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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.
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2833
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Population algorithms allow one to process several
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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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 metaoptimization. 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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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 populationbased methods. One of the most widely used classification of such methods is
a onelevel classification proposed by Wang [3].
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4677
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There are many various hybridization methods for optimization algorithms and, in particular, for populationbased methods. One of the most widely used classification of such methods is
a onelevel 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: highlevel and lowlevel hybridization.
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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 multimemetic algorithms
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[8]
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. The goal of this work is development and software implementation of a parallel multimemetic 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 multidimensional global constrained minimization is considered [3]
(1
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6004
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The goal of this work is development and software implementation of a parallel multimemetic 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 multidimensional global constrained minimization is considered
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[3]
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(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 variables, wherein the objective function takes up
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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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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 multipopulation consists of some leading groups
and some lagging groups , which include
and subpopulations correspondingly.
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When the best obtained values stops
changing, the winner of the best group from a set of leading ones is selected as a solution to the
optimization problem.
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
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[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 similartaxis stage.
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changing, the winner of the best group from a set of leading ones is selected as a solution to the
optimization problem.
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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[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 similartaxis 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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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.
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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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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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