A HYBRID DIFFERENTIAL EVOLUTION FOR NON-SMOOTH OPTIMIZATION PROBLEMS

Solving high dimentional, multimodal, non-smooth global optimization problems faces challenges concerning quality of solution, computational costs or even the impossibility of solving the problem. Evolutionary algorithms, in particular, differential evolution algorithm proved itself as good method of global optimization. On the other side, approach based on subgradient methods are good for optimizing non-smooth functions. Combination of these two approaches enables to improve the quality of the algorithm, using the best features of both methods. In this paper, a new hybrid evolutionary approach based on differential evolution and subgradient algorithm as the local search procedure is proposed. Behavior of the proposed SSGDE algorithm was studied in a numerical experiment on three groups of generated tests. Comparison of the new hybrid algorithm with the pure DE approach showed the advantage of the SSGDE. It has been experimentally established that the proposed method finds the global minimum in the best way for all considered dimensions of the problem with respect to the differential evolution method. The SSGDE algorithm showed the best results with a significant increase in the number of functions

Formation of Fuzzy Patterns in Logical Analysis of Data Using a Multi-Criteria Genetic Algorithm

The formation of patterns is one of the main stages in logical data analysis. Fuzzy approaches to pattern generation in logical analysis of data allow the pattern to cover not only objects of the target class, but also a certain proportion of objects of the opposite class. In this case, pattern search is an optimization problem with the maximum coverage of the target class as an objective function, and some allowed coverage of the opposite class as a constraint. We propose a more flexible and symmetric optimization model which does not impose a strict restriction on the pattern coverage of the opposite class observations. Instead, our model converts such a restriction (purity restriction) into an additional criterion. Both, coverage of the target class and the opposite class are two objective functions of the optimization problem. The search for a balance of these criteria is the essence of the proposed optimization method. We propose a modified evolutionary algorithm based on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to solve this problem. The new algorithm uses pattern formation as an approximation of the Pareto set and considers the solution’s representation in logical analysis of data and the informativeness of patterns. We have tested our approach on two applied medical problems of classification under conditions of sample asymmetry: one class significantly dominated the other. The classification results were comparable and, in some cases, better than the results of commonly used machine learning algorithms in terms of accuracy, without losing the interpretability

Formation of Fuzzy Patterns in Logical Analysis of Data Using a Multi-Criteria Genetic Algorithm

The formation of patterns is one of the main stages in logical data analysis. Fuzzy approaches to pattern generation in logical analysis of data allow the pattern to cover not only objects of the target class, but also a certain proportion of objects of the opposite class. In this case, pattern search is an optimization problem with the maximum coverage of the target class as an objective function, and some allowed coverage of the opposite class as a constraint. We propose a more flexible and symmetric optimization model which does not impose a strict restriction on the pattern coverage of the opposite class observations. Instead, our model converts such a restriction (purity restriction) into an additional criterion. Both, coverage of the target class and the opposite class are two objective functions of the optimization problem. The search for a balance of these criteria is the essence of the proposed optimization method. We propose a modified evolutionary algorithm based on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to solve this problem. The new algorithm uses pattern formation as an approximation of the Pareto set and considers the solution’s representation in logical analysis of data and the informativeness of patterns. We have tested our approach on two applied medical problems of classification under conditions of sample asymmetry: one class significantly dominated the other. The classification results were comparable and, in some cases, better than the results of commonly used machine learning algorithms in terms of accuracy, without losing the interpretability