Black box optimization benchmarking of the GLOBAL method.

Area of Science:

• Numerical Analysis
• Computational Optimization

Background:

• Global optimization problems with bound constraints are challenging.
• Existing methods may require numerous local searches.

Purpose of the Study:

• To introduce and evaluate the GLOBAL algorithm, a multi-start stochastic method.
• To assess the impact of clustering on reducing local search efforts.
• To compare GLOBAL's performance against standard multi-start procedures and MATLAB's GlobalSearch.

Main Methods:

• The GLOBAL algorithm combines uniform sampling, clustering, and local search.
• Clustering groups sampled points around potential local minimizers.
• Performance is evaluated on the BBOB 2009 and 2010 noiseless testbeds.

Main Results:

• GLOBAL effectively reduces the number of required local searches through clustering.
• The algorithm demonstrates competitive performance on challenging benchmark problems.
• An improved parameterization of GLOBAL shows comparable results to MATLAB's GlobalSearch.

Conclusions:

• Clustering is a viable strategy for enhancing multi-start global optimization.
• The GLOBAL algorithm offers an efficient approach for bound constrained global optimization.
• Further improvements in parameterization can enhance solver performance.