A novel hybrid metaheuristic optimization method: hypercube natural aggregation algorithm

  • Oscar Maciel
  • Arturo Valdivia
  • Diego OlivaEmail author
  • Erik Cuevas
  • Daniel Zaldívar
  • Marco Pérez-Cisneros
Methodologies and Application


The natural aggregation algorithm (NAA) is a new efficient population-based optimizer. The NAA has a competent performance when compared to other well-established optimizers. However, a problem of concern is NAA lack of exploitation in its local search. In this article, we propose an improved version of NAA. The modifications made are: hypercubes with displacement and shrink mechanism applied in each shelter, we designed a new movement operator to search inside the hypercubes, an improved readjustment of the algorithm’s parameters and “leave shelter” formula of NAA, to better mimic the aggregation behavior. To prove the effectiveness of the modified hypercube natural aggregation algorithm (HYNAA), we compared with classics optimizers, such as PSO, DE and ABC, state of the art, such as CMA-ES, MSA and NAA himself with a benchmark of 28 functions. The said functions consist of five unimodal, 19 multimodal and four hybrids, and we compared them on 30, 50 and 100 dimensions. We also made extra comparisons against NAA in 500 and 1000 dimensions to contrast the ability of the hypercubes to reduce the dimensional complexity. Finally, we tested two trajectory optimization problems. Experimental results and statistical tests demonstrate that the performance of HYNAA is significantly better than that of other optimizers.

Graphic abstract


Hybrid optimization techniques Natural aggregation algorithm (NAA) Hypercube optimization (HO) Metaheuristic optimization 


Compliance with ethical standards

Conflict of interest

It is to specifically state that “No Competing interests are at stake and there is No Conflict of Interest” with other people or organizations that could inappropriately influence or bias the content of the paper.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.División de Electrónica y ComputaciónUniversidad de Guadalajara, CUCEIGuadalajaraMexico

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