Neural Processing Letters

, Volume 48, Issue 1, pp 517–556 | Cite as

A Multimodal Optimization Algorithm Inspired by the States of Matter

  • Erik Cuevas
  • Adolfo Reyna-Orta
  • Margarita-Arimatea Díaz-Cortes


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.


Metaheuristic algorithms Multimodal optimization Evolutionary algorithms Nature-inspired algorithms 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Departamento de ElectrónicaUniversidad de Guadalajara, CUCEIGuadalajaraMexico
  2. 2.Instituto de Ingeniería, UABCBulevard Benito Juárez y calleMexicaliMexico
  3. 3.Institut für InformatikFU-BerlinBerlinGermany

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