A QUBO Model for the Traveling Salesman Problem with Time Windows for Execution on the D-Wave

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

doi:10.20944/preprints201909.0154.v1

2019

DOI: 10.20944/preprints201909.0154.v1

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A QUBO Model for the Traveling Salesman Problem with Time Windows for Execution on the D-Wave

Christos Papalitsas¹,

Theodore Andronikos²,

Konstantinos Giannakis³

et al.

Abstract: This work focuses on expressing the TSP with Time Windows (TSPTW for short) as a quadratic unconstrained binary optimization (QUBO) problem. The time windows impose time constraints that a feasible solution must satisfy. These take the form of inequality constraints, which are known to be particularly difficult to articulate within the QUBO framework. This is, we believe, the first time this major obstacle is overcome and the TSPTW is cast in the QUBO formulation. We have every reason to anticipate that this d… Show more

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Cited by 4 publications

References 51 publications

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Constructing the Neighborhood Structure of VNS Based on Binomial Distribution for Solving QUBO Problems

Pambudi

Kawamura

2022

Algorithms

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The quadratic unconstrained binary optimization (QUBO) problem is categorized as an NP-hard combinatorial optimization problem. The variable neighborhood search (VNS) algorithm is one of the leading algorithms used to solve QUBO problems. As neighborhood structure change is the central concept in the VNS algorithm, the design of the neighborhood structure is crucial. This paper presents a modified VNS algorithm called “B-VNS”, which can be used to solve QUBO problems. A binomial trial was used to construct the neighborhood structure, and this was used with the aim of reducing computation time. The B-VNS and VNS algorithms were tested on standard QUBO problems from Glover and Beasley, on standard max-cut problems from Helmberg–Rendl, and on those proposed by Burer, Monteiro, and Zhang. Finally, Mann–Whitney tests were conducted using α=0.05, to statistically compare the performance of the two algorithms. It was shown that the B-VNS and VNS algorithms are able to provide good solutions, but the B-VNS algorithm runs substantially faster. Furthermore, the B-VNS algorithm performed the best in all of the max-cut problems, regardless of problem size, and it performed the best in QUBO problems, with sizes less than 500. The results suggest that the use of binomial distribution, to construct the neighborhood structure, has the potential for further development.

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Constructing the Neighborhood Structure of VNS Based on Binomial Distribution for Solving QUBO Problems

Pambudi

Kawamura

2022

Algorithms

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The Distributed Kolkata Paise Restaurant Game

Kastampolidou

Papalitsas

Andronikos

2022

Games

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The Kolkata Paise Restaurant Problem is a challenging game in which n agents decide where to have lunch during their break. The game is not trivial because there are exactly n restaurants, and each restaurant can accommodate only one agent. We study this problem from a new angle and propose a novel strategy that results in greater utilization. Adopting a spatially distributed approach where the restaurants are uniformly distributed in the entire city area makes it possible for every agent to visit multiple restaurants. For each agent, the situation resembles that of the iconic traveling salesman, who must compute an optimal route through n cities. We rigorously prove probabilistic formulas that confirm the advantages of this policy and the increase in utilization. The derived equations generalize formulas that were previously known in the literature, which can be seen as special cases of our results.

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GPS: A New TSP Formulation for Its Generalizations Type QUBO

2022

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We propose a new Quadratic Unconstrained Binary Optimization (QUBO) formulation of the Travelling Salesman Problem (TSP), with which we overcame the best formulation of the Vehicle Routing Problem (VRP) in terms of the minimum number of necessary variables. After, we will present a detailed study of the constraints subject to the new TSP model and benchmark it with MTZ and native formulations. Finally, we will test whether the correctness of the formulation by entering it into a QUBO problem solver. The solver chosen is a D-Wave_2000Q6 quantum computer simulator due to the connection between Quantum Annealing and QUBO formulations.

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A QUBO Model for the Traveling Salesman Problem with Time Windows for Execution on the D-Wave

Cited by 4 publications

References 51 publications

Constructing the Neighborhood Structure of VNS Based on Binomial Distribution for Solving QUBO Problems

Constructing the Neighborhood Structure of VNS Based on Binomial Distribution for Solving QUBO Problems

The Distributed Kolkata Paise Restaurant Game

GPS: A New TSP Formulation for Its Generalizations Type QUBO

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