Improving evolutionary algorithms by means of an adaptive parameter control approach

Evolutionary algorithms (EA) constitute a class of optimization methods that is widely used to solve complex scientific problems. However, EA often converge prematurely over suboptimal solutions, the evolution process is computational expensive, and setting the required EA parameters is quite difficult. We believe that the best way to address these problems is to begin by improving the parameter setting strategy, which will in turn improve the search path of the optimizer, and, we hope, ultimately help prevent premature convergence and relieve the computational burden. The strategy that will achieve this outcome, and the one we adopt in this research, is to ensure that the parameter setting approach takes into account the search path and attempts to drive it in the most advantageous direction. Our objective is therefore to develop an adaptive parameter setting approach capable of controlling all the EA parameters at once. To interpret the search path, we propose to incorporate the concept of exploration and exploitation into the feedback indicator. The first step is to review and study the available genotypic diversity measurements used to characterize the exploration of the optimizer over the search space. We do this by implementing a specifically designed benchmark, and propose three diversity requirements for evaluating the meaningfulness of those measures as population diversity estimators. Results show that none of the published formulations is, in fact, a qualified diversity descriptor. To remedy this, we introduce a new genotypic formulation here, the performance analysis of which shows that it produces better results overall, notwithstanding some serious defects. We initiate a similar study aimed at describing the role of exploitation in the search process, which is to indicate promising regions. However, since exploitation is mainly driven by the individuals' fitness, we turn our attention toward phenotypic convergence measures. Again, the in-depth analysis reveals that none of the published phenotypic descriptors is capable of portraying the fitness distribution of a population. Consequently, a new phenotypic formulation is developed here, which shows perfect agreement with the expected population behavior. On the strength of these achievements, we devise an optimizer diagnostic tool based on the new genotypic and phenotypic formulations, and illustrate its value by comparing the impacts of various EA parameters. Although the main purpose of this development is to explore the relevance of using both a genotypic and a phenotypic measure to characterize the search process, our diagnostic tool proves to be one of the few tools available to practitioners for interpreting and customizing the way in which optimizers work over real-world problems. With the knowledge gained in our research, the objective of this thesis is finally met, with the proposal of a new adaptive parameter control approach. The system is based on a Bayesian network that enables all the EA parameters to be considered at once. To the authors knowledge, this is the first parameter setting proposal devised to do so. The genotypic and phenotypic measures developed are combined in the form of a credit assignment scheme for rewarding parameters by, among other things, promoting maximization of both exploration and exploitation. The proposed adaptive system is evaluated over a recognized benchmark (CEC'05) through the use of a steady-state genetic algorithm (SSGA), and then compared with seven other approaches, like FAUC-RMAB and G-CMA-ES, which are state-of-the-art adaptive methods. Overall, the results demonstrate statistically that the new proposal not only performs as well as G-CMA-ES, but outperforms almost all the other adaptive systems. Nonetheless, this investigation revealed that none of the methods tested is able to locate global optimum over complex multimodal problems. This led us to conclude that synergy and complementarity among the parameters involved is probably missing. Consequently, more research on these topics is advised, with a view to devising enhanced optimizers. We provide numerous recommendations for such research at the end of this thesis.

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