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An exploratory research of elitist probability schema and its applications in evolutionary algorithms

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Abstract

An important problem in the study of evolutionary algorithms is how to continuously predict promising solutions while simultaneously escaping from local optima. In this paper, we propose an elitist probability schema (EPS) for the first time, to the best of our knowledge. Our schema is an index of binary strings that expresses the similarity of an elitist population at every string position. EPS expresses the accumulative effect of fitness selection with respect to the coding similarity of the population. For each generation, EPS can quantify the coding similarity of the population objectively and quickly. One of our key innovations is that EPS can continuously predict promising solutions while simultaneously escaping from local optima in most cases. To demonstrate the abilities of the EPS, we designed an elitist probability schema genetic algorithm and an elitist probability schema compact genetic algorithm. These algorithms are estimations of distribution algorithms (EDAs). We provided a fair comparison with the persistent elitist compact genetic algorithm (PeCGA), quantum-inspired evolutionary algorithm (QEA), and particle swarm optimization (PSO) for the 0–1 knapsack problem. The proposed algorithms converged quicker than PeCGA, QEA, and PSO, especially for the large knapsack problem. Furthermore, the computation time of the proposed algorithms was less than some EDAs that are based on building explicit probability models, and was approximately the same as QEA and PSO. This is acceptable for evolutionary algorithms, and satisfactory for EDAs. The proposed algorithms are successful with respect to convergence performance and computation time, which implies that EPS is satisfactory.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their careful reading and constructive comments. This work was supported by National Natural Science Foundation of China (Grant No. 61272518, 61272516, 61170275), National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant No. 2012ZX03001001-002), and Guangdong Provincial Science and Technology Project (Grant No. 2011B090400433).

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Authors and Affiliations

  1. School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, China

    Hong-Guang Zhang, Yuan-An Liu, Bi-Hua Tang & Kai-Ming Liu

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  1. Hong-Guang Zhang
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  2. Yuan-An Liu
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  4. Kai-Ming Liu
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Correspondence to Hong-Guang Zhang.

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Zhang, HG., Liu, YA., Tang, BH. et al. An exploratory research of elitist probability schema and its applications in evolutionary algorithms. Appl Intell 40, 695–709 (2014). https://doi.org/10.1007/s10489-013-0494-9

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