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A Multimodal Optimization Algorithm Inspired by the States of Matter

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Abstract

The main objective of multi-modal optimization is to find multiple global and local optima for a problem in only one execution. Detecting multiple solutions to a multi-modal optimization formulation is especially useful in engineering, since the best solution could not represent the best realizable due to various practical restrictions. The States of Matter Search (SMS) is a recently proposed stochastic optimization technique. Although SMS is highly effective in locating single global optimum, it fails in providing multiple solutions within a single execution. To overcome this inconvenience, a new multimodal optimization algorithm called the Multi-modal States of Matter Search (MSMS) in introduced. Under MSMS, the original SMS is enhanced with new multimodal characteristics by means of: (1) the definition of a memory mechanism to efficiently register promising local optima according to their fitness values and the distance to other probable high quality solutions; (2) the modification of the original SMS optimization strategy to accelerate the detection of new local minima; and (3) the inclusion of a depuration procedure at the end of each state to eliminate duplicated memory elements. The performance of the proposed approach is compared to several state-of-the-art multimodal optimization algorithms considering a benchmark suite of fourteen multimodal problems. The results confirm that the proposed method achieves the best balance over its counterparts regarding accuracy and computational cost.

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Author information

Authors and Affiliations

  1. Departamento de Electrónica, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, C.P. 44430, Guadalajara, JAL, Mexico

    Erik Cuevas

  2. Instituto de Ingeniería, UABC, Bulevard Benito Juárez y calle, de la Normal s/n, C.P. 21280, Mexicali, Mexico

    Adolfo Reyna-Orta

  3. Institut für Informatik, FU-Berlin, Arnimallee 7, 14195, Berlin, Germany

    Margarita-Arimatea Díaz-Cortes

Authors
  1. Erik Cuevas
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  2. Adolfo Reyna-Orta
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  3. Margarita-Arimatea Díaz-Cortes
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Corresponding author

Correspondence to Erik Cuevas.

Appendix A: List of Benchmark Functions

Appendix A: List of Benchmark Functions

See Tables 10 and 11.

Table 10 Low dimensional test functions used in the experimental study
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Table 11 Composite test functions used in the experimental study
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Cuevas, E., Reyna-Orta, A. & Díaz-Cortes, MA. A Multimodal Optimization Algorithm Inspired by the States of Matter. Neural Process Lett 48, 517–556 (2018). https://doi.org/10.1007/s11063-017-9750-z

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