In order to overcome the low efficiency of crossover in Genetic Algorithm(GA),a modified quantum interference crossover based GA was proposed.Unlike position based classical quantum interference crossover,the improved crossover can generate better solutions through distance comparison.Simulation results on Traveling Salesman Problem(TSP) show that the new algorithm can well balance the exploration and exploitation abilities in the whole searching space,and have superior ability of searching the global optimal of near-optimal solutions.
In order to overcome the low efficiency of crossover in Genetic Algorithm(GA),a modified quantum interference crossover based GA was proposed.Unlike position based classical quantum interference crossover,the improved crossover can generate better solutions through distance comparison.Simulation results on Traveling Salesman Problem(TSP) show that the new algorithm can well balance the exploration and exploitation abilities in the whole searching space,and have superior ability of searching the global optimal of near-optimal solutions.
In this paper, we propose an improved quantum interference crossover-based genetic algorithm. The primary difference between the classical interference crossover and the new one is the chromosome reconstruction process. Unlike the position-based selection approach in classical approach, the novel method selects the city that has a shorter distance with the city selected in the previous chromosome. The new method has been used to solve the traveling salesman problem. Experimental results indicate that the new method is superior to the classical interference crossover-based genetic algorithm.
Quantum genetic algorithm(QGA) was proved to be better than the conventional genetic algorithms on numerical and combinational optimization problems,but it is usually used to solve the knapsack problems of the combinational optimization.It is also possible to use its strong ability of exploitation and exploration to other difficult problems,for example,the TSP,a class of NP-hard combinatorial optimization problems.First,a new encoding scheme with pairs of amplitudes is designed.A quantum individual is corresponding to a vector,and the vector is corresponding to the unique valid tour,and vice versa.The advantages of the encoding scheme are that it always generates feasible solution,uses less population size and storage,and can effectively enhance the diversity of the population.Second,the quantum crossover can maintain the relatively good gene blocks.Third,the two-phase local search for edge evolving is integrated into QGA to accelerate its convergent speed.The first phase is used to optimize the sparsely located cities,and the second phase is used to optimize densely located cities.Based on these,a novel and efficient QGA for TSP is proposed,and its convergence to global optimal solution with probability one is proved.The numerical experiments show that the proposed algorithm can find the global optimal solution with less computation and evolving time.
This paper presents a new algorithm for solving the travelling salesman problem (TSP). The TSP is one of the most known combinatorial optimisation problems. It is about finding the shortest Hamiltonian cycle relating N cities. The algorithm is inspired from both genetic algorithms and quantum computing fields. It extends the standard genetic algorithms by combining them to some concepts and principles provided from quantum computing field such as quantum bit, states superposition and interference. The obtained results from the application of the proposed algorithm on some instances of TSP are significantly better than those provided by standard genetic algorithms.
This paper implements a new way of solving a problem called the traveling salesman problem (TSP) using quantum genetic algorithm (QGA). We compared how well this new approach works to the traditional method known as a classical genetic algorithm (CGA). The TSP is a well-established challenge in combinatorial optimization where the objective is to find the most efficient path to visit a series of cities, minimizing the total distance, and returning to the starting point. We chose the TSP to test the performance of both algorithms because of its computational complexity and importance in practical applications. We choose the dataset from the international standard library TSPLIB for our experiments. By designing and implementing both algorithms and conducting experiments on various sizes and types of TSP instances, we provide an in-depth analysis of the accuracy of the optimal solution, the number of iterations, the execution time, and the stability of the algorithms for both. The empirical findings indicate that the CGA outperforms the QGA in terms of finding superior solutions more quickly in most of the test instances, especially when the problem size is large. This suggests that although the principle of quantum computing provides a new way to solve complex combinatorial optimisation problems, the implementation of quantum phenomena and the setting of parameters such as the optimal angle for a quantum revolving gate is challenging and need further optimisation to achieve the desired results. Additionally, it is important to note that the QGA has not been tested on real quantum hardware, so its true performance remains unverified. These limitations provide rich opportunities for further research in the future.
Intelligent optimization algorithm based on quantum behavior is the hot spot of intelligent computation. Quantum clone genetic algorithm has many shortcomings such as: low efficiency, poor population diversity, slow convergence speed, easy to trap in local minimums, blindness in global optimal searching direction and so on. An improved quantum clone genetic algorithm (IQCGA) is proposed in this paper. The algorithm have many merits: (1) Adopting the nicking probability division initialization strategy, population diversity is enhanced; (2) Introducing the quantum whole interference crossover, the information is spread in the whole population, so it helps to avoid trapping in local minimums, and accelerates convergence speed; (3) Making use of adaptation strategy in quantum rotate gate updating, searching speed for optimal solution is accelerated; (4) In order to avoid premature and evolution stagnation, the superior individual whole crossover quantum catastrophe strategy is adopted, which helps the population to search the objective solution in different directions. IQCGA is composted of initialization stage and iteration evolution stage. Furthermore, theory analysis is given to prove the convergence. Finally, Simulation results prove that the algorithms can maintain the population diversity, reduce calculation complexity, accelerate searching speed for optimal solution, and avoid trapping in local minimums. So it has the better searching optimal ability and convergence speed.
Based on quantum genetic algorithm(QGA),a novel improved quantum genetic algorithm(NIQGA)to solve combinatorial optimization problem is proposed.To make full use of interference and entanglement characteristics of quantum state,dynamic step length in adjustment of angle of quantum gate,quantum crossover operation and quantum mutation operation are introduced,therefore high efficiency for optimization is achieved.Two typical combinatorial optimization problems—0/1 knapsack problem and route selection problem,are adopted to confirm the performance of NIQGA.Experimental results show that compared with GA and QGA,NIQGA is characterized by fast convergence rate and excellent capability on global optimization,especially better performance for combinatorial optimization problem with less correlation of genes.