Abstract
The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that has been of great interest for decades for both, science and industry. The CVRP is a variant of the vehicle routing problem characterized by capacity constrained vehicles. The aim is to plan tours for vehicles to supply a given number of customers as efficiently as possible. The problem is the combinatorial explosion of possible solutions, which increases superexponentially with the number of customers. Classical solutions provide good approximations to the globally optimal solution. D-Wave's quantum annealer is a machine designed to solve optimization problems. This machine uses quantum effects to speed up computation time compared to classic computers. The problem on solving the CVRP on the quantum annealer is the particular formulation of the optimization problem. For this, it has to be mapped onto a quadratic unconstrained binary optimization (QUBO) problem. Complex optimization problems such as the CVRP can be translated to smaller subproblems and thus enable a sequential solution of the partitioned problem. This work presents a quantum-classic hybrid solution method for the CVRP. It clarifies whether the implemenation of such a method pays off in comparison to existing classical solution methods regarding computation time and solution quality. Several approaches to solving the CVRP are elaborated, the arising problems are discussed, and the results are evaluated in terms of solution quality and computation time.
Highlights
Optimization problems can be found in many different domains of applications, be it economics and finance [3], logistics [9], or healthcare [7]
In this paper we investigate different quantum-classic hybrid approaches to solve the Capacitated Vehicle Routing Problem (CVRP), expound their difficulties in finding good solutions, and propose a hybrid method based on the 2-PhaseHeuristic to solve the CVRP using D-Wave’s quantum annealer
We exclusively analyze the Travelling Salesman Problem (TSP) which is executed on the quantum annealer to see how the different-sized problem instances are handled
Summary
Optimization problems can be found in many different domains of applications, be it economics and finance [3], logistics [9], or healthcare [7]. The classic CVRP can be described as the problem of designing optimal routes from one depot to a number of geographically scattered customers subject to some side constraints (see Figure 1). It can be formulated as follows: Let G = (V, E) be a graph with V = {1, ..., n} being a set of vertices representing n customer locations with the depot located at vertex 1 and E being a set of undirected edges. The sum of costs of all routes is minimal given the constraints above; To solve the CVRP on D-Wave’s quantum annealer, the formulated QUBO problem has to be mapped to the hardware. With this paper we present an intuitive way to split the CVRP into smaller optimization problems by taking advantage of a classical 2-Phase-Heuristic [26], see Figure 1.
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