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Adaptive sampling immune algorithm solving joint chance-constrained programming

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Abstract

This work investigates one immune optimization algorithm in uncertain environments, solving linear or nonlinear joint chance-constrained programming with a general distribution of the random vector. In this algorithm, an a priori lower bound estimate is developed to deal with one joint chance constraint, while the scheme of adaptive sampling is designed to make empirically better antibodies in the current population acquire larger sample sizes in terms of our sample-allocation rule. Relying upon several simplified immune metaphors in the immune system, we design two immune operators of dynamic proliferation and adaptive mutation. The first picks up those diverse antibodies to achieve proliferation according to a dynamical suppression radius index, which can ensure empirically potential antibodies more clones, and reduce noisy influence to the optimized quality, and the second is a module of genetic diversity, which exploits those valuable regions and finds those diverse and excellent antibodies. Theoretically, the proposed approach is demonstrated to be convergent. Experimentally, the statistical results show that the approach can obtain satisfactory performances including the optimized quality, noisy suppression and efficiency.

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Authors and Affiliations

  1. Institute of System Science & Information Technology, College of Science, Guizhou University, Guiyang Guizhou, 550025, China

    Zhuhong Zhang, Lei Wang & Min Liao

Authors
  1. Zhuhong Zhang
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  2. Lei Wang
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  3. Min Liao
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Corresponding author

Correspondence to Zhuhong Zhang.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 61065010), and the Doctoral Fund of Ministry of Education of China (No. 20125201110003).

Zhuhong ZHANG received his M.S. degree from Department of Mathematics, Guizhou University, China, in 1998, and Ph.D. degree from College of Automation, Chongqing University, China, in 2004. Currently, he is a professor at the Guizhou University. His main areas of interests include uncertain programming, evolutionary algorithms, immune optimization, and signal simulation.

Lei WANG received his M.S. degree from Department of Mathematics, Guizhou University, China, in 2012. Currently, his main areas of interests include stochastic programming and immune optimization.

Min LIAO received his M.S. degree from Department of Mathematics, Guizhou University, China, in 2012. Currently, his main areas of interests include dynamic optimization and immune optimization.

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Zhang, Z., Wang, L. & Liao, M. Adaptive sampling immune algorithm solving joint chance-constrained programming. J. Control Theory Appl. 11, 237–246 (2013). https://doi.org/10.1007/s11768-013-1186-z

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  • DOI: https://doi.org/10.1007/s11768-013-1186-z

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