s > 2h 91 s 2.0x
bienst2 161 s 330 s 75 s 2.1x
neos818918 3069 s 5944 s 1105 s 2.8x
neos823206 552 s 5984 s 123 s 4.5x
neos11 153 s 40 s 15 s 10x
neos808444 481 s 125 s 10 s 48x

Advertising Up-Front Market Sales
Plan Generation
 Three harder MIPs obtained from a TV Network
 Goal was to get a 0.01% solution gap within 1 minute, for each
problem
 Computer used

A solution for a Single Advertising
Plan
start
date
6351 6352 6354 6355 6356 10084
1/1/2007 10 / 966 10 / 572 10 / 310
1/8/2007 11 / 454 10 / 1006 10 / 510 10 / 308
1/15/2007 8 / 462
1/22/2007 10 / 770 10 / 308
4/30/2007 10 / 308
6/11/2007 10 / 770 5 / 308
6/18/2007 2 / 770 10 / 308
6/25/2007 3 / 1100 7 / 440 7 / 770 10 / 462 10 / 308 1 / 770
7/2/2007 10 / 770 10 / 462 10 / 308
7/9/2007 10 / 770 7 / 462 10 / 308

Advertising Plan Generation:
Out-of-the-Box vs Tuned
MIP
Xpress Default
Settings
Xpress-Tuned
Plan A no solution 60 s
(0.3% gap)
Plan B no solution 60 s
(0.7% gap)
Plan C 60 s
(1.4%)
60 s
(0.4%)

Xpress-MP for Planogram
Optimization
 Five “hard” MIPs obtained from a Large Retailer
 Goal was to get a 1.5% solution gap within 5 minutes, for each
problem
 Computer used

Xpress-MP for Planogram Optimization:
Out-of-the-Box vs Tuned
MIP
Xpress Default
Settings
Xpress-Tuned
P2871 300 s
(2.0% gap)
187 s
(1.3% gap)
P2879 300 s
(1.7% gap)
35 s
(1.4% gap)
P2750 31 s
(1.3% gap)
31 s
(1.3% gap)
P2757 33 s
(1.1% gap)
10 s
(0.7% gap)
P2864 300 s
(8.8% gap)
300 s
(3.5% gap)

A Greedy Tuning Strategy
 Candidate Algorithms:
LP
Branching
Cutting
Diving Heuristics
Local Search Heuristics
Fixing strategy T
Tune Algorithm As
Are Results
Satisfactory?
s ← s + 1 T ← strategy(As)
A Greedy Tuning Strategy
s ← 1
Define T
Strategy
T
INPUT OUTPUT

Xpress-Tuner in Action
 Show New Features
 Illustrates how to use a Greedy Tuning Strategy
Show How to tune the LS heuristics

Conclusions
 Xpress-MP
Is a top-notch solver for MIP heuristics
Many options available
 Xpress-Tuner
It automatic tunes Xpress, resulting in solve time gains
of 2x to 10x on a typical case
Thank You

Automatic Fine-tuning Xpress-MP to Solve MIP

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