Abstract
The multi-stage Monte Carlo approach is similar to the regular Monte Carlo or random search approach that is frequently used on difficult multivariate problems. However, with multi-stage, the regular Monte Carlo search is considered to be stage one. This is followed by several more stages in an ever narrowing and re-positioning region following the best answers so far, hopefully on a trail to the optimal or a close approximation. The element of risk is certainly present in multi-stage Monte Carlo. Therefore to compare it with other algorithms for effectiveness, six test problems from the literature are selected and ‘ solved ’ with multistage. The results with multi-stage and other approaches are similar for the first five problems. However, in the last test problem, multi-stage finds many lower values than the stated ‘ minimum ’ and fourteen of them are presented here along with computer programs and a discussion of multi-stage Monte Carlo
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