ACM Transactions on Mathematical Software (TOMS)
Stopping and restarting strategy for stochastic sequential search in global optimization
Journal of Global Optimization
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While searching for the global minimum of a cost function we haveoftento decide if a restart from a different initial point would bemoreadvantageous than continuing current optimization. This is aparticularcase of the efficiency comparison between repeatedminimizations and singleextended search having the same total length.A theoretical approach forthe treatment of this general problem formsthe subject of the present paper.A fundamental role is played by theprobability of reaching the globalminimum, whose asymptoticalbehavior allows to provide useful information onthe efficiency ofrepeated trials.The second part of this work is devoted toa detailed analysis of threeoptimization algorithms whose evolution isindependent of the costfunction to be minimized: pure random search, grid search and randomwalk. These three examples give an interesting validationof thetheoretical results and provide a general procedure which can beemployed in the study of more complex optimization problems.