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A Review of the Use of Quasi-random Number Generators to Initialize the Population in Meta-heuristic Algorithms

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Abstract

Different computational tools require random numbers to operate; this is the case with Meta-heuristic Algorithms (MA's). Many studies in the literature have demonstrated that the spatial distribution of the first generation of candidate solutions has a significant influence on the effectiveness of the MA’s. This article tests and analyzes the effect of various types of initializations, specifically contrasting two classes: Low Discrepancy Sequences (LDS) such as Halton, Sobel, Hammersley, and Latin Hypercube and Pseudo-Random Number Generators (PRNG) initialization processes of popular state−of-the−art algorithms as Particle Swarm Optimization (PSO), Differential Evolution (DE), Genetic Algorithms (GA), and Stochastic Fractal Search (SFS). Experimental results are compared and analyzed, showing that, like the butterfly effect of chaos theory, small changes in the initialization of an optimization algorithm with random processes of different nature can induce significantly different results.

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Authors and Affiliations

  1. División de Tecnologías para la Integración Ciber-Humana, Universidad de Guadalajara, CUCEI, Av. Revolución 1500, Guadalajara, Jal, Mexico

    Mario A. Navarro, Diego Oliva, Alfonso Ramos-Michel, Bernardo Morales-Castañeda, Daniel Zaldívar & Alberto Luque−Chang

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  1. Mario A. Navarro
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  2. Diego Oliva
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  3. Alfonso Ramos-Michel
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Correspondence to Diego Oliva.

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Appendix A

Appendix A

The set of functions used, taken from the CEC17 [54], are shown in Table 13 and are presented in that form since every optimization problem must be presented as a black box problem. Notice that the same set of functions was used for 30 and 50 dimensions..

Table 13 The CEC17 benchmark functions
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Navarro, M.A., Oliva, D., Ramos-Michel, A. et al. A Review of the Use of Quasi-random Number Generators to Initialize the Population in Meta-heuristic Algorithms. Arch Computat Methods Eng 29, 5149–5184 (2022). https://doi.org/10.1007/s11831-022-09759-y

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