Structure of the Individual and Population Size

Each individual is made up of $p = 30$ genes, the dimensionality of the functions to optimize.

The size of the population is one of the critical parameters for many applications. If the size of the population is too small, the algorithm could converge quickly towards sub-optimal solutions; if it is too large, too much time and resources could be wasted. It is also obvious that the size of the population, together with the selective pressure, influences the diversity of the population.

Several researches have studied these problems from different points of view. Grefenstette [Gre86] used a meta-genetic algorithm for controlling the parameters of another genetic algorithm, such as population size and the selection method. Goldberg [Gol89b] made a theoretical analysis of the optimum population size. A study of the influence of the parameters on the search process was carried out by Schaffer, Caruana, Eshelman and Das [SCED89]. Smith [Smi93] proposed an algorithm that adjusts the size of the population with respect to the error probability of the selection . Another method consists of changing the size of the population [AMM94] dynamically.

The size of the population is usually chosen in an interval between 50 and 500 individuals, depending on the difficulty of the problem. As a general practice, in function optimization, the size is in the interval $[50,100]$ for unimodal functions, and in the interval $[100,500]$ for multimodal functions. However, several papers use a compromise size of 100 for all the functions in order to homogenize the comparison environment. We will also use a population size of 100 individuals like other comparative studies [ZK00,TKK99].