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Chinese Journal of Computers

A Novel Quantum Genetic Algorithm for TSP

Yu Wang

Published Jan 1, 2007• 19 citations
OpenAlex

Abstract

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.

Related papers

A Novel Improved Quantum Genetic Algorithm for Combinatorial Optimization Problems

Xihua Zou

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.

Dianzi xuebao•Jan 1, 2007•15 citations

Quantum evolutionary algorithm for TSP combinatorial optimisation problem

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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.

arXiv:2409.13788•Sep 20, 2024•0 citations

A Survey of Quantum Genetic Algorithm for Combinatorial Optimization Problems

Feng Mei Wei, Jian Pei Zhang, Bing Li +1 more

Combined with quantum computing and genetic algorithm, quantum genetic algorithm (QGA) shows considerable ability of parallelism. Experiments have shown that QGA performs quite well on TSP, job shop problem and some other typical combinatorial optimization problems. The other problems like nutritional diet which can be transformed into specific combinational optimization problem also can be solved through QGA smoothly. This paper sums up the main points of QGA for general combinatorial optimization problems. These points such as modeling of the problem, qubit decoding and rotation strategy are useful to enhance the convergence speed of QGA and avoid premature at the same time.

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This paper proposes a new parallel evolutionary algorithm called parallel quantum-inspired genetic algorithm (PQGA). Quantum-inspired genetic algorithm (QGA) is based on the concept and principles of quantum computing such as qubits and superposition of states. Instead of binary, numeric, or symbolic representation, by adopting the qubit chromosome as a representation, QGA can represent a linear superposition of solutions due to its probabilistic representation. QGA is suitable for parallel structures because of rapid convergence and good global search capability. That is, QGA is able to possess the two characteristics of exploration and exploitation simultaneously. The effectiveness and the applicability of PQGA are demonstrated by experimental results on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that PQGA is superior to QGA as well as other conventional genetic algorithms.

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Shuyuan Yang, Fang Liu

The genetic algorithm is an efficient optimization tool for its independence of problems, intrinsic parallelism and inherent learning capacity; however, it has some disadvantages such as slow convergence and prematurity. In this paper, a novel algorithm, called the quantum genetic algorithm—QGA, is proposed based on the combination of the quantum theory with the evolutionary theory. By adopting the qubit chromosome as a representation, QGA can represent a linear superposition of solutions due to its probabilistic representation. The random observation simulating the quantum collapse can bring diverse individuals, and the evolution of quantum chromosome can also pilot the evolution. So it has better diversity than the classical genetic algorithm. Rapid convergence and good global search capacity characterize the performance of QGA. The paper not only proves the global convergence of the QGA, but also some simulation experiments are shown to prove its superiority over other algorithms.

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Hybrid quantum search with genetic algorithm optimization

Mihai Udrescu, Sebastian Mihai Ardelean

Abstract Quantum Genetic Algorithms (QGAs) integrate genetic programming and quantum computing to address search and optimization problems. Most QGA approaches add quantum features to genetic algorithm operators, such as selection, crossover, or mutation. Oppositely, the Reduced Quantum Genetic Algorithm (RQGA) is a fully quantum algorithm that encodes the entire search space (i.e., population) as a superposition of all possible solutions (chromosomes) using the individuals’ quantum register; the fitness function takes the individuals’ quantum register as input to generate corresponding fitness values within the chromosomes’ superposition. RQGA finds the best fitness value and its corresponding chromosome (i.e., the solution or one of the solutions) using Grover’s algorithm. The complexity of Grover’s algorithm is O(2N⁄2), where N is the number of superposed individual chromosomes. However, RQGA operates on an exponentially-big search space (N = 2n, where n is the number of qubits in the individuals’ quantum register), which entails an exponential runtime of O(2n⁄2). This paper introduces an optimization solution for RQGA that controls the algorithm complexity by selecting a limited number of qubits in the individuals’ register and fixing the remaining ones as classical values of ’0’ and ’1’ with a genetic algorithm. We also improve the performance of the RQGA by discarding unfit solutions and bounding the search only in the valid individuals’ area. Putting it all together, we introduce a novel quantum genetic algorithm—Hybrid Quantum Algorithm with Genetic Optimization (HQAGO)—that solves search problems in O(2(n-k)⁄2) oracle queries, where k is the number of fixed classical bits in the individuals’ register. We illustrate instantiations of HQAGO that solve the NP-hard knapsack and graph coloring problems, analyze the complexity of the new algorithm, and study the convergence of its heuristic part.

•Jun 19, 2023•0 citations
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.
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.
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.
Combined with quantum computing and genetic algorithm, quantum genetic algorithm (QGA) shows considerable ability of parallelism. Experiments have shown that QGA performs quite well on TSP, job shop problem and some other typical combinatorial optimization problems. The other problems like nutritional diet which can be transformed into specific combinational optimization problem also can be solved through QGA smoothly. This paper sums up the main points of QGA for general combinatorial optimization problems. These points such as modeling of the problem, qubit decoding and rotation strategy are useful to enhance the convergence speed of QGA and avoid premature at the same time.
This paper proposes a new parallel evolutionary algorithm called parallel quantum-inspired genetic algorithm (PQGA). Quantum-inspired genetic algorithm (QGA) is based on the concept and principles of quantum computing such as qubits and superposition of states. Instead of binary, numeric, or symbolic representation, by adopting the qubit chromosome as a representation, QGA can represent a linear superposition of solutions due to its probabilistic representation. QGA is suitable for parallel structures because of rapid convergence and good global search capability. That is, QGA is able to possess the two characteristics of exploration and exploitation simultaneously. The effectiveness and the applicability of PQGA are demonstrated by experimental results on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that PQGA is superior to QGA as well as other conventional genetic algorithms.
The genetic algorithm is an efficient optimization tool for its independence of problems, intrinsic parallelism and inherent learning capacity; however, it has some disadvantages such as slow convergence and prematurity. In this paper, a novel algorithm, called the quantum genetic algorithm—QGA, is proposed based on the combination of the quantum theory with the evolutionary theory. By adopting the qubit chromosome as a representation, QGA can represent a linear superposition of solutions due to its probabilistic representation. The random observation simulating the quantum collapse can bring diverse individuals, and the evolution of quantum chromosome can also pilot the evolution. So it has better diversity than the classical genetic algorithm. Rapid convergence and good global search capacity characterize the performance of QGA. The paper not only proves the global convergence of the QGA, but also some simulation experiments are shown to prove its superiority over other algorithms.
Abstract Quantum Genetic Algorithms (QGAs) integrate genetic programming and quantum computing to address search and optimization problems. Most QGA approaches add quantum features to genetic algorithm operators, such as selection, crossover, or mutation. Oppositely, the Reduced Quantum Genetic Algorithm (RQGA) is a fully quantum algorithm that encodes the entire search space (i.e., population) as a superposition of all possible solutions (chromosomes) using the individuals’ quantum register; the fitness function takes the individuals’ quantum register as input to generate corresponding fitness values within the chromosomes’ superposition. RQGA finds the best fitness value and its corresponding chromosome (i.e., the solution or one of the solutions) using Grover’s algorithm. The complexity of Grover’s algorithm is O(2N⁄2), where N is the number of superposed individual chromosomes. However, RQGA operates on an exponentially-big search space (N = 2n, where n is the number of qubits in the individuals’ quantum register), which entails an exponential runtime of O(2n⁄2). This paper introduces an optimization solution for RQGA that controls the algorithm complexity by selecting a limited number of qubits in the individuals’ register and fixing the remaining ones as classical values of ’0’ and ’1’ with a genetic algorithm. We also improve the performance of the RQGA by discarding unfit solutions and bounding the search only in the valid individuals’ area. Putting it all together, we introduce a novel quantum genetic algorithm—Hybrid Quantum Algorithm with Genetic Optimization (HQAGO)—that solves search problems in O(2(n-k)⁄2) oracle queries, where k is the number of fixed classical bits in the individuals’ register. We illustrate instantiations of HQAGO that solve the NP-hard knapsack and graph coloring problems, analyze the complexity of the new algorithm, and study the convergence of its heuristic part.