CoJava: Optimization Modeling by Nondeterministic Simulation

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CoJava Optimization Modeling by Nondeterministic
Simulation

• Alex Brodsky
• George Mason University and
• Adaptive Decisions, Inc.
• Joint work with
• Hadon Nash
• Google

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Presentation Outline

• Optimization vs. Simulation Modeling
• CoJava by Example A Simple Supply Chain
• CoJava Syntax and Restrictions
• Semantics Optimal Execution Path
• Reduction to Constraint Optimization Formulation
• Implementation
• Related Work
• Conclusions and Future Work

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Optimization vs. Simulation Models
 
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Presentation Outline

• Optimization vs. Simulation Modeling
• CoJava by Example A Simple Supply Chain
• CoJava Syntax
• Semantics Optimal Execution Path
• Reduction to Constraint Optimization Formulation
• Implementation
• Related Work
• Conclusions and Future Work

5
Presentation Outline

• Optimization vs. Simulation Modeling
• CoJava by Example A Simple Supply Chain
• CoJava Syntax
• Semantics Optimal Execution Path
• Reduction to Constraint Optimization Formulation
• Implementation
• Related Work
• Conclusions and Future Work

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CoJava Syntax
public class Nd public double choice(double
min, double max) ... public double
checkMinObjective(double objective) ...
public double checkMaxObjective(double objective)
...
CoJava program can compile and run in Java!
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CoJava Syntax Restrictions

• Non-deterministic value
• The output of a choice method is a ND-value
• A variable is a ND-value, if it appears on the
  left-hand side of an assignment with a ND-value
  on the right-hand side.
• A variable is a ND-value, if it appears on
  the left-hand side of an assignment that
  appears in the THEN or ELSE part of a conditional
  statement, where the Boolean condition is a
  ND-value.
• The result of an arithmetic or Boolean
  operation on one or more ND- values is a
  ND-value.

• Syntactic restrictions
• No ND loops
• No ND recursive method calls
• No ND calls for checkObjective.

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Presentation Outline

• Optimization vs. Simulation Modeling
• CoJava by Example A Simple Supply Chain
• CoJava Syntax
• Semantics Optimal Execution Path
• Reduction to Constraint Optimization Formulation
• Implementation
• Related Work
• Conclusions and Future Work

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CoJava Semantics Optimal Execution Path
Given P - CoJava program I - input to
P v - variable in checkMin/MaxObjective(v),
which appears once in P We denote by EP -
the set of all feasible execution paths e, i.e.,
execution paths that reach the
statement checkMin/MaxObjective(v) when P is run
on input I v(e) - the value of program
variable v at checkMin/MaxObjective(v) on
feasible execution path e in
EP We define optimal execution path OP as a
solution to the problem
min/max v(e) subject to e in EP
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CoJava Semantics 2 step process

• Case 1 A single checkMin/MaxObjective in program
  P
• Step 1 Find an optimal execution path OP for P
  on input I
• Step 2 Execute OP deterministically as a
  regular Java program

• Case 2 No checkMin/MaxObjective in program P
• Step 1 Find a feasible execution path e for P
  on input I
• Step 2 Execute e deterministically as a
  regular Java program

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CoJava Semantics

• Case 3 Multiple checkMin/MaxObjective in
  program P
• Apply Case 1 iteratively

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Presentation Outline

• Optimization vs. Simulation Modeling
• CoJava by Example A Simple Supply Chain
• CoJava Syntax
• Semantics Optimal Execution Path
• Reduction to Constraint Optimization Formulation
• Implementation
• Related Work
• Conclusions and Future Work

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Reduction to Constraint Optimization
FormulationSmall Example
CS prices0_1 gt 100.0 /\ prices0_1 lt
200.0 /\ prices1_1 gt 105.0 /\ prices0_2 lt
205.0 .. ... ... revenue_1 0 /\ revenue_2
revenue_1 revenues0_2 /\ . revenue_3
revenue_2 revenues1_2 /\ . cost_3 cost_1
cost_2 /\ . profit_1 revenue_3 - cost_3 /\
Maximize profit_1 subject to CS
prices0 Nd.choice(100, 200) prices1
Nd.choice(105, 205) Demand demand new
Demand(prices) Manufacturer manufacturer new
Manufacturer(demand.quantities) Supplier
supplier new Supplier(manufacturer.materials)
double revenue 0 for (int i 0 i lt
2 i i 1) revenue
demand.revenuesi double cost
manufacturer.cost supplier.cost double profit
revenue - cost Nd.checkMaxObjective(profit)
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Reduction to Constraint Optimization
FormulationAnother Small Example
CS . prices0_1 gt 100 /\ prices_1 lt
200 /\ quantities0_1 1000 /\ revenues0_1
prices0_1 1000 /\ (prices0_1 lt 150) ---gt
(quantities0_2 4000 /\ revenues0_2
prices_1 4000) (prices_1 lt 150)
---gt (quantities0_2 quantities0_1 /\
revenues0_2 revenues0_1) . / Similar
for second iteration /
final double pLow 100, 105 final
double pMid 150, 185 final double
pHigh 200, 205 final double qLow
4000, 6000 final double qHigh 1000,
1800 for (int i 0 i lt 2 i i 1)
assert(pricesi gt pLowi)
assert(pricesi lt pHighi)
quantitiesi qHighi revenuesi
pricesi qHighi if (pricesi
lt pMidi) quantitiesi
qLowi revenuesi pricesi
qLowi
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Presentation Outline

• Optimization vs. Simulation Modeling
• CoJava by Example A Simple Supply Chain
• CoJava Syntax
• Semantics Optimal Execution Path
• Reduction to Constraint Optimization Formulation
• Implementation
• Related Work
• Conclusions and Future Work

16
Presentation Outline

• Optimization vs. Simulation Modeling
• CoJava by Example A Simple Supply Chain
• CoJava Syntax
• Semantics Optimal Execution Path
• Reduction to Constraint Optimization Formulation
• Implementation
• Related Work See Paper for Details
• Conclusions and Future Work

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Conclusions and Future Work

• Unified language for process simulation and
  optimization
• Java was used, but this is a general framework
  for Optimization extensions of
• process models in PL, DB QL, CAD/CAM, workflow
  systems,
• This allows to push MP and CP to other
  communities of users without them realizing
  they are using it, because they would continue to
  use their native methodologies/tools/systems
• Future research questions
• how to generalize CoJava to serve as a general
  computational paradigm
• how to extend it with intelligent debugging
  capability (including testing whether
  generated constraints fall into specific classes
  supported by external solvers)
• how to extend CoJava with CP facilities and
  extend underlying constraint solvers
• how to apply CoJava principle to optimize
  processes in diverse domain, such as a variety of
  CAD/CAM methodologies and tools
• how to extend CoJava for specifying
  templates for machine learning (regression and
  classification models)