System and method for estimation of a distribution algorithm
The underlying invention generally relates to the field of Estimation of Distribution Algorithm, especially to optimization problems, including single-objective optimization and Multi-Objective Optimization. The proposed method for optimization comprises six steps. In a first step it provides an initial population or a data set with a plurality of members respectively represented by parameter sets. Then one or a plurality of fitness functions are applied to evaluate the quality of the members of the population. In a third step offspring of the population is generated by means of a stochastic model using information from all members of the population. One or a plurality of fitness functions are applied to evaluate the quality of the offspring with respect to the underlying problem of the optimization. In a fifth step offspring is selected. Lastly the method goes back to the third step until the quality reaches a threshold value.
1. A method for optimizing a design representing a physical object, wherein said physical object is an aerodynamic or hydrodynamic structure, comprising the steps of:
(a) providing an initial population or a data set with a plurality of members respectively represented by parameter sets representing the design;
(b) applying one or a plurality of fitness functions to evaluate the quality of the members of the population;
(c) generating offspring of the population by means of a stochastic model using information from all members of the population;
(d) applying one or a plurality of fitness functions to evaluate the quality of the offspring with respect to the underlying problem of the optimization;
(e) selecting offspring,
(f) repeating steps (c) through (e) until the quality reaches a threshold value representing the optimized design, and
(g) storing said optimized design in a computer storage capable of being executed by a computing device;
wherein a Voronoi-mesh is applied in step (c) to build a stochastic model for generating offspring.
2. The method of claim 1 , wherein in step (d) the members are ranked according to their quality, and wherein in step (e) all members are stored and members of a higher respectively lower rank have a higher respectively lower selection probability.
3. The method of claim 1 , wherein each cell in the Voronoi-mesh is assigned a selection probability based on a rank of the cell.
4. The method of claim 1 , wherein the stochastic model is perturbed to avoid local optima.
5. The method of claim 1 , wherein the data in the space of the parameter sets are clustered in generating stochastic model in step (c).
6. The method of claim 1 , wherein at least one of the principal component analysis and the independent component analysis are used in generating a stochastic model in step (c).
7. The method of claim 1 , wherein at least one of a function approximation of the solution space and the fitness space is generated.
8. A computer software program product, implementing a method of claim 1 when executing when running on a computing device.
9. A system for optimizing a design representing a physical object, wherein said physical object is an aerodynamic or hydrodynamic structure, comprising:
means for providing an initial population or a data set with a plurality of members respectively represented by parameter sets;
means for applying one or a plurality of fitness functions to evaluate the quality of the members of the population;
means for generating offspring of the population by means of a stochastic model using information from all members of the population;
means for applying one or a plurality of fitness functions to evaluate the quality of the offspring with respect to the underlying problem of the optimization;
means for selecting offspring;
means for comparing the quality to a threshold value; and
means for storing said optimized design in a computer storage capable of being executed by a computing device;
wherein a Voronoi-mesh is applied in the means for generating offspring to build a stochastic model for generating offspring.