A Performance Study of the Impact of Different Perturbation Methods on the Efficiency of GVNS for Solving TSP

Andronikos³

2022

Preprint

This paper studies the Hamiltonian Cycle Problem (HCP) and the Traveling Salesman Problem (TSP) on D-Wave's quantum systems. Initially, motivated by the fact that most libraries present their benchmark instances in terms of adjacency matrices, we develop a novel matrix formulation for the HCP and TSP Hamiltonians, which enables the seamless and automatic integration of benchmark instances in quantum platforms. our extensive experimental tests have led us to some interesting conclusions. D-Wave's Advantage system4.1 is more efficient than Advantage system1.1 both in terms of qubit utilization and quality of solutions. Finally, we experimentally establish that D-Wave's Hybrid solvers always provide a valid solution to a problem, without violating the QUBO constraints, even for arbitrarily big problems, of the order of 120 nodes. When solving TSP instances, the solutions produced by the quantum annealer are often invalid, in the sense that they violate the topology of the graph. To address this use we advocate the use of min-max normalization for the coefficients of the TSP Hamiltonian. Finally, we present a thorough mathematical analysis on the precise number of constraints required to express the HCP and TSP Hamiltonians. This analysis, explains quantitatively why, almost always, running incomplete graph instances requires more qubits than complete instances. It turns out that incomplete graph require more quadratic constraints than complete graphs, a fact that has been corroborated by a series of experiments.

Section: Related Workmentioning

confidence: 99%

Experimental analysis of quantum annealers and hybrid solvers using benchmark optimization problems

Evangelos¹,

Andronikos³

2022

Preprint

“…More recently, [45] applied a quantum-inspired metaheuristic for tackling the practical problem of garbage collection with time windows that produced particularly promising experimental results, as further comparative analysis demonstrated in [46]. 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].…”

Section: The Travelling Salesman Problemmentioning

confidence: 99%

DKPRG or how to succeed in the Kolkata Paise Restaurant gamevia TSP

Kastampolidou¹,

Andronikos³

2021

Preprint

The Kolkata Paise Restaurant Problem is a challenging game, in which n agents must decide where to have lunch 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 restaurant, 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 that results in greater utilization for the restaurants. 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. This is because exact solutions of the TSP are prohibitively expensive, whereas metaheuristics produce near-optimal solutions in a short amount of time. Thus, via metaheuristics each agent can 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 0.85 to 0.95 from the first day, while rapidly attaining steady state utilization 1.0. Finally, we note that the equations we derive generalize formulas that were previously presented in the literature, which can be seen as special cases of our results.

“…More recently, [45] applied a quantum-inspired metaheuristic for tackling the practical problem of garbage collection with time windows, with particularly promising experimental results, as further comparative analysis demonstrated in [46]. 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].…”

Section: The Travelling Salesman Problemmentioning

confidence: 99%

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

Kastampolidou¹,

Andronikos

2020

Preprint

Self Cite

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.