A Constraint Programming Approach to Electric Vehicle Routing with Time Windows

Abstract

Due to the limited connectivity of gate model quantum devices, logical quantum circuits must be compiled to target hardware before they can be executed. Often, this process involves the insertion of SWAP gates into the logical circuit, usually increasing the depth of the circuit, achieved by solving a so-called qubit assignment and routing problem. Recently, a number of integer linear programming (ILP) models have been proposed for solving the qubit assignment and routing problem to proven optimality. These models encode the objective function and constraints of the problem, and leverage the use of automated solver technology to find hardware-compliant quantum circuits. In this work, we propose constraint programming (CP) models for this problem and compare their performance against ILP for circuit depth minimization for both linear and two-dimensional grid lattice device topologies on a set of randomly generated instances. Our empirical analysis indicates that the proposed CP approaches outperform the ILP models both in terms of solution quality and runtime.

Improving shuttle services quality in VUCA world: evidence from the IT industry

“…Bruno De Backer et al (2000) Hojabri et al (2018) studied the synchronized VRP and proposed a CP approach based on an adaptive large neighborhood search. Along the same line, Booth and Beck (2019) investigated a CP approach to solve an extension of VRP dedicated to electrical vehicles. The authors compare their results with an existing mixed-integer linear program (MILP).…”

Mathematical Models for Milk Dispatching Problem

“…El-Sherbeny (2010) provided a detailed review of vehicle routing problems with time windows (VRPTW), including exact, heuristic, and meta-heuristic applications. For the VRP problems, besides providing the MILP model, other exact solution techniques such as developing and solving the CP model (De Backer, Furnon, Shaw, Kilby, & Prosser, 2000;Hojabri, Gendreau, Potvin, & Rousseau, 2018;Booth & Beck, 2019;Hà et al, Hà et al, 2020;Öztop, Kizilay, & Çil, 2020) as well as lagrangian relaxation (LR) (Guimarans, Herrero, Ramos, & Padrón, 2011) are provided. Hojabri, Gendreau, Potvin, & Rousseau (2018) and Hà et al (2020) employ a CP approach for the VRP with synchronization constraints, whereas Booth & Beck (2019) propose a CP model for the electric vehicle routing with time windows and Öztop, Kizilay, & Çil (2020) develop a CP model for a periodic VRP with time windows and time spread constraints.…”

The HyperTrac Project: Recent Progress and Future Research Directions on Hypergraph Decompositions

“…[10,21,48,49,54,55]. CSPs provide convenient means to formulate combinatorial problems and are, therefore, also used in many applications in Operations Research spanning scheduling [22,40,46], vehicle routing [9,42,52], all kinds of graph problems such as colouring, matching, and many other areas [12,15,49].…”