Proyección de la estructura organizacional

The synthesis of sequences (such as in (6.3)) requires that a genetic algorithm pro- vide evolutionary operators which modify the length of individuals and a means of maintaining diversity within a population of variable length individuals. The following section discusses the choices for this particular algorithm in terms of characteristics of the problem.

6.4.1. Variable-length genomes

Compositional evolutionary operators, such as crossover, combine large pieces of preadapted genetic material, and rely upon the building-block hypothesis to yield fitter individuals [8]. The sources of the preadapted material can either be derived from the same individual or from one or more individuals in the population. The motivation for the inclusion of constructive compositional operators within the algorithm in order to grow solutions is twofold.

Firstly, the determination of the optimal length of the final solution is the ob- jective of the evolutionary search, and since no information is available to inform the initialisation process, a trial and error procedure would be required in order to determine a range of suitable lengths. Thus, this application differs significantly from other variable-length applications (e.g., [1]) where a priori information is available to initialise the population.

Secondly, even if a suitable range of lengths were known, the population must be initialised in such a way, that is neither deleterious nor biased. Owing to the characteristics of the fitness landscape, the random initialisation of a population

I. P. W. Sillitoe and A. K. Magnusson 119 of variable length individuals results in longer individuals with low initial values of fitness, and shorter individuals with relatively high values of initial fitness. The effect upon the evolutionary dynamics is that small improvements in fitness of a few short individuals rapidly reduces the genetic diversity of the population, and leads to premature convergence or failure to evolve a solution.

If, on the other hand, the population is initialised with individuals contain- ing single CLUT operators and these individuals are grown using constructive op- erators (such as concatenation), the initial population will have a higher fitness diversity, and this diversity consequently decreases less after the initial settling pe- riod (owing to greater variation in the population’s ancestors [4]). Experiments illustrating this effect are presented inSection 6.6.

6.4.2. Niche measures in diversity management schemes

Diversity management methods are introduced into genetic algorithms in order to ameliorate the problem of premature convergence in the face of complex fitness landscapes. These methods effectively partition the population into niches, and ensure that competition between individuals is restricted to those which occupy the same niche. The existence of niches allow multiple regions of the search space to be explored simultaneously. Several such methods have been proposed [15].

Thus, a modified diversity management scheme could be designed to niche groups of individuals within the population according to the length of the se- quence, and thereby mitigate the problem identified in the previous section. The management scheme developed here is a modified form of the deterministic crowding algorithm [12]. Deterministic crowding was selected because of its sim- ple, yet powerful, method of selection. The method requires no control parame- ters, and in addition, since the parents are randomly selected from the population, there is neither a need for fitness-based selection probability calculations (such as in fitness sharing [7]) nor large numbers of niche distance calculations (such as in crowding [5] and clearing [14]). The simplicity of the method also makes it suitable for possible hardware implementation.

The absence of control parameters, such as the niche radius used in fitness sharing and clearing, is of particular importance in this application. In [15], it is shown that a suitable choice of niche radius relies upon a knowledge of the struc- ture of the fitness landscape. The complex one-to-many mapping of the CLUT makes this difficult to obtain.

The niche measure required by deterministic crowding to determine the sim- ilarity of individuals is commonly based upon properties of the phenotype of the individuals. This raises two difficulties in this application. Firstly, the length of the solution is not contained within the phenotype. Secondly, the length of the phenotype grows exponentially with the dimensions of the filter neighbourhood, and so, the approach will not scale well for larger neighbourhoods. An alternative approach would be to base the measure upon the genotype of individuals (i.e., the Hamming distance). However, the use of a too simple genotype measure will degrade the performance of the genetic algorithm [10]. The method presented

120 Variable-length compositional genetic algorithms

(1)Initialiseandevaluatethe fitness of the population

(2)repeat

(3) Randomly select two parents from the population (4) ifstagnation has occurredthen

(5) Create a single offspring throughconcatenationwith probability

μ, or perform uniform parameterisedcrossover

(6) Applyduplication-rotation with probabilityν

(7) else

(8) Create a single o_ffspring using uniform parameterisedcrossover

(9) end if

(10) Applypoint mutation

(11) Evaluatethe fitness of the offspring according to (6.13)

(12) Determinethe most similar parent

(13) ifthe offspring is fitter than the most similar parentthen

(14) Replacethe parent with the offspring

(15) end if

(16)untiltermination criteria are satisfied

Algorithm6.1. An outline of the steady-state variable-length algorithm.

inSection 6.5, uses a weighted-genotype measure which is designed to reflect the

sensitivity characteristics of the CLUT.