A Hybrid Solution Method for the Capacitated Vehicle Routing Problem Using a Quantum Annealer

Feld, Sebastian; Roch, Christoph; Gabor, Thomas; Seidel, Christian; Neukart, Florian; Galter, Isabella; Mauerer, Wolfgang; Linnhoff‐Popien, Claudia

doi:10.3389/fict.2019.00013

Cited by 127 publications

(101 citation statements)

References 33 publications

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“…The potential applications of the Ising annealer can be classified into two groups, as summarized in a recent white paper by the D-Wave team [29]. First, a variety of optimization problems, such as the traveling salesman problem and generalizations thereof [30][31][32], financial portfolio optimization [33], protein folding [34], as well as constraint satisfaction problems, e.g. factorization [35] and satisfiability [36,37], can be reduced to the Ising optimization.…”

Section: Discussionmentioning

confidence: 99%

Annealing by simulating the coherent Ising machine

Tiunov¹,

Ulanov²,

Lvovsky³

2019

Opt. Express

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The coherent Ising machine (CIM) enables efficient sampling of low-lying energy states of the Ising Hamiltonian with all-to-all connectivity by encoding the spins in the amplitudes of pulsed modes in an optical parametric oscillator (OPO). The interaction between the pulses is realized by means of measurement-based optoelectronic feedforward which enhances the gain for lower-energy spin configurations. We present an efficient method of simulating the CIM on a classical computer that outperforms the CIM itself as well as the noisy mean-field annealer in terms of both the quality of the samples and the computational speed. It is furthermore advantageous with respect to the CIM in that it can handle Ising Hamiltonians with arbitrary real-valued node coupling strengths. These results illuminate the nature of the faster performance exhibited by the CIM and may give rise to a new class of quantum-inspired algorithms of classical annealing that can successfully compete with existing methods.Introduction. The Ising model, originally developed for the description of phase transitions in magnetic materials [1], is a pillar of many branches in science. Its applications range from quantum field theory [2] and quantum gravity [3] to economics [4] and machine learning [5]. The model is defined by the Hamiltonianwhere J i j = J ji , J ii = 0. The spin variable σ i can be a quantum operator or a number, continuous or discrete. In this paper we are interested in the classical discrete case, σ i = ±1. The goal is to find the configurations of spins which realize or approach the global minimum of the Ising Hamiltonian (1). This is an NP-hard problem, meaning that the number of operations needed to find the exact solution grows exponentially with the size of the spin system [6]. However, there exists a variety of classical algorithms to find an approximate solution [7][8][9][10].Recently, the Ising problem has been approached using noisy intermediate-scale quantum (NISQ) devices. One example is the D-Wave quantum annealer based on superconducting qubits. However, it has a shortcoming associated with low connectivity: each physical qubit in the D-Wave chimera graph architecture is connected to only eight others. Therefore each logical spin must be embedded in multiple physical qubits to model the fully connected Hamiltonian (1), resulting in a significant overhead [11].

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Section: Discussionmentioning

confidence: 99%

Annealing by simulating the coherent Ising machine

Tiunov¹,

Ulanov²,

Lvovsky³

2019

Opt. Express

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“…As most of the realworld applications consist of hundreds of customers or locations to be serviced, the focus has largely been on the development of approximate solution techniques that can provide high-quality solutions within reasonable computation time. Heuristic and metaheuristic algorithms can be directly applied to several variants of the vehicle routing problem [41,72], but such techniques are context dependent and require careful parameter tuning to obtain good-quality solutions [73,74].…”

Section: Qc For Vehicle Routingmentioning

confidence: 99%

Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems

Ajagekar

Humble

You

2020

Computers & Chemical Engineering

130

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Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that effectively leverage the complementary strengths of deterministic algorithms and QC techniques to overcome combinatorial complexity for solving large-scale mixed-integer programming problems. Four applications, namely the molecular conformation problem, job-shop scheduling problem, manufacturing cell formation problem, and the vehicle routing problem, are specifically addressed. Large-scale instances of these application problems across multiple scales ranging from molecular design to logistics optimization are computationally challenging for deterministic optimization algorithms on classical computers. To address the computational challenges, hybrid QC-based algorithms are proposed and extensive computational experimental results are presented to demonstrate their applicability and efficiency.The proposed QC-based solution strategies enjoy high computational efficiency in terms of solution quality and computation time, by utilizing the unique features of both classical and quantum computers.Quantum computing (QC) is the next frontier in computation and has attracted a lot of attention from the scientific community in recent years. QC provides a novel approach to help solve some of the most complex optimization problems while offering an essential speed advantage over classical methods [10]. This is evident from QC techniques like Shor's algorithm for integer factorization [11], Grover's search algorithm for unstructured databases [12], quantum algorithm for linear system of equations [13], and many more [14]. Quantum adiabatic algorithms too are efficient optimization strategies that quickly search over the solution space [15]. Quantum computers perform computation by inducing quantum speedups whose scaling far exceeds the capability of the most powerful classical computers. QC's major applications can be perceived in areas of optimization, machine learning, cryptography, and quantum chemistry [16]. Despite the contrasting views on QC's viability and performance, there is no doubt that QC holds great promise to open up a new era of computing.QC-based solution approaches are in their earliest stages of development compared to their much more matured classical counterparts. Current quantum machines have very limited functionality in the context of optimization, such that QC hardware and algorithms are inadequate for large-scale optimization problems. Although it has been shown that some optimization problems relevant to energy systems can be solved using quantum computers, their performance deteriorates with increasing size and complexity [17]. A number of technological limitations face commercially available quantum computers, such as relatively small number of qubits with limited connectivity, and lack of quantum memory. Therefore, harnessing the complementary strengths of classical and...

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“…Recent QUBO quantum computing applications, complementing earlier applications on classical computing systems, include those for graph partitioning problems in Mniszewski et al (2016) and Ushijima-Mwesigwa et al (2017); graph clustering (quantum community detection problems) in Negre et al (2018Negre et al ( , 2019; traffic-flow optimization in Neukart et al (2017); vehicle routing problems in Feld et al (2018), Clark et al (2019) and Ohzeki et al(2018); maximum clique problems in Chapuis et al (2018); cybersecurity problems in Munch et al (2018) and Reinhardt et al(2018); predictive health analytics problems in De Oliveira et al (2018) and Sahner et al (2018); and financial portfolio management problems in Elsokkary et al (2017) and Kalra et al (2018). In another recent development, QUBO models are being studied using the IBM neuromorphic computer at as reported in Alom et al (2017) and Aimone et al (2018).…”

Section: Y = 2588mentioning

confidence: 99%

Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models

Glover

Kochenberger²,

Du³

2019

4OR-Q J Oper Res

201

139

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The Quadratic Unconstrained Binary Optimization (QUBO) model has gained prominence in recent years with the discovery that it unifies a rich variety of combinatorial optimization problems. By its association with the Ising problem in physics, the QUBO model has emerged as an underpinning of the quantum computing area known as quantum annealing and Fujitsu's digital annealing, and has become a subject of study in neuromorphic computing. Through these connections, QUBO models lie at the heart of experimentation carried out with quantum computers developed by D-Wave Systems and neuromorphic computers developed by IBM. The consequences of these new computational technologies and their links to QUBO models are being explored in initiatives by organizations such as Google, Amazon and Lockheed Martin in the commercial realm and Los Alamos National Laboratory, Oak Ridge National Laboratory, Lawrence Livermore National Laboratory and NASA's Ames Research Center in the public sector. Computational experience is being amassed by both the classical and the quantum computing communities that highlights not only the potential of the QUBO model but also its effectiveness as an alternative to traditional modeling and solution methodologies.

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A Hybrid Solution Method for the Capacitated Vehicle Routing Problem Using a Quantum Annealer

Cited by 127 publications

References 33 publications

Annealing by simulating the coherent Ising machine

Annealing by simulating the coherent Ising machine

Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems

Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models

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