Adaptive random search in Quasi-Monte Carlo methods for global optimization

Quasi-Monte Carlo random search is useful in nondifferentiable optimization. Borrowing ideas of population evolution from genetic algorithms, we introduce an adaptive random search in quasi-Monte Carlo methods (AQMC) for global optimization. Adaptive technique is used such that local search can head for local maximum points quickly because the search direction and search step size are adjusted according to the previous search result. New individuals will be imported into the population adaptively according to population evolution degree. For quasi-random sequences with low discrepancy, the new generated successive points fill in the gaps in the previously generated distribution in E (the domain of function f), which ensures that E can be searched evenly and the global extremum can be found. In conclusion, the AQMC method not only speeds up the random search but also balances the global and local demand (adaptive equalization).