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IEEE Access

A Modified Quantum Bacterial Foraging Algorithm for Parameters Identification of Fractional-Order System

Lu Liu, Liang Shan, Yuewei Dai, Cheng‐Lin Liu, Zhidong Qi

Published Jan 1, 2018• 16 citations
Publisher

Abstract

For many physical systems, the fractional-order system can describe the dynamics more accurately comparing with the integer-order system. However, its parameters, which include not only the identification of model coefficients but also the estimation of fractional orders, are more difficult to be identified. This paper proposes a modified quantum bacterial foraging algorithm (MQBFA) for parameters identification of the fractional-order system, and the MQBFA algorithm is a relatively new issue in recent years with strong engineering backgrounds. Not only does the proposed MQBFA algorithm apply the real number encoding of the single gene to effectively perform encoding, but it also utilizes a continuously varying rotation angle to update the rotation gate. First, a real number encoding of the single gene is designed to improve the searching efficiency of the algorithm. Second, an improved quantum rotation angle is applied to update the rotation angle continuously and adaptively. Third, the modificatory factor of probability amplitude is introduced to enrich the population diversity. In addition, to prevent the generation of invariant solutions in the early stage of quantum evolution, probability of optimal rotation angle is presented. Furthermore, the convergence of the proposed algorithm is analyzed. Based on several benchmark functions and parameters identification of the fractional-order system, simulation results and comparisons demonstrate the effectiveness of the proposed MQBFA algorithm.

DOI
10.1109/access.2018.2791976

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This paper proposes a novel swarm intelligence optimization method which integrates bacterial foraging optimization (BFO) with quantum computing, called quantum bacterial foraging optimization (QBFO) algorithm. In QBFO, a multi-qubit which can represent a linear superposition of states in search space probabilistically is used to represent a bacterium, so that the quantum bacteria representation has a better characteristic of population diversity. A quantum rotation gate is designed to simulate the chemotactic step to drive the bacteria toward better solutions. Several tests are conducted based on benchmark functions including multi-peak function to evaluate optimization performance of the proposed algorithm. The numeric results show that the proposed QBFO has more powerful properties in convergence rate, stability and the ability of searching for the global optimal solution than the original BFO and quantum genetic algorithm. In addition, we applied our proposed QBFO to solve the traveling salesman problem, which is a well-known NP-hard problem in combinatorial optimization. The results indicate that the proposed QBFO shows better convergence behavior without premature convergence, and has more powerful properties in convergence rate, stability and the ability of searching for the global optimal solution, as compared to ant colony optimization algorithm and quantum genetic algorithm.
This article develops a quantum bacterial foraging optimization (QBFO) algorithm, a quantum intelligence algorithm based on quantum computing and bacterial foraging optimization (BFO), with application in MIMO system optimization designs. In QBFO, a multiqubit is used to represent a bacterium, and a quantum rotation gate is used to mimic chemotaxis. Because the quantum bacterium with multiqubit has the advantage that it can represent a linear superposition of states (binary solutions) in search space probabilistically, the proposed QBFO algorithms shows better performance on solving combinatorial optimization problems than its classical counterpart BFO and Quantum Genetic Algorithm (QGA), especially for parallel non-gradient optimization. A sparse channel estimation scheme based on QBFO with adaptive phase rotation (AQBFO) in 3D MIMO system is proposed, and simulation results show that AQBFO achieved a better performance than existing algorithms including least squares (LS), iteratively reweighted least squares (IRLS), matching pursuit (MP), and orthogonal matching pursuit (OMP). We further improve some critical aspects such as reproduction and dispersal processes of AQBFO, propose an improved IQBFO algorithm, and apply it for interference coordination in 3D multi-cell multi-user MIMO systems, aiming to maximize the spectral efficiency. It considers user fairness and jointly optimizes cell-center and cell-edge user specific antenna downtilts and power to maximize each user's sum rate. This problem is a combinatorial non-convex optimization problem that cannot be solved by the traditional Karush-Kuhn-Tucker Lagrangian algorithm whereas the IQBFO algorithm solves it effectively.
Bacterial Foraging Optimization(BFO) algorithm is simple,robust and has global search capability.However,the speed of BFO is slow and it often seems to fall into local optimum.To improve the search capabilities of BFO and avoid its premature convergence,a new type of Quantum Bacterial Foraging Optimization(QBFO) algorithm is proposed by integrating binary code quantum evolutionary algorithm into BFO.Quantum triploid chromosome is used to represent bacteria,and Quantum Rotation Gate(QRG) is used to update bacteria's state.To test the new algorithm's optimization performance,a research based on benchmark functions is conducted.The results indicate that the new type of QBFO shows better results than BFO and quantum genetic algorithm in convergence rate,stability and looking for the global optimal solutions weather common function or multi-peak function.
A quantum genetic algorithm based on real number encoding and gradient of fitness function is proposed in this paper.Chromosomes comprised of quantum bits are updated by quantum rotating gates,and are mutated by quantum non-gate.A convenient method to choose the direction of rotation angle of quantum rotation gate is proposed.The computation formula of the rotation angle value is constructed by the gradients of fitness function.In this method,two probability amplitude of each quantum bit are regarded as two coordinate genes;each chromosome contains two chains of genes;and each chain of genes represents an optimization result.This method can accelerate convergence process and increase successful probability with the same number of chromosomes.Its application to fuzzy controller parameters optimization illustrates that the approach is superior to common quantum genetic algorithm in searching ability.
In order to optimize the numerical functions with the continuous solution space, a new phase angle encoded quantum evolutionary algorithm(PAQEA) is proposed based on the quantum computing and real encoded evolutionary algorithm. In PAQEA, a quantum chromosome with probabilistic representation can represent all the feasible solution probabilistically, and the dynamic quantum rotation gate is used to update chromosomes. Thus, the population diversity and directional evolution realize a good balance between exploration and exploitation. Theoretical analysis shows that the PAQEA is a global convergence algorithm. Simulation results show that the algorithm is suitable for the optimization of complex numerical functions, and has the characteristics of rapider convergence, powerful global search capability and better stability.
The current quantum evolution algorithms have slow convergence rate and poor robustness. In order to overcome the two shortages, a novel self-adaptive quantum genetic algorithm is proposed. Firstly, the new algorithm adopts an encoding method which is based on the Bloch spherical coordinates. Secondly, in the process of searching the optimal solution, a self-adaptive factor is introduced to reflect the relative change rates which are relative to the difference of the best individual's objective fitness between the parent generation and the child generation. The convergence rate and direction of the algorithm can be improved by adjusting the factor. The rules of updating the rotation angle and are constructed. Finally, using hadamard gate of the quantum in the mutation strategy, it can enhance the diversity of population. The simulation results of the optimizing problem of the multidimensional complex functions show that the new algorithm has not only avoided effectively the premature and improved the convergence rate, but also boosted strikingly efficiency and stability robustness of the algorithm.