The Elements Of Optimization Problems

In every case of optimization, the problem must first be formulated and then the system to be optimized must be defined. This requires specifying the variables that affect the system's behavior. For example, in making a hot cup of tea, an obvious variable that affects the quality of the tea is the length of time the tea bag stays in the hot water. Performing experiments to measure the quality of the tea as a function of time generates a curve like the one shown in Figure 1. Choosing the maximum quality value and tracing it back to the corresponding optimum time optimizes this oversimplified and trivial system. Accounting for the effect of the water temperature on the tea quality complicates the system. In such a case a series of constant quality curves might be obtained (Fig. 2), which produce a set of optimum conditions for temperature and time.

Time

Figure 1. Quality of tea as a function of time the tea bag stays in hot water.

Time

Figure 1. Quality of tea as a function of time the tea bag stays in hot water.

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