Proposed is an enumeration technology based on search of local optimum of extremal problems with discrete variables as well as numerical values of integrals, the roots of equations, and extreme values of equations for the problems with continues variables. The aim is to propose an enumeration technology for obtaining numerical solutions of acceptable quality for a wide range of problems in minimal time to find a solution. This approach includes possibility of predictive procedures usage to reduce the time of intermediate calculations, but it does not guarantee any gain in total running time, since part of this time is spent on searching for predictive dependencies. Nevertheless, it is shown that as the enumeration volume increases, the efficiency of the proposed approach also increases. It has been analytically proved and experimentally confirmed that, in comparison with the sequential search leading to the same quality of solution, the upper bound for the gain in running time for the problems with continues variables is equal to two. All descriptions of this approach are illustrated with examples and with statistical results of experimental verification of the effectiveness of this approach in relation to problems with discrete and continuous variables.