Tag: Soft Computing – A Fusion of Foundations, Methodologies and Applications

A new hybrid mutation operator for multiobjective optimization with differential evolution

Abstract  Differential evolution has become one of the most widely used evolutionary algorithms in multiobjective optimization. Its
linear mutation operator is a simple and powerful mechanism to generate trial vectors. However, the performan…

Abstract  

Differential evolution has become one of the most widely used evolutionary algorithms in multiobjective optimization. Its
linear mutation operator is a simple and powerful mechanism to generate trial vectors. However, the performance of the mutation
operator can be improved by including a nonlinear part. In this paper, we propose a new hybrid mutation operator consisting
of a polynomial-based operator with nonlinear curve tracking capabilities and the differential evolution’s original mutation
operator, for the efficient handling of various interdependencies between decision variables. The resulting hybrid operator
is straightforward to implement and can be used within most evolutionary algorithms. Particularly, it can be used as a replacement
in all algorithms utilizing the original mutation operator of differential evolution. We demonstrate how the new hybrid operator
can be used by incorporating it into MOEA/D, a winning evolutionary multiobjective algorithm in a recent competition. The
usefulness of the hybrid operator is demonstrated with extensive numerical experiments showing improvements in performance
compared with the previous state of the art.

  • Content Type Journal Article
  • Category Original Paper
  • Pages 1-15
  • DOI 10.1007/s00500-011-0704-5
  • Authors
    • Karthik Sindhya, Department of Mathematical Information Technology, P.O. Box 35 (Agora), 40014 University of Jyväskylä, Finland
    • Sauli Ruuska, Department of Mathematical Information Technology, P.O. Box 35 (Agora), 40014 University of Jyväskylä, Finland
    • Tomi Haanpää, Department of Mathematical Information Technology, P.O. Box 35 (Agora), 40014 University of Jyväskylä, Finland
    • Kaisa Miettinen, Department of Mathematical Information Technology, P.O. Box 35 (Agora), 40014 University of Jyväskylä, Finland

An evolutionary algorithm to discover quantitative association rules in multidimensional time series

Abstract  An evolutionary approach for finding existing relationships among several variables of a multidimensional time series is presented
in this work. The proposed model to discover these relationships is based on quantitative associatio…

Abstract  

An evolutionary approach for finding existing relationships among several variables of a multidimensional time series is presented
in this work. The proposed model to discover these relationships is based on quantitative association rules. This algorithm,
called QARGA (Quantitative Association Rules by Genetic Algorithm), uses a particular codification of the individuals that
allows solving two basic problems. First, it does not perform a previous attribute discretization and, second, it is not necessary
to set which variables belong to the antecedent or consequent. Therefore, it may discover all underlying dependencies among
different variables. To evaluate the proposed algorithm three experiments have been carried out. As initial step, several
public datasets have been analyzed with the purpose of comparing with other existing evolutionary approaches. Also, the algorithm
has been applied to synthetic time series (where the relationships are known) to analyze its potential for discovering rules
in time series. Finally, a real-world multidimensional time series composed by several climatological variables has been considered.
All the results show a remarkable performance of QARGA.

  • Content Type Journal Article
  • Category Original Paper
  • Pages 1-20
  • DOI 10.1007/s00500-011-0705-4
  • Authors
    • M. Martínez-Ballesteros, Department of Computer Science, University of Seville, Seville, Spain
    • F. Martínez-Álvarez, Department of Computer Science, Pablo de Olavide University, Seville, Spain
    • A. Troncoso, Department of Computer Science, Pablo de Olavide University, Seville, Spain
    • J. C. Riquelme, Department of Computer Science, University of Seville, Seville, Spain

Brown–Robinson method for interval matrix games

Abstract  In this paper, two-person interval matrix games are considered, and by means of acceptability index, Brown–Robinson method
to find a mixed-strategy equilibrium is adapted to interval matrix games. Numerical examples are also give…

Abstract  

In this paper, two-person interval matrix games are considered, and by means of acceptability index, Brown–Robinson method
to find a mixed-strategy equilibrium is adapted to interval matrix games. Numerical examples are also given.

  • Content Type Journal Article
  • Pages 1-8
  • DOI 10.1007/s00500-011-0703-6
  • Authors
    • Emrah Akyar, Department of Mathematics, Faculty of Science, Anadolu University, 26470 Eskişehir, Turkey
    • Handan Akyar, Department of Mathematics, Faculty of Science, Anadolu University, 26470 Eskişehir, Turkey
    • Serkan Ali Düzce, Department of Mathematics, Faculty of Science, Anadolu University, 26470 Eskişehir, Turkey

States on finite linearly ordered IMTL-algebras

Abstract  The aim of this paper is to study states on finite linearly ordered IMTL-algebras. We prove that Bosbach states, Riečan states
and state-morphisms are equivalent on linearly ordered IMTL-algebras. Furthermore, we investigate the e…

Abstract  

The aim of this paper is to study states on finite linearly ordered IMTL-algebras. We prove that Bosbach states, Riečan states
and state-morphisms are equivalent on linearly ordered IMTL-algebras. Furthermore, we investigate the existence of states
on finite linearly ordered IMTL-algebra and prove that if

L

is locally finite, then

L

has a state if and only if

L

is an MV-algebra, and that if

L

is peculiar and

H(L)È{0,1}

is a subalgebra of

L

, then

L

has a state if and only if

ord(n)=|H(L)|+1

, where

H(L)={x Î L|ord(x) < ¥, ord(Øx) < ¥}, n= max H(L)

.

  • Content Type Journal Article
  • Pages 1-8
  • DOI 10.1007/s00500-011-0701-8
  • Authors
    • Lianzhen Liu, School of Science, Jiangnan University, 214122 Wuxi, China
    • Xiangyang Zhang, School of Science, Jiangnan University, 214122 Wuxi, China

Fuzzy region assignment for visual tracking

Abstract  In this work we propose a new approach based on fuzzy concepts and heuristic reasoning to deal with the visual data association
problem in real time, considering the particular conditions of the visual data segmented from images, a…

Abstract  

In this work we propose a new approach based on fuzzy concepts and heuristic reasoning to deal with the visual data association
problem in real time, considering the particular conditions of the visual data segmented from images, and the integration
of higher-level information in the tracking process such as trajectory smoothness, consistency of information, and protection
against predictable interactions such as overlap/occlusion, etc. The objects’ features are estimated from the segmented images
using a Bayesian formulation, and the regions assigned to update the tracks are computed through a fuzzy system to integrate
all the information. The algorithm is scalable, requiring linear computing resources with respect to the complexity of scenarios,
and shows competitive performance with respect to other classical methods in which the number of evaluated alternatives grows
exponentially with the number of objects.

  • Content Type Journal Article
  • Pages 1845-1864
  • DOI 10.1007/s00500-011-0698-z
  • Authors
    • Jesus Garcia, GIAA-Departamento de Informatica, Universidad Carlos III de Madrid Avda, Universidad Carlos III, 22, 28270 Colmenarejo, Spain
    • Miguel A. Patricio, GIAA-Departamento de Informatica, Universidad Carlos III de Madrid Avda, Universidad Carlos III, 22, 28270 Colmenarejo, Spain
    • Antonio Berlanga, GIAA-Departamento de Informatica, Universidad Carlos III de Madrid Avda, Universidad Carlos III, 22, 28270 Colmenarejo, Spain
    • Jose M. Molina, GIAA-Departamento de Informatica, Universidad Carlos III de Madrid Avda, Universidad Carlos III, 22, 28270 Colmenarejo, Spain

A probabilistic interpretation of the medical expert system CADIAG-2

Abstract  CADIAG-2 is a well-known expert system aimed at providing support for medical diagnose in the field of internal medicine.
CADIAG-2 consists of a knowledge base in the form of a set of IF-THEN rules that relate distinct medical enti…

Abstract  

CADIAG-2 is a well-known expert system aimed at providing support for medical diagnose in the field of internal medicine.
CADIAG-2 consists of a knowledge base in the form of a set of IF-THEN rules that relate distinct medical entities, in this paper interpreted as conditional probabilistic statements, and an inference engine constructed upon methods of fuzzy set theory. The aim underlying this paper is the understanding of the logical structure of the inference in CADIAG-2. To that purpose,
we provide a (probabilistic) logical formalisation of the inference of the system and check its adequacy with probabilistic
logic.

  • Content Type Journal Article
  • Pages 1-8
  • DOI 10.1007/s00500-011-0699-y
  • Authors
    • David Picado Muiño, Institut für Diskrete Mathematik und Geometrie, 8 Wiedner Hauptstrasse, 1040 Vienna, Austria

Depth-control strategies for crossover in tree-based genetic programming

Abstract  The standard subtree crossover operator in the tree-based genetic programming (GP) has been considered as problematic. In
order to improve the standard subtree crossover, controlling depth of crossover points becomes a research top…

Abstract  

The standard subtree crossover operator in the tree-based genetic programming (GP) has been considered as problematic. In
order to improve the standard subtree crossover, controlling depth of crossover points becomes a research topic. However,
the existence of many different and inconsistent crossover depth-control schemes and the possibility of many other depth-control
schemes make the identification of good depth-control schemes a challenging problem. This paper aims to investigate general
heuristics for making good depth-control schemes for crossover in tree-based GP. It analyses the patterns of depth of crossover
points in good predecessor programs of five GP systems that use the standard subtree crossover and four approximations of
the optimal crossover operator on three problems in different domains. The analysis results show that an effective depth-control
scheme is problem-dependent and evolutionary stage-dependent, and that good crossover events have a strong preference for
roots and (less strongly) bottoms of parent program trees. The results also show that some ranges of depths between the roots
and the bottoms are also preferred, suggesting that unequal-depth-selection-probability strategies are better than equal-depth-selection-probability
strategies.

  • Content Type Journal Article
  • Pages 1-14
  • DOI 10.1007/s00500-011-0700-9
  • Authors
    • Huayang Xie, School of Engineering and Computer Science, Victoria University of Wellington, Wellington, New Zealand
    • Mengjie Zhang, School of Engineering and Computer Science, Victoria University of Wellington, Wellington, New Zealand

Graphics processing units and genetic programming: an overview

Abstract  A top end graphics card (GPU) plus a suitable SIMD interpreter can deliver a several hundred fold speed up, yet cost less
than the computer holding it. We give highlights of AI and computational intelligence applications in the new…

Abstract  

A top end graphics card (GPU) plus a suitable SIMD interpreter can deliver a several hundred fold speed up, yet cost less
than the computer holding it. We give highlights of AI and computational intelligence applications in the new field of general
purpose computing on graphics hardware (GPGPU). In particular, we surveyed genetic programming (GP) use with GPU. We gave
several applications from Bioinformatics and showed that how the fastest GP is based on an interpreter rather than compilation.
Finally using GP to generate GPU CUDA kernel C++ code is sketched.

  • Content Type Journal Article
  • Pages 1657-1669
  • DOI 10.1007/s00500-011-0695-2
  • Authors
    • W. B. Langdon, Department of Computer Science, CREST Centre, University College, Gower Street, London, WC1E 6BT UK

An improved algorithm on the content of realizable fuzzy matrices

Abstract  An

n×n
fuzzy matrix A is called realizable if there exists an

n×t
fuzzy matrix B such that

A=B\odot BT,

where

\odot

is the max–min composition. Let

r(A)=min{p:A=B\odot BT, B Î Ln…

Abstract  

An

n×n

fuzzy matrix A is called realizable if there exists an

n×t

fuzzy matrix B such that


A=B\odot BT,

where


\odot

is the max–min composition. Let


r(A)=min{p:A=B\odot BT, B Î Ln×p}.

Then

r(A)

is called the content of A. Since 1982, how to calculate r(A) for a given

n×n

realizable fuzzy matrix A was a focus problem, many researchers have made a lot of research work. X. P. Wang in 1999 gave an algorithm to find the
fuzzy matrix B and calculate r(A) within

[r(A)]n2

steps. Therefore, to find a simpler algorithm is a problem what we have to consider. This paper makes use of the symmetry
of the realizable fuzzy matrix A to simplify the algorithm of content

r(A)

based on the work of Wang (Chin Ann Math A 6: 701–706, 1999).

  • Content Type Journal Article
  • Pages 1-9
  • DOI 10.1007/s00500-011-0697-0
  • Authors
    • Yan Mo, College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, Sichuan People’s Republic of China
    • Xue-ping Wang, College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, Sichuan People’s Republic of China

β-Interval attribute reduction in variable precision rough set model

Abstract  The differences of attribute reduction and attribute core between Pawlak’s rough set model (RSM) and variable precision rough
set model (VPRSM) are analyzed in detail. According to the interval properties of precision parameter

Abstract  

The differences of attribute reduction and attribute core between Pawlak’s rough set model (RSM) and variable precision rough
set model (VPRSM) are analyzed in detail. According to the interval properties of precision parameter β with respect to the
quality of classification, the definition of attribute reduction is extended from a specific β value to a specific β interval
in order to overcome the limitations of traditional reduct definition in VPRSM. The concept of β-interval core is put forward
which will enrich the methodology of VPRSM. With proposed ordered discernibility matrix and relevant interval characteristic
sets, a heuristic algorithm can be constructed to get β-interval reducts. Furthermore, a novel method, with which the optimal
interval of precision parameter can be determined objectively, is introduced based on shadowed sets and an evaluation function
is also given for selecting final optimal β-interval reduct. All the proposed notions in this paper will promote the development
of VPRSM both in theory and practice.

  • Content Type Journal Article
  • Pages 1643-1656
  • DOI 10.1007/s00500-011-0693-4
  • Authors
    • Jie Zhou, Department of Computer Science and Technology, Tongji University, Shanghai, 201804 People’s Republic of China
    • Duoqian Miao, Department of Computer Science and Technology, Tongji University, Shanghai, 201804 People’s Republic of China