Abstract
General variable neighborhood search (GVNS) is a well known and widely used metaheuristic for efficiently solving many NP-hard combinatorial optimization problems. We propose a novel extension of the conventional GVNS. Our approach incorporates ideas and techniques from the field of quantum computation during the shaking phase. The travelling salesman problem (TSP) is a well known NP-hard problem which has broadly been used for modelling many real life routing cases. As a consequence, TSP can be used as a basis for modelling and finding routes via the Global Positioning System (GPS). In this paper, we examine the potential use of this method for the GPS system of garbage trucks. Specifically, we provide a thorough presentation of our method accompanied with extensive computational results. The experimental data accumulated on a plethora of TSP instances, which are shown in a series of figures and tables, allow us to conclude that the novel GVNS algorithm can provide an efficient solution for this type of geographical problem.
Highlights
Many complex real world problems can be formulated as combinatorial optimization (CO)problems
This section is devoted to the presentation of the experimental results that showcase the strengths of the novel General variable neighborhood search (GVNS)
We propose a novel GVNS version based on quantum computing principles and techniques, and we apply it to a garbage collection application, an actual global positioning system (GPS)-based problem
Summary
Many complex real world problems can be formulated as combinatorial optimization (CO). The fact that TSP is NP-hard implies that there is no known polynomial-time algorithm for finding an optimal solution regardless of the size of the problem instance [3] Real world problems, such as those related to GPS, can be formulated as instances of the TSP. This class of routing problems requires good solutions computed in a short amount of time. The computational results reveal that both GVNS’s first and best improvement solutions provide efficient routes that are either optimal or near-optimal and outperform with a wide margin classic, widely used methods, such as NN and its modifications This novel GVNS is a quantum-inspired expansion of the conventional GVNS in which the shaking function is based on complex unit vectors.
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