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EN
In this paper,we proposed a modified meta-heuristic algorithm based on the blind naked mole-rat (BNMR) algorithm to solve the multiple standard benchmark problems. We then apply the proposed algorithm to solve an engineering inverse problem in the electromagnetic field to validate the results. The main objective is to modify the BNMR algorithm by employing two different types of distribution processes to improve the search strategy. Furthermore, we proposed an improvement scheme for the objective function and we have changed some parameters in the implementation of the BNMR algorithm. The performance of the BNMR algorithm was improved by introducing several new parameters to find the better target resources in the implementation of a modified BNMR algorithm. The results demonstrate that the changed candidate solutions fall into the neighborhood of the real solution. The results show the superiority of the propose method over other methods in solving various mathematical and electromagnetic problems.
EN
This paper presents characteristics of model-based optimization methods utilized within the Generalized Self-Adapting Particle Swarm Optimization (GA– PSO) – a hybrid global optimization framework proposed by the authors. GAPSO has been designed as a generalization of a Particle Swarm Optimization (PSO) algorithm on the foundations of a large degree of independence of individual particles. GAPSO serves as a platform for studying optimization algorithms in the context of the following research hypothesis: (1) it is possible to improve the performance of an optimization algorithm through utilization of more function samples than standard PSO sample-based memory, (2) combining specialized sampling methods (i.e. PSO, Differential Evolution, model-based optimization) will result in a better algorithm performance than using each of them separately. The inclusion of model-based enhancements resulted in the necessity of extending the GAPSO framework by means of an external samples memory - this enhanced model is referred to as M-GAPSO in the paper. We investigate the features of two model-based optimizers: one utilizing a quadratic function and the other one utilizing a polynomial function. We analyze the conditions under which those model-based approaches provide an effective sampling strategy. Proposed model-based optimizers are evaluated on the functions from the COCO BBOB benchmark set.
EN
Material parameters identification by inverse analysis using finite element computations leads to the resolution of complex and time-consuming optimization problems. One way to deal with these complex problems is to use meta-models to limit the number of objective function computations. In this paper, the Efficient Global Optimization (EGO) algorithm is used. The EGO algorithm is applied to specific objective functions, which are representative of material parameters identification issues. Isotropic and anisotropic correlation functions are tested. For anisotropic correlation functions, it leads to a significant reduction of the computation time. Besides, they appear to be a good way to deal with the weak sensitivity of the parameters. In order to decrease the computation time, a parallel strategy is defined. It relies on a virtual enrichment of the meta-model, in order to compute q new objective functions in a parallel environment. Different methods of choosing the qnew objective functions are presented and compared. Speed-up tests show that Kriging Believer (KB) and minimum Constant Liar (CLmin) enrichments are suitable methods for this parallel EGO (EGO-p) algorithm. However, it must be noted that the most interesting speed-ups are observed for a small number of objective functions computed in parallel. Finally, the algorithm is successfully tested on a real parameters identification problem.
EN
Numerous practical engineering applications can be formulated as non-convex, non-smooth, multi-modal and ill-conditioned optimization problems. Classical, deterministic algorithms require an enormous computational effort, which tends to fail as the problem size and its complexity increase, which is often the case. On the other hand, stochastic, biologically-inspired techniques, designed for global optimum calculation, frequently prove successful when applied to real life computational problems. While the area of bio-inspired algorithms (BIAs) is still relatively young, it is undergoing continuous, rapid development. Selection and tuning of the appropriate optimization solver for a particular task can be challenging and requires expert knowledge of the methods to be considered. Comparing the performance of viable candidates against a defined test bed environment can help in solving such dilemmas. This paper presents the benchmark results of two biologically inspired algorithms: covariance matrix adaptation evolution strategy (CMA-ES) and two variants of particle swarm optimization (PSO). COCO (COmparing Continuous Optimizers) – a platform for systematic and sound comparisons of real-parameter global optimization solvers was used to evaluate the performance of CMA-ES and PSO methods. Particular attention was paid to the effciency and scalability of both techniques.
EN
Active contour model is a typical and effective closed edge detection algorithm, which has been widely applied in remote sensing image processing. Since the variety of the image data source, the complexity of the application background and the limitations of edge detection, the robustness and universality of active contour model are greatly reduced in the practical application of edge extraction. This study presented a fast edge detection approach based on global optimization convex model and Split Bregman algorithm. Firstly, the proposed approach defined a generalized convex function variational model which incorporated the RSF model’s principle and Chan’s global optimization idea and could get the global optimal solution. Secondly, a fast numerical minimization scheme based on split Bregman iterative algorithm is employed for overcoming drawbacks of noise and others. Finally, the curve evolves to the target boundaries quickly and accurately. The approach was applied in real special sea ice SAR images and synthetic images with noise, fuzzy boundaries and intensity inhomogeneity, and the experiment results showed that the proposed approach had a better performance than the edge detection methods based on the GMAC model and RSF model. The validity and robustness of the proposed approach were also verified.
EN
Grey Wolf Optimizer (GWO) is a new meta-heuristic search algorithm inspired by the social behavior of leadership and the hunting mechanism of grey wolves. GWO algorithm is prominent in terms of finding the optimal solution without getting trapped in premature convergence. In the original GWO, half of the iterations are dedicated to exploration and the other half are devoted to exploitation, overlooking the impact of right balance between these two to guarantee an accurate approximation of global optimum. To overcome this shortcoming, an Enhanced Grey Wolf Optimization (EGWO) algorithm with a better hunting mechanism is proposed, which focuses on proper balance between exploration and exploitation that leads to an optimal performance of the algorithm and hence promising candidate solutions are generated. To verify the performance of our proposed EGWO algorithm, it is benchmarked on twenty-five benchmark functions with diverse complexities. It is then employed on range based node localization problem in wireless sensor network to demonstrate its applicability. The simulation results indicate that the proposed algorithm is able to provide superior results in comparison with some wellknown algorithms. The results of the node localization problem indicate the effectiveness of the proposed algorithm in solving real world problems with unknown search spaces.
7
Content available remote An exaple of template based protein structure modeling by global optimization
EN
CASP (Critical Assessment of protein Structure Prediction) is a community-wide experiment for protein structure prediction taking place every two years since 1994. In CASP 11 held in 2014, according to the official CASP 11 assessment, our method named `nns' was ranked as the second best server method based on models ranked as first out of 81 targets. In `nns', we applied the powerful global optimization method of conformational space annealing to three stages of optimization, including multiple sequence-structure alignment, three-dimensional (3D) chain building, and side-chain remodeling. For the fold recognition, a new alignment method called CRF align was used. The good performance of the nns server method is attributed to the successful fold recognition carried out by combined methods including CRF align, and the current modeling formulation incorporating accurate structural aspects collected from multiple templates. In this article, we provide a successful example of `nns' predictions for T0776, for which all details of intermediate modeling data are provided.
8
Content available remote A Short Introduction to Stochastic Optimization
EN
We present some typical algorithms used for finding global minimum/ maximum of a function defined on a compact finite dimensional set, discuss commonly observed procedures for assessing and comparing the algorithms’ performance and quote theoretical results on convergence of a broad class of stochastic algorithms.
EN
In this paper, an application of Evolutionary Multiagent Systems (EMAS) and its memetic version to the optimization of advisory strategy (in this case, Sudoku advisory strategy) is considered. The problem is tackled using an EMAS, which has already proven as a versatile optimization technique. Results obtained using EMAS and Parallel Evolutionary Algorithm (PEA) are compared. After giving an insight to the possibilities of decision support in Sudoku solving, an exemplary strategy is defined. Then EMAS and its memetic versions are discussed, and experimental results concerning comparison of EMAS and PEA presented.
EN
With reactive force fields it is possible to perform atomistic simulations that join the accuracy of quantum chemical treatments (including bond breaking and formation) with the ability to treat hundreds of thousands of atoms on time scales well into the nanosecond regime. To utilize this power in everyday applications requires (I) the assembly of a suitable reference data set of sufficient quality, and (II) a reliable fit of the huge and complex parameter set of a general reactive force field to these reference data. In this contribution, we show that genetic algorithms can be used to achieve goal (II). We discuss algorithm design and implementation aspects (including parallelization) and present an application to azobenzene as real-life example.
PL
Przy pomocy pól sił reakcji możliwe jest przeprowadzenie symulacji atomowych, które łączą w sobie dokładność procesów chemii kwantowej (włączając zrywanie i tworzenie wiązań) oraz zdolność przetwarzania setek tysięcy atomów na skali czasowej w reżim nanosekundowy. Aby wykorzystać takie możliwości w powszechnych aplikacjach wymagane jest (I) zgromadzenie odpowiednich danych referencyjnych zapewniających niezawodną jakość, oraz (II) dopasowanie dużego i złożonego zestawu parametrów pola sił reakcji do tychże danych referencyjnych. W niniejszej pracy wykazujemy, że algorytmy genetyczne mogą być wykorzystane do osiągnięcia celu (II). Omówiony został wstępny algorytm oraz aspekty jego implementacji (w tym zrównoleglenie). Jako rzeczywisty przykład wykorzystania algorytmu przedstawiono jego zastosowanie w azobenzenie.
EN
The paper introduces a stochastic model for a class of population-based global optimization meta-heuristics, that generalizes existing models in the following ways. First of all, an individual becomes an active software agent characterized by the constant genotype and the meme that may change during the optimization process. Second, the model embraces the asynchronous processing of agent’s actions. Third, we consider a vast variety of possible actions that include the conventional mixing operations (e.g. mutation, cloning, crossover) as well as migrations among demes and local optimization methods. Despite the fact that the model fits many popular algorithms and strategies (e.g. genetic algorithms with tournament selection) it is mainly devoted to study memetic algorithms. The model is composed of two parts: EMAS architecture (data structures and management strategies) allowing to define the space of states and the framework for stochastic agent actions and the stationary Markov chain described in terms of this architecture. The probability transition function has been obtained and the Markov kernels for sample actions have been computed. The obtained theoretical results are helpful for studying metaheuristics conforming to the EMAS architecture. The designed synchronization allows the safe, coarse-grained parallel implementation and its effective, sub-optimal scheduling in a distributed computer environment. The proved strong ergodicity of the finite state Markov chain results in the asymptotic stochastic guarantee of success, which in turn imposes the liveness of a studied metaheuristic. The Markov chain delivers the sampling measure at an arbitrary step of computations, which allows further asymptotic studies, e.g. on various kinds of the stochastic convergence.
12
Content available The island model as a Markov dynamic system
EN
Parallel multi-deme genetic algorithms are especially advantageous because they allow reducing the time of computations and can perform a much broader search than single-population ones. However, their formal analysis does not seem to have been studied exhaustively enough. In this paper we propose a mathematical framework describing a wide class of island-like strategies as a stationary Markov chain. Our approach uses extensively the modeling principles introduced by Vose, Rudolph and their collaborators. An original and crucial feature of the framework we propose is the mechanism of inter-deme agent operation synchronization. It is important from both a practical and a theoretical point of view. We show that under a mild assumption the resulting Markov chain is ergodic and the sequence of the related sampling measures converges to some invariant measure. The asymptotic guarantee of success is also obtained as a simple issue of ergodicity. Moreover, if the cardinality of each island population grows to infinity, then the sequence of the limit invariant measures contains a weakly convergent subsequence. The formal description of the island model obtained for the case of solving a single-objective problem can also be extended to the multi-objective case.
PL
Numeryczne metody optymalizacji, powszechnie stosowane w zagadnieniach hydrologicznych, nie gwarantują wyznaczenia minimum globalnego funkcji celu. Ich popularność wiąże się z tym, że mogą one być stosowane w zagadnieniach, w których liczba zmiennych decyzyjnych jest stosunkowo duża. W pracy dokonano przeglądu metod deterministycznych, które umożliwiają znalezienie optimum globalnego w przypadku, gdy funkcja celu ma więcej niż jedno minimum lokalne. Metody te mogą być podzielone na dwie kategorie: asymptotycznie kompletne oraz kompletne. Podczas gdy algorytmy należące do obu klas są w stanie generować ciąg rozwiązań przybliżonych zbieżny do rozwiązania zagadnienia optymalizacji globalnej, to tylko dla algorytmów należących do drugiej z wymienionych kategorii są dostępne nieheurystyczne kryteria stopu. Przykłady przedstawione w pracy ilustrują możliwości zastosowania metod asymptotycznie kompletnych do szacowania parametrów w modelach procesów hydrologicznych, takich jak: modele różniczkowe przepływu wód gruntowych, modele hydrauliczne wchodzące w skład modeli hydrodynamicznych wykorzystywanych do modelowania zasobów wód powierzchniowych, modele typu opad-odpływ czy też integralne modele zlewni.
EN
Most numerical optimization methods that are widely used in hydrology don't guarantee reaching the global minimum of the goal function. They became popular mainly due to their ability of handling relatively multi-dimensional problems. The paper reviews the deterministic methods capable of finding the global optimum in the presence of local optima. They can be divided into two categories: asymptotically complete methods and complete methods. While algorithms from both classes can generate a sequence converging to a solution of the global optimization problem, only for the algorithms from the latter class non-heuristic stopping criteria are available. The examples presented in the paper illustrate the applicability of asymptotically complete methods to parameter estimation in modelling hydrological processes, such as differential models of groundwater flow, hydraulic models embedded into hydrodynamic models of river systems, the precipitation–outflow models or integral catchment models.
14
Content available O kilku osobliwościach w oddziaływaniach molekuł
EN
The ground state electronic energy represents a complicated function of the nuclear coordinates. Even for relatively small molecules this function may have many minima in the corresponding "energy landscape", very often myriads of minima, each of them corresponding to a stable configuration of the nuclei. This is why predicting the lowest-energy conformation or configuration represents a formidable task. There were many attempts to solve this problem for protein molecules, for which it is believed their native conformation corresponds to the lowest free energy. The challenge to find this conformation from a given sequence of amino acids is known as a "second genetic code". In fact all of these attempts based on some smoothing of the energy landscape. In the article some of these smoothing techniques are described, from a generic one to those, which finally turned out to be highly successful in finding native structures of globular proteins. When discussing the contributions to the conformational energy the importance of the hydrophobic effect as well as of the electrostatic interactions has been stressed. In particular it turned out that the dipole moments of the NH and of the CO bonds in proteins functioning in nature are oriented to good accuracy along the local intramolecular electric field. Thanks to enormous effort of the protein folding community it is possible to design such amino acid sequences, which fold to the desired protein 3D structure. A certain reliable theoretical technique of protein folding has been used to study a possibility of conformational autocatalysis. It turned out that a small protein of 32 amino acids, with carefully predesigned amino acid sequence, exhibits indeed such an effect, which may be seen as a model of the prion disease propagation.
15
Content available remote Global minimum optimization using Diffusion Monte Carlo approach
EN
In this preliminary study we present a new approach for a global minimum search of a continuous objective function based on the Diffusion Monte Carlo (DMC) method. In this article we suggest the simple implementation of the computer algorithm. W also test the efficiency of the DMC based approach against a pure random approach based on blind search (random sampling) and random walk algorithms. We use four test problems, namely Ackley's and Griewangk's functions in 5 and 20 dimensions. We show that in all tested cases the DMC algorithm performs significantly better than pure random methods - the optimal solutions generated by DMC method are much closer to the known global minimum of the test problems than the results obtained with blind search and random walk algorithms.
PL
W artykule przedstawiona została metoda optymalizacji globalnej dowolnej funkcji ciągłej oparta o algorytm dyfuzyjnego Monte Carlo (DMC). Proponujemy sposób prostej implementacji zaproponowanego algorytmu, a także przedstawiamy wstępne rezultaty symulacji pokazujących efektywność metody DMC w porównaniu z metodami czysto losowymi - próbkowaniem losowym i błądzeniem losowym. Jako problemy testowe w symulacjach wykorzystujemy funkcję Ackley-a i Griewangk-a w wariantach 5- i 20-wymiarowym. Rezultaty przeprowadzonych symulacji wskazują na znacznie większą efektywność metody DMC w porównaniu z pozostałymi - uzyskane za jej pomocą rozwiązania są znacznie bliższe globalnemu minimum niż wyniki uzyskane metodami czysto losowymi.
EN
The several novel structures of the chaotic oscillators with piecewise-linear vector field are derived and verified. For the synthesis of the linear part of the circuit the so-called simulated annealing method is utilized. For the rapid calculation of the fitness function the circuit simulator Hspice is used. Starting with the given mathematical model, namely the eigenvalues for each state space region, the final circuits consist of parallel connection of idealized nonlinear resistor and higher-order linear admittance.
PL
Przedstawiono kilka nowych chaotycznych generatorów w częściowo liniowym wektorem pola. Do syntezy części liniowej obwodu wykorzystano metodę symulowanego wyżarzania. Do szybkich obliczeń funkcji sprawności użyto symulatora Hspice. Startując od modelu matematycznego wartości własne dla każdego regionu składają się z równoległych połączeń idealizowanych rezystorów nieliniowych i admitancji wyższego rzędu.
EN
This article comments on the development of Evolutionary Computation (EC) in the field of global optimization. A brief overview of EC fundamentals is provided together with the discussion of issues of parameter settings and adaptation, advances in the development of theory, new ideas emerging in the EC field and growing availability of massively parallel machines.
EN
We present a random perturbation of the projected variable metric method for solving linearly constrained nonsmooth (i.e., nondifferentiable) nonconvex optimization problems, and we establish the convergence to a global minimum for a locally Lipschitz continuous objective function which may be nondifferentiable on a countable set of points. Numerical results show the effectiveness of the proposed approach.
EN
A novel, neural network controlled, dynamic evolutionary algorithm is proposed for the purposes of molecular geometry optimization. The approach is tested for selected model molecules and some molecular systems of importance in biochemistry. The new algorithm is shown to compare favorably with the standard, statically parametrized memetic algorithm.
EN
A joint inversion method for the evaluation of well-logging data is presented, which is applicable to determine textural parameters, i.e., cementation exponent, saturation exponent and tortuosity factor, simultaneously with conventional petrophysical properties. The inversion techniques used today perform local interpretation. Since the number of unknowns is slightly lower than that of the data estimated locally to one depth-point, a set of marginally overdetermined inverse problems has to be solved. For preserving the overdetermination, textural parameters must be kept constant for longer depth intervals (i.e., 200-300 m), despite the fact that they seem to be varying faster with depth according to field experiences. An inversion method was developed, which inverts data of a greater depth interval jointly in a highly overdetermined inversion procedure and gives a better resolution (10 m or less) estimate for the textural parameters. In the paper, a set of inversion tests on synthetic data as well as a field example prove the feasibility of the method.
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