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Jun Sun - One of the best experts on this subject based on the ideXlab platform.

  • a decentralized quantum inspired particle swarm optimization algorithm with cellular structured population
    Information Sciences, 2016
    Co-Authors: Wei Fang, Jun Sun, Huanhuan Chen
    Abstract:

    This paper proposes a decentralized form of quantum-inspired particle swarm optimization (QPSO) with cellular structured population (called cQPSO) for keeping the population diversity and balancing the global and local search. The cQPSO is further improved by re-designing the local attractor in the sub-population (called cQPSO-lbest) in order to accelerate the diffusion of the best solution and thus enhance the performance of cQPSO. The particles in cQPSO and cQPSO-lbest are distributed in a two-dimensional (2D) grid and only allowed to interact with their neighbors according to the specified neighborhood, which plays a role in exploiting the search Space inside the neighborhood. The overlapping particles work for delivering the information among the nearest neighborhoods acting as exploring the search Space with diffusion of solutions during the evolutionary process. Theoretical studies are made to analyze the global convergence of cPSO and cQPSO-lbest based on the theory of Probabilistic Metric Space. We systematically investigate the performance of cQPSO-lbest on 42 benchmark functions with different properties (including unimodal, multimodal, separated, shifted, rotated, noisy, and mis-scaled) and compare with a set of PSO variants with different topologies and swarm-based evolutionary algorithms (EAs). The experimental results demonstrate the better performance of cQPSO-lbest. Moreover, two real-world problems, which are two-dimensional (2D) IIR digital filter design and economic dispatch (ED) problem from power systems area, are used to evaluate cQPSO-lbest and the experimental results verified the advantages of cQPSO-lbest.

  • convergence analysis and improvements of quantum behaved particle swarm optimization
    Information Sciences, 2012
    Co-Authors: Jun Sun, Wei Fang, Vasile Palade, Choihong Lai
    Abstract:

    Motivated by concepts in quantum mechanics and particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO) was proposed as a variant of PSO with better global search ability. Although it has been shown to perform well in finding optimal solutions for many optimization problems, there has so far been little theoretical analysis on its convergence and performance. This paper presents a convergence analysis and performance evaluation of the QPSO algorithm and it also proposes two variants of the QPSO algorithm. First, we investigate in detail the convergence of the QPSO algorithm on a Probabilistic Metric Space and prove that the QPSO algorithm is a form of contraction mapping and can converge to the global optimum. This is the first time that the theory of Probabilistic Metric Spaces has been employed to analyze a stochastic optimization algorithm. We provided a new definition for the convergence rate of a stochastic algorithm as well as definitions for three types of convergence according to the correlations between the convergence rate and the objective function values. With these definitions, the effectiveness of the QPSO is evaluated by computing and analyzing the time complexity and the convergence rate of the algorithm. Then, the QPSO with random mean best position (QPSO-RM) and the QPSO with ranking operator (QPSO-RO) are proposed as two improvements of the QPSO algorithm. Finally, some empirical studies on popular benchmark functions are performed in order to make a full performance evaluation and comparison between QPSO, QPSO-RM, QPSO-RO and other variants of PSO.

Wei Fang - One of the best experts on this subject based on the ideXlab platform.

  • a decentralized quantum inspired particle swarm optimization algorithm with cellular structured population
    Information Sciences, 2016
    Co-Authors: Wei Fang, Jun Sun, Huanhuan Chen
    Abstract:

    This paper proposes a decentralized form of quantum-inspired particle swarm optimization (QPSO) with cellular structured population (called cQPSO) for keeping the population diversity and balancing the global and local search. The cQPSO is further improved by re-designing the local attractor in the sub-population (called cQPSO-lbest) in order to accelerate the diffusion of the best solution and thus enhance the performance of cQPSO. The particles in cQPSO and cQPSO-lbest are distributed in a two-dimensional (2D) grid and only allowed to interact with their neighbors according to the specified neighborhood, which plays a role in exploiting the search Space inside the neighborhood. The overlapping particles work for delivering the information among the nearest neighborhoods acting as exploring the search Space with diffusion of solutions during the evolutionary process. Theoretical studies are made to analyze the global convergence of cPSO and cQPSO-lbest based on the theory of Probabilistic Metric Space. We systematically investigate the performance of cQPSO-lbest on 42 benchmark functions with different properties (including unimodal, multimodal, separated, shifted, rotated, noisy, and mis-scaled) and compare with a set of PSO variants with different topologies and swarm-based evolutionary algorithms (EAs). The experimental results demonstrate the better performance of cQPSO-lbest. Moreover, two real-world problems, which are two-dimensional (2D) IIR digital filter design and economic dispatch (ED) problem from power systems area, are used to evaluate cQPSO-lbest and the experimental results verified the advantages of cQPSO-lbest.

  • convergence analysis and improvements of quantum behaved particle swarm optimization
    Information Sciences, 2012
    Co-Authors: Jun Sun, Wei Fang, Vasile Palade, Choihong Lai
    Abstract:

    Motivated by concepts in quantum mechanics and particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO) was proposed as a variant of PSO with better global search ability. Although it has been shown to perform well in finding optimal solutions for many optimization problems, there has so far been little theoretical analysis on its convergence and performance. This paper presents a convergence analysis and performance evaluation of the QPSO algorithm and it also proposes two variants of the QPSO algorithm. First, we investigate in detail the convergence of the QPSO algorithm on a Probabilistic Metric Space and prove that the QPSO algorithm is a form of contraction mapping and can converge to the global optimum. This is the first time that the theory of Probabilistic Metric Spaces has been employed to analyze a stochastic optimization algorithm. We provided a new definition for the convergence rate of a stochastic algorithm as well as definitions for three types of convergence according to the correlations between the convergence rate and the objective function values. With these definitions, the effectiveness of the QPSO is evaluated by computing and analyzing the time complexity and the convergence rate of the algorithm. Then, the QPSO with random mean best position (QPSO-RM) and the QPSO with ranking operator (QPSO-RO) are proposed as two improvements of the QPSO algorithm. Finally, some empirical studies on popular benchmark functions are performed in order to make a full performance evaluation and comparison between QPSO, QPSO-RM, QPSO-RO and other variants of PSO.

Choihong Lai - One of the best experts on this subject based on the ideXlab platform.

  • convergence analysis and improvements of quantum behaved particle swarm optimization
    Information Sciences, 2012
    Co-Authors: Jun Sun, Wei Fang, Vasile Palade, Choihong Lai
    Abstract:

    Motivated by concepts in quantum mechanics and particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO) was proposed as a variant of PSO with better global search ability. Although it has been shown to perform well in finding optimal solutions for many optimization problems, there has so far been little theoretical analysis on its convergence and performance. This paper presents a convergence analysis and performance evaluation of the QPSO algorithm and it also proposes two variants of the QPSO algorithm. First, we investigate in detail the convergence of the QPSO algorithm on a Probabilistic Metric Space and prove that the QPSO algorithm is a form of contraction mapping and can converge to the global optimum. This is the first time that the theory of Probabilistic Metric Spaces has been employed to analyze a stochastic optimization algorithm. We provided a new definition for the convergence rate of a stochastic algorithm as well as definitions for three types of convergence according to the correlations between the convergence rate and the objective function values. With these definitions, the effectiveness of the QPSO is evaluated by computing and analyzing the time complexity and the convergence rate of the algorithm. Then, the QPSO with random mean best position (QPSO-RM) and the QPSO with ranking operator (QPSO-RO) are proposed as two improvements of the QPSO algorithm. Finally, some empirical studies on popular benchmark functions are performed in order to make a full performance evaluation and comparison between QPSO, QPSO-RM, QPSO-RO and other variants of PSO.

Bruno Nazaret - One of the best experts on this subject based on the ideXlab platform.

  • Metrization of Probabilistic Metric Spaces. Applications to fixed point theory and Arzela-Ascoli type theorem
    2019
    Co-Authors: Mohammed Bachir, Bruno Nazaret
    Abstract:

    Schweizer, Sklar and Thorp proved in 1960 that a Menger Space $(G,D,T)$ under a continuous $t$-norm $T$, induce a natural topology $\tau$ wich is metrizable. We extend this result to any Probabilistic Metric Space $(G,D,\star)$ provided that the triangle function $\star$ is continuous. We prove in this case, that the topological Space $(G,\tau)$ is uniformly homeomorphic to a (deterministic) Metric Space $(G,\sigma_D)$ for some canonical Metric $\sigma_D$ on $G$. As applications, we extend the fixed point theorem of Hicks to Probabilistic Metric Spaces which are not necessarily Menger Spaces and we prove a Probabilistic Arzela-Ascoli type theorem.

  • Probabilistic Arzela-Ascoli theorem
    2019
    Co-Authors: Bachir Mohammed, Bruno Nazaret
    Abstract:

    We prove that, in the Space of all Probabilistic continuous functions from a Probabilistic Metric Space G to the set $\Delta$ + of all cumulative distribution functions vanishing at 0, the Space of all 1-Lipschitz functions is compact if and only if the Space G is compact. This gives a Probabilistic Arzela-Ascoli type Theorem.Comment: arXiv admin note: text overlap with arXiv:1801.0058

  • Metrization of Probabilistic Metric Spaces. Applications to fixed point theory and Arzela-Ascoli type theorem
    2019
    Co-Authors: Bruno Nazaret, Bachir Mohammed, Nazaret Bruno
    Abstract:

    Schweizer, Sklar and Thorp proved in 1960 that a Menger Space $(G,D,T)$ under a continuous $t$-norm $T$, induce a natural topology $\tau$ wich is metrizable. We extend this result to any Probabilistic Metric Space $(G,D,\star)$ provided that the triangle function $\star$ is continuous. We prove in this case, that the topological Space $(G,\tau)$ is uniformly homeomorphic to a (deterministic) Metric Space $(G,\sigma_D)$ for some canonical Metric $\sigma_D$ on $G$. As applications, we extend the fixed point theorem of Hicks to Probabilistic Metric Spaces which are not necessarily Menger Spaces and we prove a Probabilistic Arzela-Ascoli type theorem.Comment: arXiv admin note: text overlap with arXiv:1904.1251

De La Sen, Manuel - One of the best experts on this subject based on the ideXlab platform.

  • Existence of common fixed points for linear combinations of contractive maps in enhanced Probabilistic Metric Spaces
    'Vilnius University Press', 2019
    Co-Authors: Jafari Shahnaz, Shams Maryam, Ibeas Asier, De La Sen, Manuel
    Abstract:

    Altres ajuts: Basque Government for its support through grant IT1207-19In this paper, we introduce the concept of enhanced Probabilistic Metric Space (briefly EPM-Space) as a type of Probabilistic Metric Space. Also, we investigate the existence of fixed points for a (finite or infinite) linear combination of different types of contractive mappings in EPM-Spaces. Furthermore, we investigate about the convergence of sequences (generated by a finite or infinite family of contractive mappings) to a common fixed point. The useful application of this research is the study of the stability of switched dynamic systems, where we study the conditions under which the iterative sequences generated by a (finite or infinite) linear combination of mappings (contractive or not), converge to the fixed point. Also, some examples are given to support the obtained results. In the end, a number of figures give us an overview of the examples

  • Existence of common fixed points for linear combinations of contractive maps in enhanced Probabilistic Metric Spaces
    'Vilnius University Press', 2019
    Co-Authors: Jafari Shahnaz, Shams Maryam, Ibeas Asier, De La Sen, Manuel
    Abstract:

    In this paper, we introduce the concept of enhanced Probabilistic Metric Space (briefly EPM-Space) as a type of Probabilistic Metric Space. Also, we investigate the existence of fixed points for a (finite or infinite) linear combination of different types of contractive mappings in EPM-Spaces. Furthermore, we investigate about the convergence of sequences (generated by a finite or infinite family of contractive mappings) to a common fixed point. The useful application of this research is the study of the stability of switched dynamic systems, where we study the conditions under which the iterative sequences generated by a (finite or infinite) linear combination of mappings (contractive or not), converge to the fixed point. Also, some examples are given to support the obtained results. In the end, a number of figures give us an overview of the examples