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Experimental study on population-based incremental learning algorithms for dynamic optimization problems

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Abstract

Evolutionary algorithms have been widely used for stationary optimization problems. However, the environments of real world problems are often dynamic. This seriously challenges traditional evolutionary algorithms. In this paper, the application of population-based incremental learning (PBIL) algorithms, a class of evolutionary algorithms, for dynamic problems is investigated. Inspired by the complementarity mechanism in nature a Dual PBIL is proposed, which operates on two probability vectors that are dual to each other with respect to the central point in the genotype space. A diversity maintaining technique of combining the central probability vector into PBIL is also proposed to improve PBIL’s adaptability in dynamic environments. In this paper, a new dynamic problem generator that can create required dynamics from any binary-encoded stationary problem is also formalized. Using this generator, a series of dynamic problems were systematically constructed from several benchmark stationary problems and an experimental study was carried out to compare the performance of several PBIL algorithms and two variants of standard genetic algorithm. Based on the experimental results, we carried out algorithm performance analysis regarding the weakness and strength of studied PBIL algorithms and identified several potential improvements to PBIL for dynamic optimization problems.

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Notes

  1. For the convenience of description in this paper we will call the probability vector that has 0.5 for all of its entries central probability vector or just central vector because it represents the central point in the genotype space.

  2. For each bit position of a solution, assuming binary encoded, if a random created real number in the range of [0.0, 1.0] is less than the probability value of corresponding element in the probability vector, the bit is set to 1 (or 0), otherwise it is set to 0 (or 1 respectively).

  3. For the convenience of analyzing experimental results on dynamic problems, we herein call the first period stationary since the behavior of an algorithm on a dynamic problem during this period is the same as that on the relevant stationary problem. And the other nine periods are called dynamic.

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Acknowledgments

The authors would like to thank Dr. Jürgen Branke and the anonymous reviewers for their thoughtful suggestions and helpful comments. Shengxiang Yang was supported by UK EPSRC under Grant GR/S79718/01.

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  1. Department of Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, UK

    Shengxiang Yang

  2. School of Computer Science, University of Birmingham Edgbaston, Birmingham, B15 2TT, UK

    Xin Yao

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  1. Shengxiang Yang
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Correspondence to Shengxiang Yang.

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Yang, S., Yao, X. Experimental study on population-based incremental learning algorithms for dynamic optimization problems. Soft Comput 9, 815–834 (2005). https://doi.org/10.1007/s00500-004-0422-3

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