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References

This page lists key academic publications and references that form the theoretical foundation of PySNE, including the Spiral Optimization Algorithm (SPO), clustering techniques, and their application to finding multiple roots of nonlinear systems.

Primary Algorithm References

1. Spiral Dynamics Inspired Optimization (SPO)

The original paper introducing the Spiral Dynamics Inspired Optimization algorithm:

Tamura, K., & Yasuda, K. (2011). Spiral Dynamics Inspired Optimization. Journal of Advanced Computational Intelligence and Intelligent Informatics, 15(8), 1116-1122.

  • Abstract: This paper proposes a new concept of a multi-point search algorithm for global optimization. The proposed algorithm is inspired by spiral dynamics, which is a deterministic model of logarithmic spirals.
  • Links: DOI: 10.20965/jaciii.2011.p1116

2. SPO with Clustering for Systems of Nonlinear Equations

The pioneering work that integrated clustering with SPO to find all solutions of a system of nonlinear equations:

Sidarto, K. A., & Kania, A. (2015). Finding All Solutions of Systems of Nonlinear Equations Using Spiral Dynamics Inspired Optimization with Clustering. Journal of Advanced Computational Intelligence and Intelligent Informatics, 19(5), 697-707.

  • Abstract: Finding all solutions of systems of nonlinear equations is a challenging task. This paper presents a hybrid method combining the Spiral Dynamics Inspired Optimization (SPO) algorithm with a clustering technique to find all real solutions in a bounded domain.
  • Links: DOI: 10.20965/jaciii.2015.p0697

3. SPO with Clustering for Multimodal Optimization

Further extension of the methodology to find multiple local and global minima:

Sidarto, K. A., Kania, A., & Sumarti, N. (2017). Finding Multiple Solutions of Multimodal Optimization Using Spiral Optimization Algorithm with Clustering. MENDEL, 23(1), 97-104.

  • Abstract: This paper discusses the implementation of a Spiral Optimization Algorithm (SPO) combined with a clustering technique to locate all global and local optimum of multimodal optimization functions.
  • Links: DOI: 10.13164/mendel.2017.1.097

Supplementary References

Sobol Sequence and Quasi-Monte Carlo Initialization

  • Joe, S., & Kuo, F. Y. (2008). Constructing Sobol sequences with Better Two-Dimensional Projections. SIAM Journal on Scientific Computing, 30(5), 2635-2654. DOI: 10.1137/070709359