Question

Let’s say I have a set of training examples where A_i is an attribute and the outcome is binary (yes or no):

A1,             A2,             A3,             Outcome
red             dark            large           yes
green           dark            small           yes
orange          bright          large           no

I know I have to define the fitness function. But what is it for this problem? In my actual problem there are 10 parameters and 100 training examples but this is a similar problem.

Answer 1

I think the confusion here is coming from the fact that usually fitness functions give you back some scalar, sometimes on a discrete scale, but never a binary yes/no (or true/false). In this sense, this looks more like a ‘classification’ problem to be solved with neural nets (or possibly bayesian logic). Said so, you could certainly devise a GA to evolve whatever kind of classifier, and the fitness function would basically be expressed in terms of correct classifications over total evaluations.

Another pure GA approach to this – probably more relevant to the question – is to encode the whole classification rule set as a given individual for the genetic algorithm. In this sense, the fitness function could be expressed as a scalar representing how many yes/no classifications the given candidate solution at hand gets right over the total, and so forth. A similar approach can be found in this paper Using Real-Valued Genetic: Algorithms to Evolve R,de Sets for
Classification.

Example (one of the possible ways to encode this):

A1,             A2,             A3,             Outcome
red             dark            large           yes
green           dark            small           yes
orange          bright          large           no

Encoding: red = 000, dark = 001, large = 010, green = 011, small = 100, orange = 101, bright = 111, etc.
Outcome: yes = 1, no = 0

Chromosome:

A1,             A2,             A3,             Outcome
000             001             010             1
011             001             100             1
101             111             010             0

All of the above gets translated into a candidate solution as:

000001010-1/011001100-1/101111010-0

You will generate a random bunch of these and evolve them whichever way you like by testing fitness (correct classification/ total classifications in the ruleset) of the entire rule set (be careful picking your cross-over strategy here!).

I also suggest you listen to a binary solo, to get you in the mood.

NOTE: I highly doubt this would work with a rule-set composed by only 3 rules, not enough breadth for the GA.