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Improvements of the adaptive radial basis function algo-rithm (ARBF) for computationally costly optimization are presented. A new target value search algorithm and modifications to improve robustness and speed are discussed. The algoritm is implemented in solver ARBFMIP in the TOM-LAB Optimization Environment (http://tomopt.com/). Solvers in TOMLAB are used to solve global and local subproblems. Results and comparisons with other solvers are presented for global optimization test problems. Performance on costly real-life applications are reported.

When dealing with costly objective functions in optimization, one good alternative is to use a surrogate model approach. A common feature for all such methods is the need of an initial set of points, or "experimental design", in order to start the algorithm. Since the behavior of the algorithms often depends heavily on this set, the question is how to choose a good experimental design. We investigate this by solving a number of problems using different designs, and compare the outcome with respect to function evaluations and a root mean square error test of the true function versus the surrogate model produced. Each combination of problem and design is solved by 3 different solvers available in the TOMLAB optimization environment. Results indicate two designs as superior.

Almost every Costly Global Optimization (CGO) solver utilizes a surrogate model, or response surface, to approximate the true (costly) function. The EGO algorithm introduced by Jones et al. utilizes the DACE framework to build an approximating surrogate model. By optimizing a less costly utility function, the algorithm determines a new point where the original objective function is evaluated. This is repeated until some convergence criteria is fulfilled.The original EGO algorithm finds the new point to sample in a two-stage process. In its first stage, the estimates of the interpolation parameters are optimized with respect to already sampled points. In the second stage, these estimated values are considered true in order to optimize the location of the new point. The use of estimate values as correct introduces a source of error.Instead, in the One-stage EGO algorithm, both parameter values and the location of a new point are optimized at the same time, removing the source of error. This new subproblem becomes more difficult, but eliminates the need of solving two subproblems.Difficulties in implementing a fast and robust One-Stage EGO algorithm in TOMLAB are discussed, especially the solution of the new subproblem.