Combinatorial GVNS (General Variable Neighborhood Search) Optimization for Dynamic Garbage Collection

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.

A QUBO Model for the Traveling Salesman Problem with Time Windows

“…Subsequently, a novel quantum-inspired unconventional metaheuristic method, based on the original General Variable Neighborhood Search (GVNS), was proposed in order to solve the standard TSP [73]. This quantum inspired metaheuristic was applied to the solution of the garbage collection problem modeled as a TSP instance [18]. Recently, Papalitsas et al [74] applied this quantum-inspired metaheuristic to the practical real-life problem of garbage collection with time windows.…”

“…The prospect of employing quantum computing principles for solving optimization problems is particularly promising [15][16][17][18][19]. In this approach, which can be considered as an "analog" method to tackle optimization problems, the ground state of a Hamiltonian represents an optimal solution of the optimization problem at hand.…”

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

“…A hybrid genetic algorithm for finding guaranteed and reliable solutions of global optimization problems using the branch-and-bound technique was proposed by Sotiropoulos et al [67]. A branch-and-bound approach was, also, used in the work of Pardalos et al in [68], where dynamic was applied to the solution of the garbage collection problem modeled as a TSP instance [17]. Recently, Papalitsas et al [72] applied this quantum-inspired metaheuristic to the practical real-life problem of garbage collection with time windows.…”

“…Inequality constraints such as these in (16) and (17) are notoriously difficult to express within the QUBO framework. For an extensive analysis we refer the interested reader to [28,59,74].…”

“…The preceding facts explain why optimization problems have been associated with quantum computing principles [14][15][16][17][18]. In this approach, which can be considered as an "analog" method to tackle optimization problems, the ground state of a Hamiltonian represents an optimal solution of the optimization problem at hand.…”