Harmonic competition: A self-organizing multiple criteria optimization

Yasuo Matsuyama*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    28 Citations (Scopus)


    Harmonic competition is a learning strategy based upon winner-take-all or winner-take-quota with respect to a composite of heterogeneous subcosts. This learning is unsupervised and organizes itself. The subcosts may conflict with each other. Thus, the total learning system realizes a self-organizing multiple criteria optimization. The subcosts are combined additively and multiplicatively using adjusting parameters. For such a total cost, a general successive learning algorithm is derived first. Then, specific problems in the Euclidian space are addressed. Vector quantization with various constraints and traveling salesperson problems are selected as test problems. The former is a typical class of problems where the number of neurons is less than that of the data. The latter is an opposite case. Duality exists in these two classes. In both cases, the combination parameters of the subcosts show wide dynamic ranges in the course of learning. It is possible, however, to decide the parameter control from the structure of the total cost. This method finds a preferred solution from the Pareto optimal set of the multiple object optimization. Controlled mutations motivated by genetic algorithms are proved to be effective in finding near-optimal solutions. All results show significance of the additional constraints and the effectiveness of the dynamic parameter control.

    Original languageEnglish
    Pages (from-to)652-668
    Number of pages17
    JournalIEEE Transactions on Neural Networks
    Issue number3
    Publication statusPublished - 1996

    ASJC Scopus subject areas

    • Control and Systems Engineering
    • Theoretical Computer Science
    • Electrical and Electronic Engineering
    • Artificial Intelligence
    • Computational Theory and Mathematics
    • Hardware and Architecture


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