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Register a new userHybrid Quantum Computing -- Tabu Search Algorithm for Partitioning Problems: preliminary study on the Traveling Salesman Problem
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Added by
Eneko Osaba
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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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.
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Quantum Computing is an emerging paradigm which is gathering a lot of popularity in the current scientific and technological community. Widely conceived as the next frontier of computation, Quantum Computing is still at the dawn of its development. Thus, current solving systems suffer from significant limitations in terms of performance and capabilities. Some interesting approaches have been devised by researchers and practitioners in order to overcome these barriers, being quantum-classical hybrid algorithms one of the most often used solving schemes. The main goal of this paper is to extend the results and findings of the recently proposed hybrid Quantum Computing - Tabu Search Algorithm for partitioning problems. To do that, we focus our research on the adaptation of this method to the Asymmetric Traveling Salesman Problem. In overall, we have employed six well-known instances belonging to TSPLIB to assess the performance of Quantum Computing - Tabu Search Algorithm in comparison to QBSolv, a state-of-the-art decomposing solver. Furthermore, as an additional contribution, this work also supposes the first solving of the Asymmetric Traveling Salesman Problem using a Quantum Computing based method. Aiming to boost whole communitys research in QC, we have released the projects repository as open source code for further application and improvements.
With progress in quantum technology more sophisticated quantum annealing devices are becoming available. While they offer new possibilities for solving optimization problems, their true potential is still an open question. As the optimal design of adiabatic algorithms plays an important role in their assessment, we illustrate the aspects and challenges to consider when implementing optimization problems on quantum annealing hardware based on the example of the traveling salesman problem (TSP). We demonstrate that tunneling between local minima can be exponentially suppressed if the quantum dynamics are not carefully tailored to the problem. Furthermore we show that inequality constraints, in particular, present a major hurdle for the implementation on analog quantum annealers. We finally argue that programmable digital quantum annealers can overcome many of these obstacles and can - once large enough quantum computers exist - provide an interesting route to using quantum annealing on a large class of problems.
Theory of computer calculations strongly depends on the nature of elements the computer is made of. Quantum interference allows to formulate the Shor factorization algorithm turned out to be more effective than any one written for classical computers. Similarly, quantum wave packet reduction allows to devise the Grover search algorithm which outperforms any classical one. In the present paper we argue that the quantum incoherent tunneling can be used for elaboration of new algorithms able to solve some NP-hard problems, such as the Traveling Salesman Problem, considered to be intractable in the classical theory of computer computations.
One of the most fundamental results in combinatorial optimization is the polynomial-time 3/2-approximation algorithm for the metric traveling salesman problem. It was presented by Christofides in 1976 and is well known as the Christofides algorithm. Recently, some authors started calling it Christofides-Serdyukov algorithm, pointing out that it was published independently in the USSR in 1978. We provide some historic background on Serdyukovs findings and a translation of his article from Russian into English.
Proposed initially from a practical circumstance, the traveling salesman problem caught the attention of numerous economists, computer scientists, and mathematicians. These theorists were instead intrigued by seeking a systemic way to find the optimal route. Many attempts have been made along the way and all concluded the nonexistence of a general algorithm that determines optimal solution to all traveling salesman problems alike. In this study, we present proof for the nonexistence of such an algorithm for both asymmetric (with oriented roads) and symmetric (with unoriented roads) traveling salesman problems in the setup of constructive mathematics.
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