July 13, 2015

SBO Algorithms for Expensive Functions Optimization

There is a unique family of methods for optimization in pSeven Core embedded in pSeven - Surrogate-Based Optimization (SBO) or optimization based on surrogate models (approximation models). This approach allows dealing with computationally expensive problems since optimization algorithm acts on the surrogate model instead of direct functions evaluations.

Here is just a short list of SBO advantages:

• Is purely global optimization method
• Is insensitive to noisy responses
• Explicitly supports linear and quadratic constraints
• Allows to set a budget (number of function evaluations)

All this make SBO perfect for engineering optimization.

To build surrogate models for optimization purpose Design space exploration block in pSeven uses GP (Gaussian processes) technique. In addition to function prediction, GP model can estimate the accuracy of the surrogate model. This is crucial for SBO algorithms: search of the global optimum of the function turns into a search of the best probability to discover global optimum. On pic 1. you can see the evolution of surrogate model while SBO is discovering the global optimum.

Pic. 1. Evolution of the surrogate model (green surface) while SBO is working. True function is  blue surface

The outline of the algorithm is as follows (see pic. 2):

1. Evaluate Design of Experiment;
2. Build initial surrogate model;
3. Iteratively improve the approximation model evaluating the best candidates for the global optimum.

Pic. 2. Typical Surrogate-Based Optimization history

Along with single-objective optimization, SBO in pSeven Core supports multi-objective problems. In this case, Multi-Objective Surrogate-Based Optimization algorithm works. MSBO can efficiently handle complicated optimization problems with tens of goal functions and hundreds of parameters.