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An ellipsoidal distance-based search strategy of ants for nonlinear single and multiple response optimization problems


  • Bera, Sasadhar
  • Mukherjee, Indrajit


Various continuous ant colony optimization (CACO) strategies are proposed by researchers to resolve continuous single response optimization problems. However, no such work is reported which also verifies suitability of CACO in case of both single and multiple response situations. In addition, as per literature survey, no variant of CACO can balance simultaneously all the three important aspects of an efficient search strategy, viz. escaping local optima, balancing between intensification and diversification scheme, and handling correlated variable search space structure. In this paper, a variant of CACO, so-called ‘CACO-MDS’ is proposed, which attempts to address all these three aspects. CACO-MDS strategy is based on a Mahalanobis distance-based diversification, and Nelder–Mead simplex-based intensification search scheme. Mahalanobis distance-based diversification search ensures exact measure of multivariate distance for correlated structured search space. The proposed CACO-MDS strategy is verified using fourteen single and multiple response multimodal function optimization test problems. A comparative analysis of CACO-MDS, with three different metaheuristic strategies, viz. ant colony optimization in real space (ACOR), a variant of local-best particle swarm optimization (SPSO) and simplex-simulated annealing (SIMPSA), also indicates its superiority in most of the test situations.

Suggested Citation

  • Bera, Sasadhar & Mukherjee, Indrajit, 2012. "An ellipsoidal distance-based search strategy of ants for nonlinear single and multiple response optimization problems," European Journal of Operational Research, Elsevier, vol. 223(2), pages 321-332.
  • Handle: RePEc:eee:ejores:v:223:y:2012:i:2:p:321-332
    DOI: 10.1016/j.ejor.2012.06.045

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    References listed on IDEAS

    1. Kwang-Jae Kim & Dennis K. J. Lin, 2000. "Simultaneous optimization of mechanical properties of steel by maximizing exponential desirability functions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(3), pages 311-325.
    2. S. Madadgar & A. Afshar, 2009. "An Improved Continuous Ant Algorithm for Optimization of Water Resources Problems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(10), pages 2119-2139, August.
    3. Socha, Krzysztof & Dorigo, Marco, 2008. "Ant colony optimization for continuous domains," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1155-1173, March.
    4. Akbar Karimi & Hadi Nobahari & Patrick Siarry, 2010. "Continuous ant colony system and tabu search algorithms hybridized for global minimization of continuous multi-minima functions," Computational Optimization and Applications, Springer, vol. 45(3), pages 639-661, April.
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    Cited by:

    1. Bera, Sasadhar & Mukherjee, Indrajit, 2016. "A multistage and multiple response optimization approach for serial manufacturing system," European Journal of Operational Research, Elsevier, vol. 248(2), pages 444-452.


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