Soft Computing

, Volume 22, Issue 7, pp 2139–2158 | Cite as

Adaptive racing ranking-based immune optimization approach solving multi-objective expected value programming

  • Kai Yang
  • Zhuhong Zhang
  • Jiaxuan Lu
Methodologies and Application


This work investigates a bio-inspired adaptive sampling immune optimization approach to solve a general kind of nonlinear multi-objective expected value programming without any prior noise distribution. A useful lower bound estimate is first developed to restrict the sample sizes of random variables. Second, an adaptive racing ranking scheme is designed to identify those valuable individuals in the current population, by which high-quality individuals in the process of solution search can acquire large sample sizes and high importance levels. Thereafter, an immune-inspired optimization approach is constructed to seek \(\varepsilon \)-Pareto optimal solutions, depending on a novel polymerization degree model. Comparative experiments have validated that the proposed approach with high efficiency is a competitive optimizer.


Immune optimization Multi-objective expected value programming Sample bound estimate Adaptive racing ranking Computational complexity 



This work is supported by National Natural Science Foundation NSFC (61563009).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.College of Computer Science & TechnologyGuizhou UniversityGuiyangChina
  2. 2.Department of Big Data Science and Engineering, College of Big Data and Information EngineeringGuizhou UniversityGuiyangChina

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