The TOMLAB /CGO toolbox aims at efficiently solving global non-convex (integer) problems where the function f(x) is very costly to compute.

The toolbox consists of three general solvers:

Response surface methods are discussed in a paper by Donald R. Jones:

A Taxonomy of Global optimization Methods Based on Response Surfaces Journal of Global Optimization 21 (4), 345:383, 2001.

Jones draws the conclusion that methods based on EGO and RBF algorithms are the most promising. The TOMLAB /CGO toolbox is based on these promising methods, and is continuously developed based on the state-of-the-art research in the field.

One example that motivated the research was industrial design of trains, where one f(x) value consumed 30 minutes to compute. The function value was the result of a simulation of 30 seconds of train ride. This problem is discussed in our paper:

Mattias Björkman, Kenneth Holmström: Global Optimization of Costly Nonconvex Functions Using Radial Basis Functions, Optimization and Engineering 1, 373-397, 2000.

The train design included costly nonlinear constraints. They were assigned a weight and added to the objective function. This approach showed to be very successful. The choice of weights was not very crucial.

  Main features: