Fred Glover OptTek Systems, Inc. Boulder, Colorado Andreas Reinholz University of Dortmund Dortmund, Germany Metaheuristics International Conference June.

Fred GloverOptTek Systems, Inc.Boulder, Colorado

Andreas ReinholzUniversity of DortmundDortmund, Germany

Metaheuristics International ConferenceJune 25-29, 2007

METAHEURISTICSIN SCIENCE AND INDUSTRY: NEW DEVELOPMENTS

OptTek Customized Simulation Optimization Applications

• Portfolio Management• Supply Chain Applications• Strategic and Operational Planning• Financial Planning• Manufacturing Process Flow • Resource-Constrained Scheduling• Network Planning• Routing & Distribution• Data Mining• Biotechnology• Health Care

Standard Optimization SoftwareOptQuest®

• AnyLogic (a product of XJ Technologies Company)• Arena (a product of Rockwell Software/Systems Modeling Corp.)• Crystal Ball (a product of Decisioneering, Inc.)• CSIM (a product of Mesquite Software)• Enterprise Dynamics (a product of Incontrol)• FlexSim (a product of FlexSim Software Products, Inc.)• Micro Saint (a product of Micro Analysis and Design, Inc.)• OQNLP (a joint product developed with Optimal Methods, Inc.)• Parallel OptQuest® (enabled by Paradise®, a product of Scientific Computing)• Premium Solver Platform (a product of Frontline Systems)• Promodel/Innovate (products of Promodel Corporation)• Quest (a product of Delmia Corp.)• SimFlex (a product of Flextronics)• SIMPROCESS (a product of CACI)• SIMUL8 (a product of SIMUL8 Corporation)• TERAS (a product of Halliburton’s Landmark Graphics)• VIEO 1000 (a product of VIEO Corporation)

Metaheuristic – BasedSimulation Optimization

MetaheuristicOptimizer

SimulationModel

Input parameters Objective function value

Realistic Optimization

The Optimization Challenge

• Function to be Optimized• Highly Nonlinear• Nondifferentiable• Discrete or Continuous or Mixed

• Function Evaluations• Complex• Extremely Computation Intensive• One second to One Day per Evaluation!

• Evolutionary Scatter Search• Advanced Tabu Search• Linear & Mixed Integer Programming• Pattern Classification & Curve Fitting

• Neural Networks• Support Vector Machines & Trees• SAT Data Mining

OptQuest® Components

Example 5 Problem 14 Best solution = -8695.012285

-4397.23 Risk Pop 10-4576.85 Risk Pop 20

-4272.22 Risk Pop 50

-4765.34 Risk Pop 100

-8543.49 OptQuest Pop 20

-8695.01 OCL Boundary=.7

-9000

-8000

-7000

-6000

-5000

-4000

-3000

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Simulations

Ob

ject

ive

Efficiency is Critical!

OptQuest® vs. RiskOptimizer

Oil/Gas Financial Planning using

Problem

• Given a set of opportunities and limited resources…

• …determine the best set of projects that maximizes performance

Portfolio Selection Problem

• Constraints: • Budget • Resource Availability • Scheduling and Sequencing of Projects • Project Dependencies, etc.

• Objectives:• Maximize Net Present Value (NPV)• Maximize Internal Rate of Return (IRR)• Maximize Business-Case Value (BCV)

Application Example

• 5 Projects:• Tight Gas Play Scenario (TGP)• Oil – Water Flood Prospect (OWF)• Dependent Layer Gas Play Scenario (DL)• Oil – Offshore Prospect (OOP)• Oil – Horizontal Well Prospect (OHW)

• Ten year models that incorporate multiple types of uncertainty

• Evaluation Time: 1s / Scenario

Base CaseDetermine project participation levels [0,1] that• Maximize E(NPV) • Keep < 10,000 M$ (Risk Control)• All projects start in year 1

Frequency Chart

M$

Mean = $37,393.13.000

.007

.014

.021

.028

0

7

14

21

28

$15,382.13 $27,100.03 $38,817.92 $50,535.82 $62,253.71

1,000 Trials 16 Outliers

Forecast: NPV

Base Case

TGP = 0.4, OWF = 0.4, DL = 0.8, OHW = 1.0

E(NPV) = 37,393 =9,501

Deferment CaseDetermine project participation levels [0,1] AND starting times for each project that• Maximize E(NPV) • Keep < 10,000 M$ (Risk Control)• Projects may start in year 1, 2, or 3

Frequency Chart

M$

Mean = $47,455.10.000

.007

.014

.020

.027

0

6.75

13.5

20.25

27

$25,668.28 $37,721.53 $49,774.78 $61,828.04 $73,881.29

1,000 Trials 8 Outliers

Forecast: NPV

TGP1 = 0.6, DL1=0.4, OHW3=0.2

E(NPV) = 47,455 =9,513 10th Pc.=36,096

Deferment Case

Frequency Chart

M$

Mean = $37,393.13.000

.007

.014

.021

.028

0

7

14

21

28

$15,382.13 $27,100.03 $38,817.92 $50,535.82 $62,253.71

1,000 Trials 16 Outliers

Forecast: NPV

Base Case

TGP = 0.4, OWF = 0.4, DL = 0.8, OHW = 1.0

E(NPV) = 37,393 =9,501

Probability of Success CaseDetermine project participation levels AND starting times for each project that• Maximize P(NPV > 47,455 M$) • Keep 10th Percentile of NPV > 36,096 M$• Projects may start in year 1, 2, or 3

Frequency Chart

M$

Mean = $47,455.10.000

.007

.014

.020

.027

0

6.75

13.5

20.25

27

$25,668.28 $37,721.53 $49,774.78 $61,828.04 $73,881.29

1,000 Trials 8 Outliers

Forecast: NPV

TGP1 = 0.6, DL1=0.4, OHW3=0.2

E(NPV) = 47,455 =9,513 10th Pc.=36,096

Deferment Case

Frequency Chart

M$

Mean = $37,393.13.000

.007

.014

.021

.028

0

7

14

21

28

$15,382.13 $27,100.03 $38,817.92 $50,535.82 $62,253.71

1,000 Trials 16 Outliers

Forecast: NPV

Base Case

TGP = 0.4, OWF = 0.4, DL = 0.8, OHW = 1.0

E(NPV) = 37,393 =9,501

Frequency Chart

M$

Mean = $83,971.65.000

.008

.016

.024

.032

0

8

16

24

32

$43,258.81 $65,476.45 $87,694.09 $109,911.73 $132,129.38

1,000 Trials 13 Outliers

Forecast: NPV

TGP1 = 1.0, OWF1=1.0, DL1=1.0, OHW3=0.2

E(NPV) = 83,972 =18,522 P(NPV > 47,455) = 0.99 10th Pc.=43,359

Probability of Success Case

Extensions…

• Cash Flow Control• Capital Expenditure Control• Reserve Replacement Goals• Production Goals• Finding Costs Control• Dry Hole Expectations Control• Reserve Goals• Net Profit Goals

Hospital Emergency Room Process

Treatment

Patient Arrival

Emergency Room (ER)

Approach= optimize current process, redesign process and re-optimize.

Objective = minimize expected total asset

cost while ensuring a reasonable average

patient cycle time

Release

Admit

Joseph DeFee, CACI, Inc.

ER Resources

• Nurses• Physicians• Patient Care Technicians (PCTs)• Administrative Clerks• Emergency Rooms (ER)

Problem

• Minimize E[Total Asset Cost]• Subject to:

– E[Cycle Time] for Level 1 Patients < 2.4 hours– Number of Nurses between 1 and 7– Number of Physicians between 1 and 3– Number of PCTs between 1 and 4– Number of Clerks between 1 and 4– Number of ER between 1 and 20

Solution

• Set up OptQuest to run for 100 iterations and 5 runs per iteration

• Each run simulates 5 days of ER operation

• Results:– Best solution found in 6 minutes – E[TAC] = $ 25.2K (31% improvement)– E[CT] for P1 = 2.17 hours

Process RedesignPossible to improve E[CT] for P1 even further?

Arrive at ER

Transfer toroom

Receivetreatment

Fill outregistration OK? Released

AdmittedInto

Hospital

Y

N

Current Process

Arrive at ER

Transfer toroom

Receivetreatment

Fill outregistration

OK? Released

AdmittedInto

Hospital

Y

N

Redesigned Process

Solution of the Redesigned Process

• Set up OptQuest to run for 100 iterations and 5 runs per iteration

• Each run simulates 5 days of ER operation

• Results:– Best solution found in 8 minutes– E[TAC] = $ 24.6K (new best, 3.4% improvement)– E[CT] for P1 = 1.94 hours (12% improvement)

Conclusions

Simulation Optimization with OptQuest is able to

• fully address uncertainty from multiple sources• find high-quality solutions in reasonable time• follow modified models and re-optimize them• handle problems that are not solvable by classical

methods

Global Conclusions - 1

• These applications are only a fraction of the ways that metaheuristics and simulation are used in optimization involving non-linearity and uncertainty

• Over 60,000 user licenses of the system have been sold (each licensed user might have multiple kinds of problems)

Global Conclusions - 2

Key methodology is an integration of:

• Adaptive Memory Metaheuristics (TS)

• Evolutionary Metaheuristics

• Math Programming

• Data Mining (Pattern Analysis)

Wave of Future

Bootstrapping (Mutual Iterated Design):

• Metaheuristics (Sim Opt)

• Tuning (parameters) and Tailoring

• General Non-linear Models/Methods

• General Mixed Integer Models/Methods

• Knowledge Representation by Meta-Models