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EN
This paper presents the results of calculations that demonstrate the possibility of using hybrid optimization method (with variable structure) for determining the approximate solutions to NP-hard problems. The Travelling Salesman Problem (TSP) is a classic combinatorial optimization subject, which has found widespread use in practice. Simple in definition, have remained hard to solve for many years. Not only an efficient solution would yield benefits in a substantial amount of routing problems, but it would also affect planning and logistics in a positive way.
PL
W prezentowanym artykule pokazano możliwość wykorzystania hybrydy optymalizacyjnej do uzyskania przybliżonego rozwiązania zadania NP-trudnego, czyli problemu obliczeniowego o ponad wykładniczym zapotrzebowaniu na moc obliczeniową. Do badań wybrano znany od wielu lat problem komiwojażera, którego od lat nie udało się ostatecznie rozwiązać. Wybór ten jednak umożliwił uzyskanie pokaźnego materiału porównawczego.
EN
The paper discusses the complex, agent-oriented hierarchic memetic strategy (HMS) dedicated to solving inverse parametric problems. The strategy goes beyond the idea of two-phase global optimization algorithms. The global search performed by a tree of dependent demes is dynamically alternated with local, steepest descent searches. The strategy offers exceptionally low computational costs, mainly because the direct solver accuracy (performed by the hp-adaptive finite element method) is dynamically adjusted for each inverse search step. The computational cost is further decreased by the strategy employed for solution inter-processing and fitness deterioration. The HMS efficiency is compared with the results of a standard evolutionary technique, as well as with the multi-start strategy on benchmarks that exhibit typical inverse problems’ difficulties. Finally, an HMS application to a real-life engineering problem leading to the identification of oil deposits by inverting magnetotelluric measurements is presented. The HMS applicability to the inversion of magnetotelluric data is also mathematically verified.
EN
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.
EN
Classic optimization methods are bound to have many limitations. As a result, such methods are of ten not suitable for efficient problem solving. This paper puts forth aproposal for a new hybrid optimization method which combines together two basic methods, i.e. Monte Carlo method and Rosenbrock method. The combination produces a method that has all of its constituents' advantages, yet does not in herit any oft heir drawbacks, resulting in higher convergence rates and greater computation speeds. Due to its simplified approach towards modeling, our method can be easily adapted to parallel or distributed computing systems, enabling researchers to use clusters consisting of many separate machines. Those clusters can provide the computational power needed to solve complicated optimization problems..
EN
The main research objective of this paper is the development, analysis, implementation and determination of the efficiency of hybrid optimization methods applied to a variety of mathematical concepts describing real-life problems which involve a large number of variables. The optimization is carried out by a hybrid serialized cascading procedure which combines several different sub-procedures with dissimilar characteristics, sharing the same objective function. During the efficiency-determination phase, several effectiveness tests were conducted, comparing the hybrid method with other optimization techniques.
EN
This paper is devoted to the application of an Evolutionary Algorithm to the design of Finite Impulse Response filters (FIR). A hybrid algorithm is proposed, which consists of a robust global optimization method (Evolutionary Algorithm - EA) and a good local optimization method (Quasi-Newton - QN). An experimental comparison of the hybrid algorithm against EA and QN alone indicates that EA yields filters with the better amplitude characteristics than QN. Furthermore the hybrid method yields filters with even better amplitude characteristics and in some times, it needs significantly less time than EA alone to reach good solutions.
7
Content available remote Hybrydowa optymalizacja topologiczna dynamicznych układów mechanicznych
EN
In this paper scientific research on using the hybrid algorithm in optimization of the dynamic structures was carried out. The boundary-initial problem for elastodynamics was solved by using boundary element method (BEM) [2]. The hybrid algorithm being the coupling of the evolutionary algorithm, gradient algorithm and the artificial neural network was carried out. Topology and shape optimization problems were considered for different criteria, which concern: mass, displacements, stresses, compliance and natural frequencies. As a tool for the modeling of boundary shape the NURBS curves were applied. Several numerical examples testifying to the effectiveness and efficiency of the proposed methods of optimization were carried out, a few interesting tests are included in the paper.
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