Method and system for optimization of general problems

• US 20060173661A1
• Filed: 03/15/2006
• Published: 08/03/2006
• Est. Priority Date: 10/23/2002
• Status: Active Grant

• Current Assignee: Vladimir Brayman, Wolf Kohn
• Original Assignee: Vladimir Brayman, Wolf Kohn
• Inventors: Brayman, Vladimir, Kohn, Wolf
• Granted Patent: US 7,216,004 B2
• Time in Patent Office: Days
• US Class Current: 703/2
• CPC Class Codes: G05B 13/024 in which a parameter or coefficient is automatically adjusted to optimise the performance
• CPC Class Codes: G06F 17/11 for solving equations , e.g. nonlinear equations, general mathematical optimization problems optimization specially adapted for a specific administrative, business or logistic context G06Q10/04
• CPC Class Codes: G06N 5/01 Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound

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.

Claims

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 the 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.