Recognizing Sets in Evolutionary Multiobjective Optimization, Journal of Telecommunications and Information Technology, 2012, nr 1

Among Evolutionary Multiobjective Optimization Algorithms (EMOA) there are many which find only Paretooptimal solutions. These may not be enough in case of multimodal problems and non-connected Pareto fronts, where more information about the shape of the landscape is required. We propose a Multiobjective Clustered Evolutionary Strategy (MCES) which combines a hierarchic genetic algorithm consisting of multiple populations with EMOA rank selection. In the next stage, the genetic sample is clustered to recognize regions with high density of individuals. These regions are occupied by solutions from the neighborhood of the Pareto set. We discuss genetic algorithms with heuristic and the concept of well-tuning which allows for theoretical verification of the presented strategy. Numerical results begin with one example of clustering in a single-objective benchmark problem. Afterwards, we give an illustration of the EMOA rank selection in a simple two-criteria minimization problem and provide results of the simulation of MCES for multimodal, multi-connected example. The strategy copes with multimodal problems without losing local solutions and gives better insight into the shape of the evolutionary landscape. What is more, the stability of solutions in MCES may be analyzed analytically

Adaptive population-based algorithms for solving single- and multiobjective inverse problems

Promotor: Robert Schaefer.Recenzent: Andrzej Obuchowicz, Witold Dzwinel.Niepublikowana praca doktorska.Tyt. z ekranu tyt.Praca doktorska. AGH University of Science and Technology. Faculty of Computer Science, Electronics and Telecommunications. Department of Computer Science, 2015.Zawiera bibliogr.Dostępna również w wersji drukowanej.Tryb dostępu: Internet.State-of-the-art, forward and inverse problems, forward problem definition, forward numerical solvers, inverse problem definition, inverse numerical solvers, stochastic algorithms for global optimization, stochastic sampling with simple adaptation, single-objective genetic algorithms, detecting basins of attraction, multiobjective optimization techniques, traditional techniques, evolutionary algorithms for multiobjective optimization , single-objective analysis, inversion of resistivity logging measurements for direct current, forward problem definition, relation between approximate forward and inverse solution errors, inversion of resistivity logging measurements for alternate current, forward problem definition, inverse problem definition, relation between approximate forward and inverse solution errors, restoring mechanical parameters of elastic body, forward and inverse problem, relation between approximate forward and inverse solution errors, algorithms and strategies, Hierarchic Genetic Strategy, hp-Hierarchic Genetic Strategy, local methods, hybrid strategy, simulations, inversion of resistivity logging measurements for direct current, inversion of resistivity logging measurements for alternate current, parameter identification in elasticity, multiobjective inverse problems, general motivation for multiobjective inverse problems, pareto problem, Hierarchic Genetic Strategy for multiobjective optimization, Multiobjective Clustered Evolutionary Strategy, rank modification based on incidence, theoretical analysis, MOEA Markov model, well-tuning, well-filtering, simulations, MCES benchmark example, MO-HGS benchmark exampl

A hybrid algorithm for solving inverse problems in elasticity

The paper offers a new approach to handling difficult parametric inverse problems in elasticity and thermo-elasticity, formulated as global optimization ones. The proposed strategy is composed of two phases. In the first, global phase, the stochastic hp-HGS algorithm recognizes the basins of attraction of various objective minima. In the second phase, the local objective minimizers are closer approached by steepest descent processes executed singly in each basin of attraction. The proposed complex strategy is especially dedicated to ill-posed problems with multimodal objective functionals. The strategy offers comparatively low computational and memory costs resulting from a double-adaptive technique in both forward and inverse problem domains. We provide a result on the Lipschitz continuity of the objective functional composed of the elastic energy and the boundary displacement misfits with respect to the unknown constitutive parameters. It allows common scaling of the accuracy of solving forward and inverse problems, which is the core of the introduced double-adaptive technique. The capability of the proposed method of finding multiple solutions is illustrated by a computational example which consists in restoring all feasible Young modulus distributions minimizing an objective functional in a 3D domain of a photo polymer template obtained during step and flash imprint lithography