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International Journal of Multimedia and Ubiquitous Engineering

An Improved Quantum Ant Colony Optimization Algorithm for Solving Complex Function Problems

Changai Chen, Yanwen Xu

Published Nov 30, 2015• 2 citations
Publisher

Abstract

In order to improve the slow convergence speed and avoid falling into the local optimum in ant colony optimization algorithm, an improved quantum ant colony optimization (IMAQACO) algorithm based on combing quantum evolutionary algorithm with ant colony optimization algorithm is proposed for solving complex function problems in this paper.In the IMAQACO algorithm, the quantum state vectors are used to represent the pheromone, the adaptively dynamical updating strategy is used to control pheromone evaporation factor, the quantum rotation gate is used to realize the ant movement and change the convergence tend of quantum probability amplitude, quantum non-gate is used to realize ant location variation, so the IMAQACO algorithm has better global search ability and population diversity than ACO algorithm.In order to test the optimization performance of IMAQACO algorithm, several benchmark functions are selected in here.The tested results indicate that the IMAQACO can effectively improve the convergence speed and avoid falling into the local optimum, and has a stronger global optimization ability and higher convergence speed in solving complex function problems.

DOI
10.14257/ijmue.2015.10.11.19

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In order to improve the slow convergence speed and avoid falling into the local optimum in ant colony optimization algorithm, an improved quantum ant colony optimization (IMAQACO) algorithm based on combing quantum evolutionary algorithm with ant colony optimization algorithm is proposed for solving complex function problems in this paper.In the IMAQACO algorithm, the quantum state vectors are used to represent the pheromone, the adaptively dynamical updating strategy is used to control pheromone evaporation factor, the quantum rotation gate is used to realize the ant movement and change the convergence tend of quantum probability amplitude, quantum non-gate is used to realize ant location variation, so the IMAQACO algorithm has better global search ability and population diversity than ACO algorithm.In order to test the optimization performance of IMAQACO algorithm, several benchmark functions are selected in here.The tested results indicate that the IMAQACO can effectively improve the convergence speed and avoid falling into the local optimum, and has a stronger global optimization ability and higher convergence speed in solving complex function problems.
The Ant Colony Algorithm is an effective method for solving combinatorial optimization problems. However, in practical applications, there also exist issues such as slow convergence speed and easy to fall into local extremum. This paper proposes an improved Quantum Ant Colony Algorithm based on Bloch coordinates by combining Quantum Evolutionary Algorithm with Ant Colony Algorithm. In this algorithm, the current position information of ants is represented by the Bloch spherical coordinates of qubits; position update, position variation and random behavior of ants are all achieved with quantum rotation gate. Simulations of function extremum problem, TSP problem and QoS multicast routing problem were conducted, the results indicated that the algorithm could overcome prematurity, with a faster convergence speed and higher solution accuracy.
Aiming at the Traveling Salesman Problem based on ant colony optimization which is easy to fall into local optimums and has a slow convergence rate,a hybrid quantum ant colony optimization algorithm is presented.In this algorithm,the pheromone on each path is encoded by a group of quantum bits,the quantum rotation gate and ant's tour are used to update the pheromone so as to accelerate its convergence speed.To avoid the search falling into local optimum,the new neighborhood exchange strategy is designed to improve solution efficiency.Some cases from the TSP library(TSPLIB)are used to experiment,the results show that the algorithm has rapider convergence speed and higher accuracy than the classical ant colony algorithm.
According to extension of ant colony optimization converging slowly and easily falling into the local optimum,some improved strategies were presented.First,a group of quantum bits which represent the position of the ant increased the diversity of the solution.Secondly,some quantum bits were mutated by a quantum non-gate so as to avoid ants involving in the local optimum.Thirdly,quantum bits of the ant were updated by quantum rotation gates and Gaussian kernel functions so as to find the optimization in continuous space.Lastly,in order to obtain the optimal solution quickly and increase the direction,the weight of each solution in the memory was improved by the importance of the weight.The simulation and comparison on the many two-dimensional and multi-dimensional continuous functions prove the effectiveness of the algorithm.
The algorithm in this paper is based on the combination of Quantum Evolutionary algorithm (QEA) and Ant Colony System (ACS), a new algorithm, Quantum Ant Colony Algorithm (QACA) is proposed in this paper. The core is that Q-bit and quantum rotation gate adopted in QEA are introduced into ACS to represent and update the pheromone respectively, so it has better diversity and global search capacity. The experimental result demonstrates that QACA can get better solutions to some Traveling Salesman Problems (TSP) than the solutions given in TSPLIB
For the low efficiency and poor performance of the ant colony algorithm in solving TSP problems, a new quantum ant colony algorithm proposed. The models of probability selection and pheromone are redefined, integrated with the quantum information intensity factor; The factor updated by quantum rotating gate according to iteration process; Some important parameters are self-adapted controlled at the same time; And 3-opt is used to further local optimization. Stimulation shows the performance is greatly improved.
The logistics distribution route problem is a NP problem which possesses important practical value. A novel optimization method of logistics distribution route is proposed based on Quantum Ant Colony Algorithm(QACA)to overcome the problems such as long computing time and easy to fall into local best for traditional heuristic optimization algorithm. The optimization problem of logistics distribution routing is analyzed, and the mathematical model is established, and then the quantum ant colony algorithm is used to solve it, and the pheromone on each path is encoded by a group of quantum bits,and a new pheromone representation is designed,called quantum pheromone, and the quantum rotation gate and the best tour are applied to updating the pheromone. The simulation test is carried out to test the performance of QACA. The simulation results show that, QACA has a strong global search ability and convergence speed, and can effectively solve the logistics distribution routing problem.