Causality in Genetic Programming
Proceedings of the 6th International Conference on Genetic Algorithms
A Survey And Analysis Of Diversity Measures In Genetic Programming
GECCO '02 Proceedings of the Genetic and Evolutionary Computation Conference
Diversity in genetic programming: an analysis of measures and correlation with fitness
IEEE Transactions on Evolutionary Computation
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Image features with similar spectral information but with distinct textural characteristics can be extracted through the use of textural operators. The challenge resides in the selection of the appropriate texture operators and their parameters from a larger set of possible textural operators. This matter is especially difficult when addressing problems using remotely sensed imagery. The presence of additional spectral channels increases the search space. Genetic programming (GP) algorithms have being used as a cost-effective alternative to trial-and-error approach performed by human image analysts due to its optimized combinatorial search. Despite successful usage of GP to define and select the appropriate image texture operators for feature extraction from remotely sensed imagery [5, 3], the increased search space can lead to sub-optimal situations as result of the algorithm being trapped in local minimum regions. The causality involved in the randomly generated seed, from which the algorithm begins, can impact the algorithm's final outcome [7]. Burke et al. [1] described the correlation between population heterogeneity, or diversity, and best-of-generation fitness. Population diversity is a key component of the biological evolution theory and its maintenance during the evolutionary process is a vital procedure to avoid premature convergence (sub-optimal solutions) [1,2]. The case of discerning timber forests from naturally occurring forests using high spatial resolution satellite-borne imagery was chosen to evaluate two methods of population restarting. Despite of the spectral similarities of these features, the row patterns present in the timber forests were explored using six convolution type textural operators. The new image has 76 channels: four original channels plus 72 new channels from the textural operators. Two methods for the introduction of new genetic material during the evolutionary process were investigated: one in which the new population is created by fitness sorting (method 1) and another in which the new population is created by mixing (method 2). A total of 220 realizations were performed for each of the population restarting methods considered (no restarting, method 1, and method 2).. The top plot in Figure 1 shows the averaged best of population fitness values for all realizations of each generation. The middle plot shows average dissimilarity and the lower plot average entropy values for all the realizations for each generation. On average, the experiment with no restarting asymptotically converges to a ceiling fitness value starting approximately at generation 20. This coincides with the lack of population diversity represented by both dissimilarity and entropy. Conversely, on average, restarting methods 1 and 2 maintained more diverse populations, yielding higher final fitness values representing a better convergence toward the global minimum. The overall variability, represented by standard deviation of final fitness values, was reduced from 9.913 for the experiment with no restarting, to 7.235 and 7.285 for methods 1 and 2 respectively. The enlarged search space caused by the additional textural channels increased the system overall variability compromising the system's convergence toward the global minimum. The significant positive relationship between population diversity, indicated by the results, is supported by similar results found in the literature [4, 1, 6]. Introducing new genetic material into the evolutionary process; designed to increase and to maintain population diversity, improved convergence, and ultimately reduced the system's overall variability