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Seating Arrangement Optimization in COVID-19 Era: a quantum computing approach

Ilaria Gioda

Published Apr 16, 2021• 0 citations
OpenAlex

Abstract

2020 year has been a turning point for the entire humanity. The COVID-19 pandemic has not only revolutionized our way of thinking, but it has changed the way we live, leading to having limitations on any aspect of our daily life, from the smallest things to the biggest. This extraordinary situation has afflicted the railway world, too, since the movements have been limited drastically and new rules have been introduced. This thesis focuses on analyzing passenger transport's current situation on high-speed trains in this particular historical period we are experiencing, the COVID-19 Era. It aims to create hypothetical scenarios of passengers' distribution inside a train wagon with current health and hygiene rules. The main goal of what has been defined as the Seating Arrangement Optimization problem is to fill the train wagon as much as possible and therefore transport the largest number of people by maximizing the number of passengers belonging to the same family sitting in nearest seats. In this work, two different optimization models for formalizing the identified problem are presented and compared: a Mixed-Integer Linear Programming (MILP) model, one of the most common formulations in literature in the optimization field, and a Quadratic Unconstrained Binary Optimization (QUBO) model, a novel type of problem that can be solved on a quantum computer. In particular, for the resolution of the first type of model, the Gurobi commercial solver is used while, for the latter one, the QBSolv and a classical-quantum hybrid solver provided by D-Wave Systems Inc., a leader company in the quantum computing field, are considered. Quantum computing is an innovative research field currently still under development, on which time and money have begun to be invested only in recent years. What makes this research field attractive is the particular way with which quantum technology operates and the great potential it can offer to solve real-world problems. Due to the current physical capabilities, quantum computers' computational resources are not sufficient to execute too large optimization problems. Still, even with small instances like the ones considered in this work, it can be seen how much they can find highly optimized solutions in a short time.

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2020 year has been a turning point for the entire humanity. The COVID-19 pandemic has not only revolutionized our way of thinking, but it has changed the way we live, leading to having limitations on any aspect of our daily life, from the smallest things to the biggest. This extraordinary situation has afflicted the railway world, too, since the movements have been limited drastically and new rules have been introduced. This thesis focuses on analyzing passenger transport's current situation on high-speed trains in this particular historical period we are experiencing, the COVID-19 Era. It aims to create hypothetical scenarios of passengers' distribution inside a train wagon with current health and hygiene rules. The main goal of what has been defined as the Seating Arrangement Optimization problem is to fill the train wagon as much as possible and therefore transport the largest number of people by maximizing the number of passengers belonging to the same family sitting in nearest seats. In this work, two different optimization models for formalizing the identified problem are presented and compared: a Mixed-Integer Linear Programming (MILP) model, one of the most common formulations in literature in the optimization field, and a Quadratic Unconstrained Binary Optimization (QUBO) model, a novel type of problem that can be solved on a quantum computer. In particular, for the resolution of the first type of model, the Gurobi commercial solver is used while, for the latter one, the QBSolv and a classical-quantum hybrid solver provided by D-Wave Systems Inc., a leader company in the quantum computing field, are considered. Quantum computing is an innovative research field currently still under development, on which time and money have begun to be invested only in recent years. What makes this research field attractive is the particular way with which quantum technology operates and the great potential it can offer to solve real-world problems. Due to the current physical capabilities, quantum computers' computational resources are not sufficient to execute too large optimization problems. Still, even with small instances like the ones considered in this work, it can be seen how much they can find highly optimized solutions in a short time.
In recent years, researchers have oriented their studies towards new technologies based on quantum physics that should resolve complex problems currently considered to be intractable. This new research area is called Quantum Computing. What makes Quantum Computing so attractive is the particular way with which quantum technology operates and the great potential it can offer to solve real-world problems. This work focuses on solving assignment-like combinatorial optimization problems by exploiting this novel computational approach. A case-study, denoted as the Seating Arrangement Optimization problem, is considered. It is modeled through the Quadratic Unconstrained Binary Optimization paradigm and solved through two tools made available by the D-Wave Systems company, QBSolv, and a quantum-classical hybrid system. The obtained experimental results are compared in terms of solution quality and computational efficiency.
Abstract As consequences of disruptions in railway traffic affect passenger experience and satisfaction, appropriate rerouting and/or rescheduling is necessary. These problems are known to be NP-hard, given the numerous restrictions of traffic nature. With the recent advances in quantum technologies, quantum annealing has become an alternative method to solve such optimization problems. To use quantum annealing, the problem needs to be encoded in quadratic unconstrained binary optimization (QUBO) or higher-order binary optimization (HOBO) formulation that can be recast as a QUBO. This paper introduces QUBO and HOBO representations for rescheduling problems of railway traffic management; the latter is a new approach up to our knowledge. This new approach takes into account not only the single-track lines but also the double- and multi-track lines, as well as stations composed of tracks and switches. We consider the conditions of minimal headway between trains, minimal stay on stations, track occupation, and rolling stock circulation. Furthermore, a hybrid quantum-classical procedure is presented that includes rerouting. We demonstrate the proof of concept implementation on the D-Wave Quantum Processing Unit and D-Wave hybrid solver.
Abstract. COVID-19 is an airborne virus that can be spread directly or indirectly from one person to another. Spreading the virus strongly depends on the location and time and hence, a Spatio-temporal event. Moreover, traffic congestion will increase the spread of the virus not only because of the vicinity but also because of increased temperature and humidity in these spaces for a short or long time. This paper introduces a vehicle routing optimization model to reduce COVID-19 exposure risk during a city journey by solving it as a quadratic unconstrained binary optimization problem on a quantum annealing computer. Indeed, the objective of the COVID-19 prevention optimization problem is to minimize the risk of exposure for a given set of road users between origins and destinations. Microsoft Taxi data from the city of Beijing have been used to simulate road users’ movement. The problem has been run onto three different solvers. One of the solvers is executed on classical computers, and two other solvers are executed on hybrid quantum solvers. Hybrid solvers return the solution within less than 0.03 seconds on quantum processing unit time. However, the results will be returned at least 5 seconds after the execution in the classical solver. It is worth mentioning that, as there is no direct access to the quantum computers, it is hard to compare the results on the same scale as the queries will go on a queue in D-wave quantum computers. Applying the proposed model on the trajectory data shows a better distribution of the vehicles on the road network.
Abstract Airline itinerary and scheduling represent some of the most difficult computational problems that exist in transportation. The problems require choosing the best flight routes while determining schedules and allocating resources through various constraints which include regulatory requirements and maintenance schedules and dynamic demand patterns. The solution of small and medium-scale instances has been achieved through mixed-integer programming and heuristic methods including simulated annealing and genetic algorithms and branch-and-price but these methods become impractical for larger real-world instances due to exponential scaling issues. Quantum computing has introduced fresh solutions which enable the resolution of these problems. Quantum mechanical phenomena particularly superposition and entanglement enable optimization algorithms to examine an exponentially expanded solution space simultaneously. Our research applies a basic airline scheduling problem to the Traveling Salesman Problem (TSP) before converting it into a Quadratic Unconstrained Binary Optimization (QUBO) problem. The Quantum Approximate Optimization Algorithm (QAOA) serves as a hybrid quantum-classical method to solve this formulation. The experimental evaluation of a 4-city scenario shows that quantum-based optimization generates performance levels comparable to traditional methods and indicates that improved quantum hardware development will provide computational benefits for complex airline scheduling problems. This research holds dual importance because it can minimize operational expenses and improve scheduling performance and it establishes fundamental principles for complex combinatorial problem optimization across the transportation industry. The research establishes fundamental principles for quantum-enabled applications that will revolutionize airline operations and other transportation networks by solving critical scalability and solution quality problems.
Public transport systems play a crucial role in the development of large cities. Bus network design to optimize passenger flow coverage in a global metropolis is a challenging task. As an essential part of bus travel planning, considering the bus transfer factor in the existing extremely complex and extensive public bus network usually leads to a optimization problem characterized by high-dimensionality and non-linearity. While classical computers struggle to deal with this kind of problems, quantum computers shed new light into this field. The coherent Ising machine (CIM), a specialized optical quantum computer using a photonic dissipative architecture, has shown its remarkable computational power in combinatorial optimization problems. We construct the classical model and the quadratic unconstrained binary optimization (QUBO) model of the bus route optimization problem, and solve it using a classical computer and CIM, respectively. Our experimental results demonstrate the significant acceleration capability of CIM over classical computers in finding the optimal or near-optimal solutions, albeit subject to the hardware limitations of the 100-qubit CIM.
Vehicle Routing Problem is a well-known optimization issue, which has many extensions resulting from practical appliances. The problem is NP-hard, therefore it may be impossible to find an optimal solution for big instances, with traditional computation methods. Recent development of quantum technology, may be a response for this challenge, which however requires a different formulation of the model. The problem is then modeled using Quadratic Unconstrained Binary Optimization (QUBO) equations. Such model can be run using quantum annealers (QA), designed specifically for optimization purposes. This paper is a systematic survey of Vehicle Routing Problem models that are formulated using QUBO, to be solved on quantum computers. The main goal of the paper is to check research gaps in this subject, compare and explain different approaches of modeling various problem extensions with QUBO. The results obtained in reviewed papers will be presented and analyzed. Moreover, the theoretical basis for quantum computation will be presented, with focus on D-Wave company solutions.