Engineering Optimization

13Dynamic Programming

13.1 Introduction

Decision variables can be considered as the influence (the independent variable), while the dependent variable, as the process response (state). Most optimization techniques seek the influence values as the trial solution variables and calculate the process response using the model in the normal calculation procedure: given the input values, the output values are determined.

Contrasting these approaches, dynamic programming (DP) is a method of optimization by choosing a state path (the response) through stages or time. Here, the DV values are the outputs of the model. Then the inputs are calculated to achieve the state path. This can be considered as using the inverse of the process model.

DP is applied to processes that change in time, such as process control or scheduling of events as a process evolves. Although other optimization methods can be used on such applications, and often more efficiently, there are three paradigm shifts that are associated with DP that make it notable.

First, the DV for optimization, the TS, is the output of the process, not the input. Conventionally, as mentioned earlier, the TS is a DV choice of the influence or independent variable values, and the process states are the response. In most optimization procedures, the model is used to determine the values of the process states that respond to the TS. By contrast, DP seeks to choose the dependent variable values (the states) and to specify a best evolution ...