6.3 Results

A GA was used to select the membership functions for the liquid level fuzzy controller described in Chapter 2. When the coding scheme described in the previous section is employed, the GA must search a space that contains 2^k possible solutions where k is the length of the bit strings. Thus, in this problem the search space contained 2⁸⁸=3.09* 10²⁶ possible solutions to the problem; no wonder selecting high-quality membership functions is such a time-consuming task. After having sampled an amazingly small portion of the search space (approximately 3200 of the 2⁸⁸=3.09* 10²⁶ possible points), the GA was able to select membership functions that provided for better control than those defined by the authors.

Figures 6.5 and 6.6 represent comparisons of the genetic algorithm-designed fuzzy logic controller (GA-FLC) to the liquid level FLC developed by the authors (AD-FLC) for two sets of initial conditions. Figure 6.5 represents an initial condition that appeared explicitly in the fitness function employed by a GA to tune the controller. Thus, this figure depicts the performance of the GA-FLC on a set of initial conditions for which it was specifically trained. Naturally, the GA-FLC performs well in this instance. Perhaps a better indication of the GA-FLC’s robustness is its ability to perform in conditions for which it has not been specifically trained. Figure 6.6 represents an initial condition that did not appear specifically in the fitness function employed by a GA. As in the previous case, the GA-FLC outperforms the AD-FLC, thereby indicating that the GA-FLC is robust. And, in fact, the GA-FLC outperforms the AD-FLC across a spectrum of initial condition cases.

Figure 6.5  The GA-FLC outperforms the AD-FLC for an initial condition that appeared in the fitness function.

Figure 6.6  The GA-FLC outperforms the AD-FLC for an initial condition that did not appear in the fitness function.

6.4 Review/Preview

In this chapter we have described the details of using a GA to define membership functions that improve the efficiency of a liquid level fuzzy control system. The two main issues discussed are the coding scheme and fitness function definition. The coding scheme introduced in Chapter 5 for a curve-fitting example was applied with little to no alteration. The fitness function was defined based on the objectives initially set forth for the controller in Chapter 2. With an appropriate coding scheme and a reasonable fitness function the GA was able to select membership functions that produced a controller that was more effective than the control system originally developed by the authors.

When we first implemented the approach presented in this chapter to membership function selection, we realized that this technique produced better controllers in substantially less time than the trial-and-error process previously employed. In fact, this approach effectively eliminates the need for a developer to use trial and error; it allows a GA to efficiently search the space of possible fuzzy systems, and as we saw in Chapter 5 GAs are capable of rapidly locating quality points in the search space. We immediately began to consider whether the approach was applicable to other control systems; to the selection of rule sets; to the selection of portions of rules sets. The answer to all of these questions, we learned, is a definite yes.

Chapters 7 and 8 demonstrate the extension of GA methods for the design of fuzzy controllers to other systems. The remainder of this book demonstrates some of the other ways GAs can empower fuzzy systems. As we were to discover, our quest for efficient and powerful fuzzy control systems was to be an amazing journey.