Method and apparatus for adaptively determining weight factors within the context of an objective function

• US 20040059696A1
• Filed: 09/19/2002
• Published: 03/25/2004
• Est. Priority Date: 09/19/2002
• Status: Active Grant

• Current Assignee: Global Nuclear Fuel Americas, LLC (General Electric Company)
• Original Assignee: Global Nuclear Fuel Americas, LLC (General Electric Company)
• Inventors: Russell, William Earl II, Kropaczek, David Joseph, Cline, William Charles
• Granted Patent: US 7,487,133 B2
• Time in Patent Office: Days
• US Class Current: 706/46
• CPC Class Codes: G06F 2111/04 Constraint-based CAD
• CPC Class Codes: G06F 2111/06 Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
• CPC Class Codes: G06F 30/00 Computer-aided design [CAD]
• CPC Class Codes: G06Q 10/04 Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem" market predictions or forecasting for commercial activities G06Q30/0202
• CPC Class Codes: G21D 3/001 Computer implemented control
• CPC Class Codes: Y02E 30/00 Energy generation of nuclear origin
• CPC Class Codes: Y02E 30/30 Nuclear fission reactors

Abstract

The method and apparatus adaptively determine weighting factors within the context of an objective function for handling optimality conditions and constraints within an optimization search. The objective function is defined as a sum of credit and penalty components. The credit components represent the optimality conditions for the problem. The penalty components represent the constraint violations for the problem. Initially, each component is made up of a weight multiplied by a mathematical expression, called a term, that quantifies either an optimality condition or a constraint violation. The set of credit and penalty weights are adaptively determined based on the progress of an optimization search. Both static and dynamic representations of the modified objective function are used to perform the adaption.

Claims

1. A method of adaptively adjusting an objective function providing a figure of merit for a proposed solution to a constraint problem, comprising:

determining a value for each penalty component of the objective function, each penalty component including a penalty term multiplied by a weight factor from a first set of weight factors, the objective function including at least two penalty components;

determining a worst penalty component using the determined penalty component values; and

changing weight factors in a second set of weight factors that correspond to the determined worst penalty component and at least one other penalty component to create an adapted objective function such that the worst penalty component has increased emphasis.

2. The method of claim 1, wherein the changing step comprises:

increasing the weight factor corresponding to the determined worst penalty component; and

decreasing the weight factor corresponding to the at least one other penalty component.

3. The method of claim 2, wherein the decreasing step decreases the weight factor corresponding to each penalty component other than the determined worst penalty component.

4. The method of claim 2, wherein the increasing step increases the weight factor corresponding to the determined worst penalty component by multiplying the weight factor corresponding to the determined worst penalty component by a fixed amount.

5. The method of claim 2, wherein the decreasing step decreases the weight factor corresponding to the at least one other penalty component by multiplying the weight factor corresponding to the at least one other penalty component by a fixed amount.

6. The method of claim 1, wherein

the objective function includes at least one credit component, each credit component including a credit term multiplied by a weight factor;

and

the changing step further changes a weight factor corresponding to the credit component in the second set of weight factors.

7. The method of claim 6, wherein the changing step decreases the weight factor corresponding to the credit component.

8. The method of claim 6, wherein the changing step comprises:

increasing the weight factor corresponding to the determined worst penalty component by multiplying the weight factor corresponding to the determined worst penalty component by a first fixed amount; and

decreasing the weight factor corresponding to the at least one other penalty component and the credit component by multiplying the weight factors corresponding to the at least one other penalty component and the credit component by a second fixed amount.

9. The method of claim 1, wherein the determining a value for each component step receives a value for a term in at least one component from a simulator.

10. The method of claim 1, wherein the constraint problem relates to one of a boiling water reactor core design and a pressurized water reactor core design.

11. The method of claim 1, wherein the constraint problem relates to a large-scale, combinatorial optimization problem in discrete or continuous control variables.

12. The method of claim 1, wherein the first and second sets of weight factors are different.

13. The method of claim 1, wherein

the first set of weight factors is a set of static weight values;

and

the second set of weight factors includes current weight factor values used in an iterative optimization process, which includes the determining and changing steps.

14. The method of claim 13, wherein the static weights are weights initially supplied by a user.

15. A method of adaptively adjusting an objective function providing a figure of merit for a proposed solution to a constraint problem, comprising:

first determining a value for each penalty component of the objective function, each component of the objective function including a term multiplied by a weight factor from a first set of weight factors, the objective function including at least one penalty component and at least one credit component;

second determining whether a constraint violation exists based on output from the determining a value step; and

first changing a weight factor in a second set of weight factors that corresponds to the credit component if the second determining step determines that a constraint violation does not exist.

16. The method of claim 15, wherein the second determining step determines that a constraint violation exists if a determined penalty component value is greater than zero.

17. The method of claim 15, wherein the changing step increases the weight factor corresponding to the credit component if the second determining step determines that a constraint violation does not exist.

18. The method of claim 16, wherein the changing step increases the weight factor corresponding to the credit component by multiplying the weight factor corresponding to the credit component by a fixed amount.

19. The method of claim 15, wherein, if the second determining step determines that a constraint violation does exist, the method comprising:

third determining a worst penalty component using the determined penalty component values;

second changing weight factors in the second set of weight factors corresponding to the determined worst penalty component and at least one other component in the second set of weight factors to create an adapted objective function such that the worst penalty component has increased emphasis.

20. The method of claim 19, wherein the second changing step changes the weight factors corresponding to the determined worst penalty component and the credit component.

21. The method of claim 19, wherein the second changing step increases the weight factor corresponding to the determined worst penalty component and decreases the weight factors corresponding to each component other than the determined worst penalty component.

22. The method of claim 15, wherein the first determining step receives a value for a term in at least one component from a simulator.

23. The method of claim 15, wherein the constraint problem relates to one of a boiling water reactor core design and a pressurized water reactor core design.

25. The method of claim 15, wherein the first and second sets of weight factors are different.

26. The method of claim 15, wherein

the first set of weight factors is a set of static weight values;

and

the second set of weight factors includes current weight factor values used in an iterative optimization process, which includes the determining and changing steps.

27. The method of claim 26, wherein the static weights are weights initially supplied by a user.

24. The method of clam 15, wherein the constraint problem relates to a large-scale, combinatorial optimization problem in discrete or continuous control variables.

28. A computer readable medium, comprising:

a code arrangement instructing a processor to determine a value for each penalty component of an objective function, each penalty component including a penalty term multiplied by a weight factor from a first set of weight factors, the objective function including at least two penalty components;

a code arrangement instructing a processor to determine a worst penalty component using the determined penalty component values; and

a code arrangement instructing a processor to change weight factors in a second set of weight factors that correspond to the determined worst penalty component and at least one other penalty component to create an adapted objective function such that the worst penalty component has increased emphasis.

29. A computer readable medium, comprising:

a code arrangement instructing a processor to determine a value for each penalty component of an objective function, each component of the objective function including a term multiplied by a weight factor from a first set of weight factors, the objective function including at least one penalty component and at least one credit component;

a code arrangement instructing a processor to determine whether a constraint violation exists based on the determined penalty component values; and

a code arrangement instructing a processor to change a weight factor in a second set of weight factors that corresponds to the credit component if the second determining step determines that a constraint violation does not exist.

30. A method of adaptively adjusting an objective function providing a figure of merit for a proposed solution to a nuclear constraint problem, comprising:

determining a value for each penalty component of the objective function, each penalty component including a penalty term multiplied by a weight factor from a first set of weight factors, the objective function including at least two penalty components;

determining a worst penalty component using the determined penalty component values; and

changing weight factors in a second set of weight factors that correspond to the determined worst penalty component and at least one other penalty component to create an adapted objective function such that the worst penalty component has increased emphasis.

31. The method of claim 30, wherein the determining and changing steps form part of an optimization process run at a computer system in response to a request from a user.

32. A method of adaptively adjusting an objective function providing a figure of merit for a proposed solution to a nuclear reactor constraint problem, comprising:

determining a value for each penalty component of the objective function, each component of the objective function including a term multiplied by a weight factor from a first set of weight factors, the objective function including at least one penalty component and at least one credit component;

determining whether a constraint violation exists based on output from the determining a value step; and

changing a weight factor in a second set of weight factors that corresponds to the credit component if the second determining step determines that a constraint violation does not exist.

33. The method of claim 32, wherein the determining and changing steps form part of an optimization process run at a computer system in response to a request from a user.