This paper presents hierarchical improvements to the combinatorial stochastic annealing algorithm using a new and efficient sampling technique. The Hammersley sequence sampling technique is used for updating discrete combinations, reducing the Markov chain length, determining the number of samples automatically, and embedding better confidence intervals of the samples. The improved algorithm, Hammersley stochastic annealing, can significantly improve computational efficiency over traditional stochastic programming methods. Three distinctive example functions considered proved the efficiency improvement of Hammersley stochastic annealing to be up to 99.3% better than the traditional counterparts. Thus, this new method can be a useful tool for large-scale combinatorial stochastic programming problems. Application of this new algorithm to a real world problem of solvent selection under uncertainty is presented in part 2 of this series
