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Journal of the University of Shanghai for Science and Technology

Hybrid quantum algorithm for solving traveling salesman problems

Chunming Ye

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

Hybrid quantum algorithm(HQA) was put forward to solve traveling salesman problems.On the basis of quantum computing,displacement decoding was designed which enables the algorithm to overcome the difficulties in route configuration.Evolutionary mode and best tracing and keeping mode,derived from particle swarm optimization algorithm,were adopted,dynamic inertia weight was configured to update quantum angles effectively,and local optimization was taken to carry out lean search.The capability of HQA to solve traveling salesman problems was demonstrated by the results of several examples.

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Hybrid quantum algorithm(HQA) was put forward to solve traveling salesman problems.On the basis of quantum computing,displacement decoding was designed which enables the algorithm to overcome the difficulties in route configuration.Evolutionary mode and best tracing and keeping mode,derived from particle swarm optimization algorithm,were adopted,dynamic inertia weight was configured to update quantum angles effectively,and local optimization was taken to carry out lean search.The capability of HQA to solve traveling salesman problems was demonstrated by the results of several examples.
A novel method of coding was brought forward and the essence of evolutionary algorithm(EA) and particle swarm optimization algorithm(PSO) was put into consideration in terms of the characteristics of Traveling Salesman Problem(TSP),and a distinctive hybrid quantum algorithm(HQA) was constructed.The breakthrough was taken as the means of updating the individual to improve the capability of HQA.Still further,the updating of inertial weight was guided dynamically,and the decision that individual would turn out to be attractive or repulsive in the next iteration was made.This new algorithm is called improved hybrid quantum algorithm(IHQA).The result of the test manifests that both two algorithms are of strong capability in optimum-searching,and IAQA performs better.
Quantum Evolutionary Algorithm(QEA) is a distinctive type of algorithm for optimization currently,and the theoretical basis of QEA is quantum computation.The algorithm takes advantage of intervention and parallelism of quantum bit thoroughly,which enables QEA to solve combinatorial optimization problems.While solving scheduling problems,QEA has defects that it converges slowly and doesn’t use other immature individual.Hybrid Quantum Algorithm(HQA) is formed and it sucks Particle Swarm Optimization algorithm(PSO) and evolutionary computation into QEA.Classical flow shop problem is employed to test the algorithm,and the result shows that the hybrid algorithm overcomes the defects of QEA and it has universality to solve scheduling problems.
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.
Quantum Computing is considered as the next frontier in computing, and it is attracting a lot of attention from the current scientific community. This kind of computation provides to researchers with a revolutionary paradigm for addressing complex optimization problems, offering a significant speed advantage and an efficient search ability. Anyway, Quantum Computing is still in an incipient stage of development. For this reason, present architectures show certain limitations, which have motivated the carrying out of this paper. In this paper, we introduce a novel solving scheme coined as hybrid Quantum Computing - Tabu Search Algorithm. Main pillars of operation of the proposed method are a greater control over the access to quantum resources, and a considerable reduction of non-profitable accesses. To assess the quality of our method, we have used 7 different Traveling Salesman Problem instances as benchmarking set. The obtained outcomes support the preliminary conclusion that our algorithm is an approach which offers promising results for solving partitioning problems while it drastically reduces the access to quantum computing resources. We also contribute to the field of Transfer Optimization by developing an evolutionary multiform multitasking algorithm as initialization method.
A hybrid quantum-classical framework is exploited to solve the Traveling Salesman Problem (TSP) based on a Quantum Approximate Optimization Algorithm (QAOA). To overcome the computational limitation of the Grover’s Search Algorithm (GSA) stemming from path encoding and arithmetic subroutines, a clustering-based strategy is employed to decompose a 16-city TSP into four 4-city subproblems, each of which can be solved with a 16-qubit budget. Intra-cluster solutions are optimized with QAOA, and are classically stitched to construct the global tour. Our results clearly validate the effectiveness of the hierarchical design of the algorithm, highlighting its feasibility for mid-scale quantum optimizations.
The Traveling Salesman Problem (TSP) is a widely studied NP-complete optimization challenge with significant theoretical and practical implications. This study proposes a hybrid quantum-classical framework using a Quantum-Inspired Evolutionary Algorithm (QEA) with Sort Gray Binary Encoding to solve the TSP. The proposed method guarantees the generation of valid TSP tours by eliminating invalid solutions. It employs quantum superposition with intrinsic randomness to enhance computational efficiency and scalability. The framework was implemented on cloud-based NISQ platforms, including IBM Quantum and AWS Braket, demonstrating its practicality and effectiveness. Experimental evaluations revealed that the proposed framework successfully solved TSP instances with up to 15 cities, achieving superior performance compared to classical methods and showcasing its ability to scale under NISQ constraints. The results also highlight the potential of hybrid quantum-classical approaches to overcome hardware limitations in current quantum systems. This study establishes a robust hybrid methodology for solving combinatorial optimization problems. It also sets a benchmark for leveraging the capabilities of NISQ-era quantum devices in real-world applications, thereby providing a foundation for future research in hybrid quantum-classical optimization techniques.