The document discusses various factors that can affect optimization solution performance, including modeling languages and formulation, data management and sources, solver selection and tuning, and machine hardware. It provides examples of how to improve model formulation through techniques like using compound sets, reducing big M values, adding cuts, and reformulating constraints. The presentation concludes that achieving optimal performance requires considering all factors but that model formulation, data handling, solver selection and tuning, and fast multicore hardware can best help.

1. INFORMS Phoenix 2012
Achieving Optimal Solution Performance
for Your Optimization Modeling Project
Presented by
Sandip Pindoria
Maximal Software, Inc.
Copyright © 2012 Maximal Software, Inc. All rights reserved
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2. Presentation Overview
Many Different Factors can Affect the Overall Best
Solution Performance for Optimization Projects
Modeling
• Modeling Languages
• Model Formulation
Data
• Data Management
• Data Sources
Solvers
• Solver Performance
• Solver Tuning
Machine Hardware (CPU)
Copyright © 2012 Maximal Software, Inc. All rights reserved
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3. Achieving Optimal Solution Performance
Speed is not everything…
Connectivity
Flexibility
Scalability
Productivity
but can still be quite important!
Data Management
Large-scale models
Real-time optimization
Applications for end-users
Copyright © 2012 Maximal Software, Inc. All rights reserved
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4. Achieving Optimal Solution Performance
Modeling Languages
Independent Languages (GAMS, AMPL, AIMMS, MPL)
Solver Based Languages (OPL, MOSEL, LINGO)
Modeling Languages vs. Callable Libraries
Memory based vs. File based
Parsing speed
Memory Management
Model Formulation
Index sets (numeric vs. named)
Compound sets (set of sets)
Data computations
Modeling pitfalls
Copyright © 2012 Maximal Software, Inc. All rights reserved
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5. Achieving Optimal Solution Performance
Formulating Compound Sets
Using IN Statements
PalCapRoute[route,truck IN ExistTrckRt]:
SUM(cust IN setDeliveryShip: Pal* XCust)
<=
CapTruck * XTruck;
Using WHERE Statements
PalCapRoutes[route,truck] WHERE dtExistTrckRt:
SUM(cust: Pal* XCust WHERE dtsetDeliveryShip)
<=
CapTruck * XTruck;
Copyright © 2012 Maximal Software, Inc. All rights reserved
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6. Achieving Optimal Solution Performance
Data Management
Importing vs. Exporting Data
Local vs. Network
ODBC vs. Native Drivers
Flexibility vs. Speed
Data Sources
Text Files
Binary Files
Spreadsheets
Databases
ERP Systems
XML Files
Copyright © 2012 Maximal Software, Inc. All rights reserved
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7. Achieving Optimal Solution Performance
Importing Data (50K)
0.6
0.5
0.4
0.3
50K
0.2
0.1
0
Text Access Access Excel
No Trans ODBC
Copyright © 2012 Maximal Software, Inc. All rights reserved
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8. Achieving Optimal Solution Performance
Exporting Data
200
150
30K
100
300K
3000K
50
0
Text Access No Trans
Copyright © 2012 Maximal Software, Inc. All rights reserved
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9. Achieving Optimal Solution Performance
Solver Categories
High-end Solvers
Mid-range Solvers
Open Source Solvers
Nonlinear Solvers
Solver Performance
Newest Release
Algorithms (Primal/Dual vs. Barrier)
Parallel Solvers
Local Machine vs. Server
Grid Computing
Copyright © 2012 Maximal Software, Inc. All rights reserved
9

10. Achieving Optimal Solution Performance
Solver Tuning (specifically CPLEX MIP)
Cuts (Automatic vs. Aggressive)
Variable Selection (Pseudo Cost vs. Strong)
Probing/Heuristics
Emphasis (Feasibility vs. Optimality)
Tolerance Gaps
Automatic Tuning
Copyright © 2012 Maximal Software, Inc. All rights reserved
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11. Achieving Optimal Solution Performance
No single tuning parameter gives always the best results
harp2 mas74 mzzv11 10teams aflow30a air04 air05 TOTAL
Defaults 124.2 284.7 120.3 4.75 13.531 9.016 9.203 565.8
Prob1 81.0 280.4 122.6 5.172 12.641 10.531 10.781 523.1
Prob2 106.4 284.2 36.2 5.328 12.688 10.25 10.765 465.8
Prob3 102.3 278.9 104.1 5.234 12.641 87.093 88.172 678.5
PsuedoCost 126.7 279.5 120.4 6.266 13.422 9 8.906 564.2
StrongBranch 126.8 279.9 120.4 5.985 13.406 8.984 8.719 564.2
PsuedoRedCost 126.4 277.6 120.1 5.25 13.391 9 9.078 560.8
Optimality 135.1 311.3 215.5 34.937 13.922 22.891 23.078 756.7
AggressiveCut 126.8 279.5 120.3 5.188 13.328 8.906 8.954 563.0
NoCuts 207.4 271.2 166.2 30.188 125.39 17.297 18.657 836.3
Combination 126.9 280.1 120.2 5.218 13.39 8.86 8.953 563.6
AVERAGE 126.4 282.5 124.2 10.3 13.2 11.5 11.7 596.3
MAX 207.4 311.3 215.5 34.9 125.4 87.1 88.2 836.3
MIN 81.0 271.2 36.2 4.8 12.6 8.9 8.7 465.8
DIFF 126.4 40.1 179.3 30.2 112.7 78.2 79.5 370.6
Copyright © 2012 Maximal Software, Inc. All rights reserved
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12. Achieving Optimal Solution Performance
Model Formulation improvements
Usually MIP models can improved by tinkering with the
formulation
Modeling Presolve
Strategic vs. Detailed decisions
Identifying Global cuts
Tightening constraints/bounds
Reformulating constraints
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13. Presolve
Principal aim of Presolve is:
• Reduce the scope of the problem
• Eliminate constraints and variables
• Tighten Bounds, RHS values
• Modify matrix coefficients to tighten constraints
• High end solvers have very good Presolvers but:
• Computationally expensive
• Not always comprehensive
Copyright © 2012 Maximal Software, Inc. All rights reserved
13

14. Presolve
Eliminating binary/integer variables
SWITCHMINMAXE[plant,modes2,t]:
SUM(modes: BIN_SWITCH[modes:=modes2,modes2:=modes])
+ SUM(modes IN m_plant_mode: BIN_SWITCHEX[modes,modes2])
=
BIN_SWITCH_MIN + BIN_SWITCH_MAX;
Can change the type of variable to continuous for
BIN_SWITCH_MIN or BIN_SWITCH_MAX
Copyright © 2012 Maximal Software, Inc. All rights reserved
14

15. Tightening the formulation
Try to get the formulation as close as possible to the convex
hull of the integer feasible solutions
Copyright © 2012 Maximal Software, Inc. All rights reserved
15

16. Big M
BigM Reduction
• Reduce the size of the Big M value in logical constraints.
• Seeing formulations with arbitrary Big M is still common:
SUM(stream: Prod_Reservere) <= 99999 * Bin_UseReserve;
BigM often linked to a data parameter which will be much smaller:
SUM(stream: Prod_Reservere) <= limitInput_reserves *
Bin_UseReserve;
Copyright © 2012 Maximal Software, Inc. All rights reserved
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17. Cuts
These are essentially redundant constraints that cut off part
of the LP relaxed solution
• Tightens the formulation
• Increases model size
Cuts can be either:
• Local
• Global
Formulation stand point aim is to identify global cuts
Copyright © 2012 Maximal Software, Inc. All rights reserved
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18. Clique Cuts
A good global cut to seek out are clique cuts
Set of pairwise incompatible variables
BIN_OVERMODE + BIN_UNDERMODE <= 1;
BIN_OVERMODE + BIN_SWITCHMODE <= 1;
BIN_SWITCHMODE + BIN_UNDERMODE <= 1;
From the above one can imply the following cut:
BIN_OVERMODE + BIN_UNDERMODE + BIN_SWITCHMODE <= 1;
Copyright © 2012 Maximal Software, Inc. All rights reserved
18

19. Reformulation
Constraint or a set of constraints that are stated to do a
function in the model can be re done that may aid the
solving process
DICE_EQ2[plant,mode,mode2,t,t2]:
BIN_SWITCH <= BIN_INSTANTAITE;
VARIABLES
BIN_SWITCH[plant,mode,mode2,t,t2];
BIN_INSTANTAITE[plant,mode,t];
Copyright © 2012 Maximal Software, Inc. All rights reserved
19

20. Reformulation
Due to the indexing difference, reformulated by:
DICE_EQ2[plant,mode,t]:
SUM(mode2,t2: BIN_SWITCH)
<= DATSWITCH * BIN_INSTANTAITE;
Where DATSWITCH is a data scalar
DATA
DATSWITCH = COUNT(mode2) * COUNT(t2);
• Formulation becomes less tighter
• Reduces the number of constraints
Copyright © 2012 Maximal Software, Inc. All rights reserved
20

21. Achieving Optimal Solution Performance
Hardware
PC vs. Unix
Windows vs. Linux
Intel vs. AMD
Duo Core vs. Quad Core
CPU Speed (GHz)
Overclocking
Level2 Cache
Random Memory
Copyright © 2012 Maximal Software, Inc. All rights reserved
21

22. Achieving Optimal Solution Performance
Which Factors Can Best Help Achieve the
Overall Optimal Solution Performance?
Model Formulation
• Fast modeling language
• Use compound indexes
Data Sources
• Store data locally
• Binary or text files
Solving
• Newest version of fast, high-end solver
• Aggressive solver tuning
Machine Hardware
• Fastest/newest multi-core CPU
Copyright © 2012 Maximal Software, Inc. All rights reserved
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