Towards the Evolutionary Process Algebra

Genetic algorithms, GA's are metaheuristic techniques that have obtained good results in problems in which exhaustive techniques fail due to the size of the search space. GA's have been widely used to solve problems in the fields of combinatorial and numerical optimization. Due to their stochastic nature, their behaviour when dealing with some problems is difficult to predict. However, there have been many attempts to develop models related with some of their features. Thus, in their origin, Holland developed the schemata theory which tried to demonstrate their functioning by assuming that those configurations of variables, schemata, which contribute to build a good solution, tend to spread through the population as generations pass. Later on, many other attempts have been carried out in order to model some features of these algorithms. Thus, statistical models to predict population sizing or time to convergence have been developed. In other works, Markov chains have been used for the same purposes. In this paper, as first step to define an evolutionary process algebra (a process algebra which contemplates the basic selection and variation operators in its syntax and therefore provides a semantics), a basic GA is formally defined and specified by the Markovian process algebra ROSA.