Abstract
The article discusses the solution of applied problems, for which the dynamic programming method developed by R. Bellman in the middle of the last century was previously proposed. Currently, dynamic programming algorithms are successfully used to solve applied problems, but with an increase in the dimension of the task, the reduction of the counting time remains relevant. This is especially important when designing systems in which dynamic programming is embedded in a computational cycle that is repeated many times. Therefore, the article analyzes various possibilities of increasing the speed of the dynamic programming algorithm. For some problems, using the Bellman optimality principle, recurrence formulas were obtained for calculating the optimal trajectory without any analysis of the set of options for its construction step by step. It is shown that many applied problems when using dynamic programming, in addition to rejecting unpromising paths lead to a specific state, also allow rejecting hopeless states. The article proposes a new algorithm for implementing the R. Bellman principle for solving such problems and establishes the conditions for its applicability. The results of solving two-parameter problems of various dimensions presented in the article showed that the exclusion of hopeless states can reduce the counting time by 10 or more times.
Highlights
The main provisions of dynamic programming were formulated when considering a dynamic system, whose state is determined by one or more parameters
Bellman [1,2,3,4] formulated the principle of optimality, the meaning of which is to go along the optimal trajectory from any state to the final state if the “past history” does not matter
The main goals of this article are to show how the idea of rejecting hopeless states is realized in solving many applied problems for which traditional dynamic programming algorithms were previously proposed, formulate additional conditions for the applicability of the algorithm with rejecting states, and present the results of comparative calculations which confirm the effectiveness of the new algorithm
Summary
The main provisions of dynamic programming were formulated when considering a dynamic system, whose state is determined by one or more parameters. It is required to find a sequence of impacts that transfers the system from a given initial state to a final state with minimal total cost. The sequence of actions determines the sequence of states, i.e. the trajectory (path) of the system. R. Bellman [1,2,3,4] formulated the principle of optimality, the meaning of which is to go along the optimal trajectory from any state to the final state if the “past history” does not matter. The objective function (costs) can be calculated in stages, which are determined by the given moments of the impact The applicability conditions of dynamic programming are as follows: 1. The objective function (costs) can be calculated in stages, which are determined by the given moments of the impact
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
