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An optimization algorithm inspired by the States of Matter that improves the balance between exploration and exploitation

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Abstract

The ability of an Evolutionary Algorithm (EA) to find a global optimal solution depends on its capacity to find a good rate between exploitation of found-so-far elements and exploration of the search space. Inspired by natural phenomena, researchers have developed many successful evolutionary algorithms which, at original versions, define operators that mimic the way nature solves complex problems, with no actual consideration of the exploration-exploitation balance. In this paper, a novel nature-inspired algorithm called the States of Matter Search (SMS) is introduced. The SMS algorithm is based on the simulation of the states of matter phenomenon. In SMS, individuals emulate molecules which interact to each other by using evolutionary operations which are based on the physical principles of the thermal-energy motion mechanism. The algorithm is devised by considering each state of matter at one different exploration–exploitation ratio. The evolutionary process is divided into three phases which emulate the three states of matter: gas, liquid and solid. In each state, molecules (individuals) exhibit different movement capacities. Beginning from the gas state (pure exploration), the algorithm modifies the intensities of exploration and exploitation until the solid state (pure exploitation) is reached. As a result, the approach can substantially improve the balance between exploration–exploitation, yet preserving the good search capabilities of an evolutionary approach. To illustrate the proficiency and robustness of the proposed algorithm, it is compared to other well-known evolutionary methods including novel variants that incorporate diversity preservation schemes. The comparison examines several standard benchmark functions which are commonly considered within the EA field. Experimental results show that the proposed method achieves a good performance in comparison to its counterparts as a consequence of its better exploration–exploitation balance.

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Acknowledgements

The proposed algorithm is part of the optimization system used by a biped robot supported under the grant CONACYT CB 181053.

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Authors and Affiliations

  1. Departamento de Electrónica, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, Guadalajara, Jal, México

    Erik Cuevas & Alonso Echavarría

  2. Institut für Nachrichtentechnik, Technische Universität Braunschweig, Schleinitzstrae 22, 38106, Braunschweig, Germany

    Marte A. Ramírez-Ortegón

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  1. Erik Cuevas
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  2. Alonso Echavarría
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  3. Marte A. Ramírez-Ortegón
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Correspondence to Erik Cuevas.

Appendix A: List of benchmark functions

Appendix A: List of benchmark functions

Table 8 Unimodal test functions
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Table 9 Multimodal test functions
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Table 10 Multimodal test functions with fixed dimensions
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Table 11 Set of representative GECCO functions
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Cuevas, E., Echavarría, A. & Ramírez-Ortegón, M.A. An optimization algorithm inspired by the States of Matter that improves the balance between exploration and exploitation. Appl Intell 40, 256–272 (2014). https://doi.org/10.1007/s10489-013-0458-0

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