A QUBO Model for the Traveling Salesman Problem with Time Windows

Papalitsas, Christos; Andronikos, Theodore; Giannakis, Konstantinos; Theocharopoulou, Georgia; Fanarioti, Sofia

doi:10.3390/a12110224

Cited by 74 publications

(53 citation statements)

References 62 publications

(108 reference statements)

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“…Essa estratégia consiste em dividirmos um problema de caixeiro viajante em subproblemas e depois conectar esses subproblemas como se fossem um núcleos e tratar esses núcleos como um outro caixeiro viajante. As referências [52][53][54] mostram o uso do computador quântico para resolver problemas deste tipo.…”

Section: Problema Do Caixeiro Viajanteunclassified

Computação Quântica Adiabática: Do Teorema Adiabático ao Computador da D-Wave

Souza

Mendonça

Oliveira

et al. 2021

Rev. Bras. Ensino Fís.

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Neste artigo descrevemos os fundamentos da computação quântica adiabática, que consiste na interpolação de diferentes Hamiltonianos, desde um Hamiltoniano inicial, com autoestados e autoenergias conhecidos, até um Hamiltoniano final, onde é codificada a solução de um dado problema. Em particular, discutimos o método do annealing quântico, que é utilizado pela empresa canadense D-Wave, pioneira nessa área. Primeiramente apresentamos uma das demonstrações do teorema adiabático quântico e de uma condição de adiabaticidade para evolução de sistemas quânticos. Para exemplificar, descrevemos a implementação do algoritmo de Grover via computação quântica adiabática, discutindo os impactos da escolha da forma de interpolação dos Hamiltonianos inicial e final na complexidade do algoritmo. Em seguida, mostramos um algoritmo para o problema do caixeiro viajante executável na plataforma da D-Wave. Por fim, apresentamos aspectos físicos importantes da tecnologia dos computadores quânticos da D-Wave, expondo suas vantagens e desvantagens, além de descrever qualitativamente a engenharia de seu processador quântico.

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Section: Problema Do Caixeiro Viajanteunclassified

Computação Quântica Adiabática: Do Teorema Adiabático ao Computador da D-Wave

Souza

Mendonça

Oliveira

et al. 2021

Rev. Bras. Ensino Fís.

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“…TSP with time windows (TSPTW) is another popular variant of TSP, which restricts the salesman to visit each target location within a particular time window. Reviews of existing solutions for TSPTW can be found in [38]- [40] and the references therein.…”

Section: B Tsp/vrpmentioning

confidence: 99%

Path Planning for UAV to Cover Multiple Separated Convex Polygonal Regions

2020

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In many unmanned aerial vehicle (UAV) applications such as land assessment, search and rescue, and precision agriculture, UAVs are often required to survey multiple spatially distributed regions. To perform these applications, one of the key steps is to plan the path for the UAV to quickly cover all regions. The new path planning problem explored here, which we call the TSP-CPP problem, can be viewed as an integration of the traveling salesman problem (TSP) and the coverage path planning (CPP) problem, which has not been well studied in the literature. In this paper, we conduct a systematic investigation on the TSP-CPP problem. In particular, we first provide a mixed integer programming formulation for this new problem, and then introduce a CPP method for covering a single convex polygonal region. Based on this method, we then develop two approaches to solve the TSP-CPP problem, including 1) a dynamic programming-based exact approach that can find the (near) optimal tour, and 2) a heuristic approach that can generate high-quality tours very efficiently. Through comprehensive theoretical analyses and simulation studies, we demonstrate the optimality and efficiency of the proposed approaches. INDEX TERMS Path planning, traveling salesman problem, coverage path planning, multiple convex polygonal regions, unmanned aerial vehicle, optimal path, heuristic algorithm.

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“…A thorough statistical and computational analysis on asymmetric, symmetric, and national TSP benchmarks from the well known TSPLIB benchmark library, was conducted in [47]. Very recently, Papalitsas et al parameterized the TSPTW into the QUBO (Quadratic Unconstrained Binary Optimization) model [48]. This last QUBO formulation enables TSPTW to run on a Quantum Annealer and is an important step towards the ultimate goal of running the TSPTW utilizing pure quantum optimization methods.…”

Section: The Travelling Salesman Problemmentioning

confidence: 99%

DKPRG or How to Succeed in the Kolkata Paise Restaurant Game via TSP

Kastampolidou¹,

Papalitsas²,

Andronikos

2020

Preprint

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The Kolkata Paise Restaurant Problem is a very challenging game, where n agents have to decide where they will have lunch on a busy day during their lunch break. The game is very interesting because there are exactly n restaurants and each restaurant can accommodate only one agent. If two or more agents happen to choose the same restaurants, only one gets served and the others have to return back to work hungry. In this paper, we tackle this problem from an entirely new angle. We abolish certain implicit assumptions, which allows us to propose a novel strategy with greater utilization of the restaurants and overall efficiency. We emphasize the spatially distributed nature of our approach, which, for the first time, perceives the locations of the restaurants as uniformly distributed in the entire city area. This critical change in perspective has profound ramifications in the topological layout of the restaurants, which now makes it completely realistic to assume that every agent has a second chance. Every agent now may visit, in case of failure, more than one restaurants, within the predefined time constraints. From the point of view of each agent, the situation now resembles more that of the iconic travelling salesman, who must compute an optimal route through n cities. Following this shift in paradigm, we advocate the use of metaheuristics, as exacts solution of the TSP are prohibitively expensive, because they can produce near-optimal solutions in a very short amount of time. The use of metaheuristics enables each agent to compute her own personalized solution, incorporating her preferences, and providing alternative destinations in case of successive failures. We analyze rigorously the resulting situation, proving probabilistic formulas that confirm the advantages of this policy and the increase in utilization. The detailed mathematical analysis of our scheme demonstrates that it can achieve utilization ranging from .85 to 0.95 from the first day, while rapidly attaining steady state utilization 1.0. Moreover, the equations we have developed generalize previously presented formulas in the literature, which can be shown to be special cases of our results.

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A QUBO Model for the Traveling Salesman Problem with Time Windows

Cited by 74 publications

References 62 publications

Computação Quântica Adiabática: Do Teorema Adiabático ao Computador da D-Wave

Computação Quântica Adiabática: Do Teorema Adiabático ao Computador da D-Wave

Path Planning for UAV to Cover Multiple Separated Convex Polygonal Regions

DKPRG or How to Succeed in the Kolkata Paise Restaurant Game via TSP

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