Expert-Based Method of Integrated Waste Management Systems for Developing Fuzzy Cognitive Map - Complex System Modelling and Control Through Intelligent Soft Computations - page 123

initializes the population. In most cases, the individuals are random generated, but
sometimes a priori information about the problem helps to create near-optimal start
population. In the next step GA calculates the values of the objective function for
every individual. These values are the basis of

fitness value calculation. In the most

straightforward case, the fitness value and the objective value of the same individual

is the same, but some advanced technique (ranking, scaling) helps to prevent some
undesirable effects (primarily premature convergence) during optimisation. The
next generation of the population contains new individuals (temporary population)
created by recombination (combination of the parents

' genetic data) and mutation

(random modi cation of the child ' s chromosome with small probability). The

parent individuals are selected with fitness-proportional selection. The reproduction

step forms the next generation of the population using the current and the temporary
population. Next, the whole process starts again from the evaluation of the objective
function values. GA iteratively runs this process until some termination condition is
ful

lled.
A special descendant of GA was suggested by Nawa et al. at the late 1990s.
Because this algorithm was inspired by the evolution of bacteria, they named it
pseudo-bacterial genetic algorithm (PBGA) (Nawa et al. 1997 ). PBGA uses bac-
terial mutation instead of GA

'

s mutation operator. Some years later PBGA was
further improved, and BEA (Nawa and Furuhashi 1998 , 1999 ) was born. BEA
includes a new gene transfer operator instead of crossover and contains bacterial
mutation as well.
BEA was originally developed to determine and optimise the parameters of
fuzzy rule bases made for solving general approximation and optimisation prob-
lems. The algorithms can be used in other engineering applications as well. BEA
has some positive properties contrary to GA, e.g. simpler, shorter implementation;
the gene transfer operator ensures the survival of the fittest bacteria without addi-

tional operator (called elitism in GA).
The exhaustive review of BEA can be found e.g. in Nawa and Furuhashi ( 1999 ),
thus we will give only a short introduction here. Similarly to GA, BEA also uses a
record of possible solutions. These candidate solutions are often called bacteria as
well. The bacteria together form the population. The repeated utilization of bacterial
mutation and gene transfer results in a series of generations. When some kind of
termination condition is ful lled, the best bacterium of the last population is

accepted as the result of the optimization (see Fig. 3 ).
Bacterial mutation (Fig. 4 ) optimizes all the bacteria individually. The mutation
functions in the following way. At

first, K clones (exact copies) are generated for
every bacterium. All genes of the bacteria are mutated during mutation in random
order. In each step of it, exactly one gene at a speci ed

randomly in every clone. If a better gene value (allele) has been found, it is copied
into the other clones, too. On the end of mutation, if the objective value of the best
clone is better than the value of the original bacterium, the bacterium is replaced
with this clone.

ed position is modi