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Definition of "dynamic programming" |
Dynamic programming (usually referred to as DP ) is a very powerful technique to solve a particular class of problems. It demands very elegant formulation of the approach and simple thinking and the coding part is very easy. The idea is very simple, If you have solved a problem with the given input, then save the result for future reference, so as to avoid solving the same problem again. If the given problem can be broken up in to smaller sub-problems and these smaller subproblems are in turn divided in to still-smaller ones, and in this process, if you observe some over-lappping subproblems, then its a big hint for DP. Also, the optimal solutions to the subproblems contribute to the optimal solution of the given problem. / introduced by Bellman, one of the best known methods for solving the optimal control problems. A recursive method to compute the optimal control as a function of the state, dynamic programming is used in multistage systems by working backward from the final stage. Dynamic programming is based on The Optimality Principle. The Principle says that optimal control strategy has the feature that regardless of initial state and initial decision, decision in the next step must form an optimal control strategy with respect to the final state of the previous decisions. This principle allows us to find an optimal strategy in a numericalway. The principle serves to limit the number of potentially optimal control strategies that must be investigated. It also implies that optimal control strategies must be determined by working backward from the final stage. |
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