An Incremental Model of Lexicon Consensus in a Population of Agents by Means of Grammatical Evolution, Reinforcement Learning and Semantic Rules - Foundations on Natural and Artificial Computation - page 45

fitness =1 − [ WUW ∗ ( uW/mUqW )+ WWMS ∗ ( wmSP/ ( mWMP ∗ nA ))] (1)

where WUW and WWMS stand for a percentage we assign to each contribution,
uW means the number of unique words in the generated vocabulary, mUqW
means the maximum number of unique words that we can build with the gram-
mar, wmSP represents the number of successes in the language games, i.e. the
number of right word-meaning pairs, mWMP stands for the maximum number
of associations and nA is the number of agents in the environment. We subtract
1 because in GER a minimum value of fitness is better.

4.2 Environment and Experiments

To elaborate the experiments we checked several robots simulators but finally we
decided to build a simple model because we are only interested in analysing the
language and we do not need to devote too much time with low level functions
as it is usual when we work with perceptive and locomotive skills. We use a
closed grid environment with a size of 15x15 squares where a maximum of 16
objects and 16 agents can be situated. Walls are considered like an object and
we use them as separators. All the experiments initially start with four objects
( wall, box, ball and dice ) and four agents. Figure 2 shows an example of the
environment with the initial objects randomly situated.

Fig. 2. Environment with walls (light gray), balls (BA), boxes (BO) and dices (DI)

Agents are also randomly located in the environment and they can move in
horizontal, vertical or diagonal but they only can fill a square if it is free. Each
agent has sensors to check what there is on a square. As we mentioned the symbol
grounding problem is simplified and we associate the combinations 'WA', 'BO',
'BA' and 'DI' as representations for the meaning of the initial objects. Although
we use letters for clarity whatever representation way we choose would be similar.
The initial set of objects can be enhanced when GER has found a consensual
lexicon. Thus, the complete set of symbols (S) and meanings (M) we work in the
experiments is the following: