Industrial Applications of Genetic Algorithms:What Can I Do with a Learning Classifier System?

Previous | Table of Contents | Next

Explicit sharing is difficult to implement and computationally expensive. A simpler method is implicit sharing (Horn et al., 1994; Smith, 1993). This form of sharing is based on information about the way the individuals are interpreted in phenotype space, i.e., the similar behaviors between individuals indicate similarity. For the purposes of this study, implicit sharing is easier to implement and well suited to ANNs.

Figure 16.3 A complete LCS-like ANN. Notice the conditional connections, they implement the input to the rules (hidden layer neurons). The strength connections denote the strength of a given rule with respect to an action.

Using Equation 16.2, the “raw” fitnesses are calculated. To implement implicit sharing, the state information about each neuron (whether it is active or not) is recorded. This information is then used to degrade the fitnesses by the number of active and inactive nodes. In addition, a constraint of unique connectivity is imposed on the population. This is done because redundant rules are unnecessary. GA populations, typically, have multiple copies of an individual (many individuals of the same specie), to compensate a copy count is kept to emulate multiple copies of a specie. The concept of copy count and unique rules can be found in Wilson’s (1994; 1995) work on LCSs.

Equation 16.3 shows the sharing method applied to the fitness calculated by Equation 16.2. The domain of this function is every node in the hidden layer, H. The first term is sharing between like acting nodes, i.e., it compares node `i`’s firing state to node `j`’s and returns 1 for a match and 0 otherwise. For the purposes of this study, a node’s output will either be +1 or -1 (the latter indicating the “active” state). The first term can be considered sharing by like acting neurons (sharing by behavior or phenotype), while the second term simply shares by the number of copies (sharing by specie or genotype) that “exist in the population.” Sharing is applied by multiplying the fitness value of an individual by the corresponding sharing value.

The novel LCS approach to ANNs appeared first as a batch learning method that evaluated each input pattern of a training set and formed fitness values and sharing terms only after all the patterns in the training set had been evaluated (Smith & Cribbs, 1994). The test problem used to validate the “batch version” is called the “multiplexor problem” due to the similarity of function with the discrete electronic device of the same name. The multiplexor problem description and results of an incremental learning version are presented in the next section. Equations 16.2 and 16.3 represent the “incremental versions” used to obtain the results presented.

THE MULTIPLEXOR PROBLEM

The multiplexor problem was shown by Wilson (1990) to be an effective test-bed for GA-based input partitioning. A stochastic (incremental) version of this problem was used to test the characteristics of online learning in an ANN (Cribbs, 1995). The selected test problem consists of 64 input patterns, mapping 1 of 4 input signals (either -1 or 1) based on two address lines. The number of inputs to the ANN is the 2 address lines plus the 4 input signals. The goal of the problem is to select the correct output signal (either -1 or 1).

Figure 16.4 shows the performance history over a training run. The figure shows the ANN error sampled at 128 training cycles per data point. Each data point represents an exponentially smoothed “running average” of the system’s performance (training case error). The training parameters used to obtain this result correspond to the values in Table 16.1.

While its performance is worse than Cribbs (1995) incremental result, the system is able to learn a mapping for the problem. A discussion of the ANN’s performance on the 6 multiplexor test problem follows.

Previous | Table of Contents | Next

Copyright © CRC Press LLC