- 1
- Karpenko A., Posypkin M., Rubtsov A., Sakharov M. Multi-memetic Global Optimization based on the Mind Evolutionary Computation // Proceedings of the IV International Conference on Optimization Methods and Application “Optimization and Applications” (OPTIMA-2013). Moscow: Dorodnicyn Computing Centre of RAS, 2013. P. 83-84.

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- Several desktop computers connected into a parallel computing system are often used as a part of such framework. The advantage of this type of networks is that their capacity can be increased literally with no limit by means of scaling
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- . However, in order to make such calculations possible one needs a special software implementation which would be based on a data exchange interface. In this work MPI was utilized as one of the most widely used interfaces, designed for loosely coupled systems.

- In-text reference with the coordinate start=8516
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- Science & Education of the Bauman MSTU 440 3.2 Hybrid MEC There are several modifications of the canonical MEC algorithm proposed by different authors, for instance, Extended MEC, Improved MEC, Chaotic MEC and so forth [10]. This paper utilizes a modification proposed by the authors in one of their previous works
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- and named HMEC. The distinct feature of that algorithm is an addition of the decomposition stage and modification of the similar-taxis stage. The choice is made after a certain number of iteration what meme out of a set of available memes is the most suitable for a given search subdomain.

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- Карпенко А.П. Современные алгоритмы поисковой оптимизации. Алгоритмы, вдохновленные природой. М.: Изд-во МГТУ им. Н.Э. Баумана, 2014. 446.

Total in-text references: 3- In-text reference with the coordinate start=1709
- Prefix
- Several desktop computers connected into a parallel computing system are often used as a part of such framework. The advantage of this type of networks is that their capacity can be increased literally with no limit by means of scaling
- Exact
- [1, 2]
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- . However, in order to make such calculations possible one needs a special software implementation which would be based on a data exchange interface. In this work MPI was utilized as one of the most widely used interfaces, designed for loosely coupled systems.

- In-text reference with the coordinate start=8516
- Prefix
- Science & Education of the Bauman MSTU 440 3.2 Hybrid MEC There are several modifications of the canonical MEC algorithm proposed by different authors, for instance, Extended MEC, Improved MEC, Chaotic MEC and so forth [10]. This paper utilizes a modification proposed by the authors in one of their previous works
- Exact
- [1, 2]
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- and named HMEC. The distinct feature of that algorithm is an addition of the decomposition stage and modification of the similar-taxis stage. The choice is made after a certain number of iteration what meme out of a set of available memes is the most suitable for a given search subdomain.

- In-text reference with the coordinate start=9396
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- The greedy strategy suggests that the best meme is selected at each iteration in accordance with the local improvement it has demonstrated. The value of an objective function after the improvement was taken as a choice criterion. A general scheme of that algorithm can be described as follows
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- . 1. Initialization of groups within the search domain . a. Divide domain into subdomains by means of decomposing interval into equal subintervals. Here , – the algorithm's free parameters. b.

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- Карпенко А.П., Сахаров М.К. Мультимемеевая глобальная оптимизация на основе алгоритма эволюции разума // Информационные технологии. 2014. No 7. С. 23-30.

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- Population algorithms allow one to process several Science & Education of the Bauman MSTU 438 solutions independently in parallel. Subsequently, the main advantage of this type of algorithms is their decentralization and elegancy of parallelization
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- . Among main parallelization models for population algorithms one can highlight a global model, an island model, a diffusion model and other hybrid models. In this paper an island model was utilized as it takes into account a low carrying capacity of communication network of desktop computers.

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- There are many various hybridization methods for optimization algorithms and, in particular, for population-based methods. One of the most widely used classification of such methods is a one-level classification proposed by Wang
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- [3]
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- . In accordance with this classification there are three groups of hybrid algorithms: embedded algorithms, preprocessor/postprocessor algorithms and coalgorithms. The first category can be also divided into two subgroups: high-level and lowlevel hybridization.

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- The goal of this work is development and software implementation of a parallel multi-memetic algorithm for loosely coupled computing systems as well as the investigation of its performance with a use of several benchmark optimization functions. 2 Problem statement In this paper a multi-dimensional global constrained minimization is considered
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- Science & Education of the Bauman MSTU 439 (1) where set D is determined with inequality constraints (2) Here – the objective function being minimized and defined in every point of search domain D, – the desired minimum value of the objective function , – a vector of variables, – the desired vector of variab

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- Weise T. Global Optimization Algorithms. Theory and Application. University of Kassel, 2008. 758 p.

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- Prefix
- Population algorithms allow one to process several Science & Education of the Bauman MSTU 438 solutions independently in parallel. Subsequently, the main advantage of this type of algorithms is their decentralization and elegancy of parallelization
- Exact
- [3, 4]
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- . Among main parallelization models for population algorithms one can highlight a global model, an island model, a diffusion model and other hybrid models. In this paper an island model was utilized as it takes into account a low carrying capacity of communication network of desktop computers.

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- Talbi E. A Taxonomy of Hybrid Metaheuristics // Journal of Heuristics. 2002. Vol. 8, iss. 5. P. 541-564. DOI: 10.1023/A:1016540724870

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- In the meantime, if one speaks about loosely coupled systems where communication between subpopulations is absent it's appropriate to use a special case of an island model called a model of noncommuting population
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- . In order to increase performance of the specified global optimization methods researchers use either hybridization or meta-optimization. A development of hybrid algorithms implies a combination of various or same methods with different values of free parameters in such a way that advantages of one method would overcome disadvantages of another one.

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- Dawkins R. The Selfish Gene. Oxford University Press, 1976. 384 p.

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- In this context, a meme represents any local optimization method, which improves a current solution at the particular stages of the main algorithm. Generally, memetic algorithms are hybridization of a population method and one or several local optimization methods
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- . There are many various hybridization methods for optimization algorithms and, in particular, for population-based methods. One of the most widely used classification of such methods is a one-level classification proposed by Wang [3].

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- Nguyen Q.H., Ong Y.S., Krasnogor N. A Study on the Design Issues of Memetic Algorithm // IEEE Congress on Evolutionary Computation (CEC 2007). IEEE Publ., 2007. P. 23902397. DOI: 10.1109/CEC.2007.4424770

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- Prefix
- In this context, a meme represents any local optimization method, which improves a current solution at the particular stages of the main algorithm. Generally, memetic algorithms are hybridization of a population method and one or several local optimization methods
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- [6, 7]
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- . There are many various hybridization methods for optimization algorithms and, in particular, for population-based methods. One of the most widely used classification of such methods is a one-level classification proposed by Wang [3].

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- Ong Y.S., Lim M.H., Zhu N., Wong K.W. Classification of adaptive memetic algorithms: A comparative study // IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics. 2006. Vol. 36, iss. 1. P. 141-152. DOI: 10.1109/TSMCB.2005.856143

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- provides researchers with a lot of different opportunities for developing their modifications which could differ from one another, for instance, by the frequency of local search appliance, its termination criteria and other parameters. Modification of MAs that are most frequently used in practice implies a simultaneous usage of various memes and called multi-memetic algorithms
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- . The goal of this work is development and software implementation of a parallel multi-memetic algorithm for loosely coupled computing systems as well as the investigation of its performance with a use of several benchmark optimization functions. 2 Problem statement In this paper a multi-dimensional global constrained minimization is considered [3] Science & Education of the Bau

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- The choice is made after a certain number of iteration what meme out of a set of available memes is the most suitable for a given search subdomain. This choice is independent for each group
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- [8]
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- . In this particular modification a greedy hyperheuristic was used for determining the best meme in the groups, however other hyperheuristics are applicable as well [8]. The greedy strategy suggests that the best meme is selected at each iteration in accordance with the local improvement it has demonstrated.

- In-text reference with the coordinate start=9067
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- This choice is independent for each group [8]. In this particular modification a greedy hyperheuristic was used for determining the best meme in the groups, however other hyperheuristics are applicable as well
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- [8]
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- . The greedy strategy suggests that the best meme is selected at each iteration in accordance with the local improvement it has demonstrated. The value of an objective function after the improvement was taken as a choice criterion.

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- Chengyi S., Yan S., Wanzhen W. A Survey of MEC: 1998-2001 // 2002 IEEE International Conference on Systems, Man and Cybernetics. Vol. 6. IEEE Publ., 2002. P. 445-453. DOI:

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- a vector of variables, – the desired vector of variables, wherein the objective function takes up its minimal value, – the dimension of vector . 3 Utilized Algorithms 3.1 Base Algorithm In this paper Mind Evolutionary Computation, MEC was selected as a base algorithm for the considered hybridization scheme. Its concept was firstly proposed in 1998
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- . This choice is justified, first of all, by the commitment to loosely coupled computing systems. MEC is capable of providing the minimal number of connections between subpopulations which evolve on the separate computational nodes.

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- 1109/ICSMC.2002.1175629 Наука и образование. МГТУ им. Н.Э. Баумана 451 10. Jie J., Zeng J. Improved Mind Evolutionary Computation for Optimizations // Proceedings of 5th World Congress on Intelligent Control and Automation. Vol. 3. IEEE Publ., 2004. P. 2200-2204. DOI: 10.1109/WCICA.2004.1341978

Total in-text references: 3- In-text reference with the coordinate start=6569
- Prefix
- a vector of variables, – the desired vector of variables, wherein the objective function takes up its minimal value, – the dimension of vector . 3 Utilized Algorithms 3.1 Base Algorithm In this paper Mind Evolutionary Computation, MEC was selected as a base algorithm for the considered hybridization scheme. Its concept was firstly proposed in 1998
- Exact
- [9, 10]
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- . This choice is justified, first of all, by the commitment to loosely coupled computing systems. MEC is capable of providing the minimal number of connections between subpopulations which evolve on the separate computational nodes.

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- In order to achieve a high position within its group, an individual has to study from the most successful individuals in this group. And groups themselves should follow the same principle to stay alive in the intergroup competition
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- . In accordance with the algorithm a multi-population consists of some leading groups and some lagging groups , which include and subpopulations correspondingly.

- In-text reference with the coordinate start=8420
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- Science & Education of the Bauman MSTU 440 3.2 Hybrid MEC There are several modifications of the canonical MEC algorithm proposed by different authors, for instance, Extended MEC, Improved MEC, Chaotic MEC and so forth
- Exact
- [10]
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- . This paper utilizes a modification proposed by the authors in one of their previous works [1, 2] and named HMEC. The distinct feature of that algorithm is an addition of the decomposition stage and modification of the similar-taxis stage.

- In-text reference with the coordinate start=6569
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- Floudas A.A., Pardalos P.M., Adjiman C., Esposito W.R., Gümüs Z.H., Harding S.T., Klepeis J.L., Meyer C.A., Schweiger C.A. Handbook of Test Problems in Local and Global Optimization. Kluwer, Dordrecht, 1999. 441 p.

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- process should be stopped, otherwise it continues and goes to point 2. 3.3 Local search methods At the stage of local optimization HMEC chooses the best meme (in accordance with selected hyperheuristic) for each search subdomain from a set of local unconstrained optimization algorithms, which in this work consists of the methods of Nelder–Mead, Hooke-Jeeves and Monte-Carlo
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- . The first method belongs to the class of zero-order deterministic optimization methods, i.e. based only on the objective function’s values. The advantage of this method is that the shape of a deformable polyhedron conforms to the topography of the objective function due to the expansion and reduction operations.

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- Nelder J.A., Meade R. A Simplex Method for Function Minimization // Computer Journal. 1965. Vol. 7, iss. 4. P. 308-313. DOI: 10.1093/comjnl/7.4.308

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- process should be stopped, otherwise it continues and goes to point 2. 3.3 Local search methods At the stage of local optimization HMEC chooses the best meme (in accordance with selected hyperheuristic) for each search subdomain from a set of local unconstrained optimization algorithms, which in this work consists of the methods of Nelder–Mead, Hooke-Jeeves and Monte-Carlo
- Exact
- [11, 12]
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- . The first method belongs to the class of zero-order deterministic optimization methods, i.e. based only on the objective function’s values. The advantage of this method is that the shape of a deformable polyhedron conforms to the topography of the objective function due to the expansion and reduction operations.

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- Liang J.J., Qu B.Y., Suganthan P.N. Problem Definitions and Evaluation Criteria for the CEC 2014 Special Session and Competition on Single Objective Real-Parameter Numerical Optimization. Technical Report 201311. Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou, China; Technical Report. Nanyang Technological University, Singapore, 2013. 32 p. Наука и образование. МГТУ

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- Due to the large computational expenses the dimension of vector was limited to . Science & Education of the Bauman MSTU 443 For performance investigation of the software implementation the following benchmark multi-modal optimization functions were utilized
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- : shifted and rotated Rosenbrock function; shifted and rotated Weierstrass function; shifted and rotated Griewank function; shifted Schwefel function. The dependency of an estimation of the probability of global minimum localization on the number of CPUs is presented on the figure 1.

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