Method and system for optimization of general problems
First Claim
1. A method for computationally modeling a complex, hierarchical problem with n hierarchical levels, the method comprising:
- encoding a first, discrete problem in a computer readable form to represent a first level of the hierarchical problem;
parameterizing the first discrete problem using a continuous iteration variable to produce a next, continuous problem encoded in a computer readable medium;
for each subsequent level of the remaining n−
1 levels of the hierarchical problem,adding additional constraints to the next continuous problem to produce a next discrete problem; and
parameterizing the next discrete problem using a continuous iteration variable to produce a next, continuous problem encoded in a computer readable medium.
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Abstract
Embodiments of the disclosed invention include optimization methods and systems that receive a mathematical description of a system, in symbolic form, that includes decision variables of various types, including real-number-valued, integer-valued, and Boolean-valued decision variables, and that may also include a variety of constraints on the values of the decision variables, including inequality and equality constraints. The objective function and constraints are incorporated into a global objective function. The global objective function is transformed into a system of differential equations in terms of continuous variables and parameters, so that polynomial-time methods for solving differential equations can be applied to calculate near-optimal solutions for the global objective function.
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Citations
1 Claim
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1. A method for computationally modeling a complex, hierarchical problem with n hierarchical levels, the method comprising:
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encoding a first, discrete problem in a computer readable form to represent a first level of the hierarchical problem; parameterizing the first discrete problem using a continuous iteration variable to produce a next, continuous problem encoded in a computer readable medium; for each subsequent level of the remaining n−
1 levels of the hierarchical problem,adding additional constraints to the next continuous problem to produce a next discrete problem; and parameterizing the next discrete problem using a continuous iteration variable to produce a next, continuous problem encoded in a computer readable medium.
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Specification