Soft Computing

, Volume 21, Issue 3, pp 781–793

A multiagent evolutionary algorithm with direct and indirect combined representation for constraint satisfaction problems

Methodologies and Application

DOI: 10.1007/s00500-015-1815-1

Cite this article as:
Hao, X. & Liu, J. Soft Comput (2017) 21: 781. doi:10.1007/s00500-015-1815-1


The evolutionary algorithms (EAs) became more and more important in solving NP-hard problems in recent years. The representation of specific problems in EAs is very important and it has a great influence on the performance of EAs. The constraint satisfaction problems (CSPs) are typical NP-hard problems and the representation of CSPs can be traditionally divided into two types, namely the direct and indirect representations. The variables in direct representation represent the actual values that they can take, and can be evaluated directly. Whereas in indirect representation, a specific permutation is assigned to variables, and the individual is incapable of being evaluated without a decoder. In order to take advantage of both representations to enforce the ability of EAs in solving CSPs, we propose a combination of these two representations in this article. The minimum conflict decoder is employed to transform indirect representation to direct representation and several new behaviors are designed for agents in multiagent evolutionary algorithms. In experiments, 250 benchmark binary CSPs and 79 graph coloring problems are tested. The comparisons among the direct, indirect and the combined representation methods are conducted. Experimental results illustrate that the method of combined representation outperforms the two other methods.


Constraint satisfaction problem Direct representation Indirect representation Direct and indirect combined representation Multiagent evolutionary algorithm 

Funding information

Funder NameGrant NumberFunding Note
FN:National Natural Science Foundation of China
  • GN:61271301
FN:Research Fund for the Doctoral Program of Higher Education of China
  • GN:20130203110010
FN:Fundamental Research Funds for the Central Universities
  • GN:K5051202052

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Key Laboratory of Intelligent Perception and Image Understanding of Ministry of EducationXidian UniversityXi’anChina

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