Abstract
Memorizing the past information for later environments is an effective and widely employed approach to optimize dynamic problems. Although the existing explicit memories for dynamic optimization differ widely in the literature, all of them organize memory entries in a linear list. This naive structure leads to problems, such as heavy computational overhead and small memory capacity, and thus restricts the performance of the memories. In this paper, the binary space partition tree is adopted to organize the memory entries, and then a memory tree is constructed. The memory tree partitions the search space into regions. In order to make use of the memory tree, a neighbor shift strategy is proposed. When a new individual is generated in a region that has never been visited since the last change, the new individual is shifted to the neighboring memory individual of that region, if it is less fit than the memory individual. The proposed approach can be easily combined with many population-based algorithms for dynamic optimization in the real space. As examples, the proposed approach was combined with a basic particle swarm optimizer and two state-of-the-art dynamic optimizers. The experimental results showed that it significantly enhanced the performance of the three optimizers on various test problems. The proposed approach demonstrates the importance of memory structure in memory approaches.
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Notes
The cycle length means is the number of states or problem instances in a cyclic dynamic problem.
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Acknowledgments
This work is partly supported by the 2006-2007 Excellent Young and Middle-aged Academic Leader Development Program of Anhui Province Research Experiment Bases. We would like to thank Dr. Stefan Bird and Dr. Changhe Li for the source codes of SPSO and CPSO, respectively. We also would like to express our great appreciation to the anonymous reviewers for their valuable comments which contribute a lot to the improvement of the paper.
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Communicated by A. Castiglione.
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Zhu, T., Luo, W. & Yue, L. Dynamic optimization facilitated by the memory tree. Soft Comput 19, 547–566 (2015). https://doi.org/10.1007/s00500-014-1273-1
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DOI: https://doi.org/10.1007/s00500-014-1273-1