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IEEE Congress on Evolutionary Computation (CEC)

Quantum bacterial foraging optimization algorithm

Fei Li, Yuting Zhang, Jiulong Wu, Haibo Li

Published Jul 1, 2014• 14 citations
Publisher

Abstract

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.

DOI
10.1109/cec.2014.6900230

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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.
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.
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.
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.
Aiming at the shortcoming of optimization problems in continuous space based on ant colony optimization which is easy to fall into local optimums and has a slow convergence rate,a novel quantum ant colony optimization algorithm is presented.In this algorithm,each ant position is represented by a group of quantum bits;a new quantum rotation gates are designed to update the position of the ant so as to enable the ant to move.Some quantum bits are mutated by quantum non-gate so as to increase the variety of ant positions.It not only proves the convergence of the proposed algorithms through theoretical analysis,but also demonstrates that the algorithm can double searching space,maintain better population diversity,rapider convergence speed and global optimal ability than the classical ant colony algorithm by simulation experiments.
A novel self-adaptive Ant Colony Optimization algorithm based on Quantum mechanism for Traveling salesman problem(TQACO) is proposed. Firstly, initializing the population of the ant colony with superposition of Q-bit, Secondly, using self-adaptive operator, namely in prophase we use higher probability to explore more search space and to collect useful global information; otherwise in anaphase we use higher probability to accelerate convergence. This mechanism offers the ability to escape from local optima and can self-regulate the production of diverse antibodies. Because of the quantum superposition and rotation it can maintain quite nicely the population diversity than the classical evolutionary algorithm, because of the self-adaptive operator it can obtain more optimal solution and the solution quality is improved significantly. TSP benchmark instances Chn144 results demonstrate the superiority of TQACO in this paper.
The quantum ant colony algorithm (QACO) is explored as a solution to the traveling salesman problem (TSP), targeting inefficiencies such as slow convergence and local optima entrapment found in traditional ant colony optimization (ACO) methods. By integrating quantum computing elements, specifically quantum rotation gates and qubits, into the ACO framework, QACO demonstrates enhanced efficiency and faster convergence. This paper delves into the foundational principles of quantum computing and their application to refine ACO, effectively solving the TSP. An in-depth analysis is provided, showcasing QACO's advantages over traditional ACO through empirical examples. These examples illustrate QACO's potential to improve path planning for applications within the rapidly growing e-commerce and logistics sectors. The integration of quantum mechanisms facilitates a more dynamic pheromone update process, which significantly reduces the likelihood of premature convergence and enhances solution quality in complex optimization scenarios. This advancement indicates a promising direction for future research in algorithmic optimization in both theoretical and practical applications.