Hybridization of genetic algorithms with local search approaches can enhance their performance in global optimization. Genetic algorithms, as most population based algorithms, require a considerable number of function evaluations. This may be an important drawback when the functions involved in the problem are computationally expensive as it occurs in most real world problems. Thus, in order to reduce the total number of function evaluations, local and global techniques may be combined. Moreover, the hybridization may provide a more effective trade-off between exploitation and exploration of the search space. In this study, we propose a new hybrid genetic algorithm based on a local pattern search that relies on an augmented Lagrangian function for constraint-handling. The local search strategy is used to improve the best approximation found by the genetic algorithm. Convergence to an εglobal minimizer is proved. Numerical results and comparisons with other stochastic algorithms using a set of benchmark constrained problems are provided.
This paper describes the optimal design and operation of an activated sludge system in wastewater treatment plants. The optimization problem is represented as a smooth programming problem with linear and nonlinear equality and inequality constraints, in which the objective is to minimize the total cost required to design and operate the activated sludge system under imposed effluent quality laws. We analyze four real world plants in the Trás-os-Montes region (Portugal) and report the numerical results obtained with the FILTER, IPOPT, SNOPT and LOQO optimizers.
In this paper, we propose an evolutionary algorithm for handling many-objective optimization problems called MyO-DEMR (many-objective differential evolution with mutation restriction). The algorithm uses the concept of Pareto dominance coupled with the inverted generational distance metric to select the population of the next generation from the combined multi-set of parents and offspring. Furthermore, we suggest a strategy for the restriction of the difference vector in DE operator in order to improve the convergence property in multi-modal fitness landscape.We compare MyO-DEMR with other state-of-the-art multiobjective evolutionary algorithms on a number of multiobjective optimization problems having up to 20 dimensions. The results reveal that the proposed selection scheme is able to effectively guide the search in high-dimensional objective space. Moreover, MyO-DEMR demonstrates significantly superior performance on multi-modal problems comparing with other DE-based approaches.
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