Dynamical methods for solving large-scale discrete and continuous optimization problems
AssigneeBigwood Technology, Inc.
InventorsHsiao-Dong Chiang, Hua Li
Life of this patent
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Abstract
Dynamical methods for obtaining the global optimal solution of general optimization problems having closed form or black box objective functions, including the steps of first finding, in a deterministic manner, one local optimal solution starting from an initial point, and then finding another local optimal solution starting from the previously found one until all the local optimal solutions starting from any initial point are found, and then finding from said points the global optimal solution.
Claims58
A continuous-based dynamical method for solving general unconstrained optimization problems having objective functions and a solution space of finite dimension, comprising the steps of:
- a) constructing a nonlinear continuous dynamical system possessing selected properties at least including the property that a point is a stable equilibrium point of the constructed nonlinear dynamical system if and only if it is a local optimal solution of the unconstrained optimization problem;
- b) finding all local optimal solutions of the general unconstrained optimization problem by the steps of:
- i) starting from an initial point;
- ii) finding a local optimal solution;
- iii) starting at the local optimal solution found in step (b)(ii), finding a set of local optimal solutions which are all stable equilibrium points of the constructed nonlinear dynamical system tier-by-tier by a method selected from the group comprising the exit point (EP) method and the dynamical decomposition point (DDP) method;
- c) choosing a global optimal solution as a best optimal solution from among the stable equilibrium points found in step (b)(iii).
A discrete-based dynamical method for solving general discrete optimization problems having objective functions and a solution space of finite dimension, comprising the steps of:
- a) constructing a discrete nonlinear dynamical system possessing selected properties at least including the property that a point is a local optimal solution of the discrete optimization problem if and only if it is a stable fixed point of the discrete nonlinear dynamical system;
- b) finding all local optimal solutions of the general discrete optimization problem by the steps of:
- i) starting from an initial point x0;
- ii) finding a local optimal solution;
- iii) starting at the local optimal solution found in step (b)(ii), finding the set of local optimal solutions which are all stable fixed points of the constructed discrete nonlinear dynamical system;
- c) choosing the global optimal solution as the best optimal solution from among the stable fixed points found in step (b)(iii).
Dependencies are inferred from the claim text.