3,012 research outputs found
Route Planning in Transportation Networks
We survey recent advances in algorithms for route planning in transportation
networks. For road networks, we show that one can compute driving directions in
milliseconds or less even at continental scale. A variety of techniques provide
different trade-offs between preprocessing effort, space requirements, and
query time. Some algorithms can answer queries in a fraction of a microsecond,
while others can deal efficiently with real-time traffic. Journey planning on
public transportation systems, although conceptually similar, is a
significantly harder problem due to its inherent time-dependent and
multicriteria nature. Although exact algorithms are fast enough for interactive
queries on metropolitan transit systems, dealing with continent-sized instances
requires simplifications or heavy preprocessing. The multimodal route planning
problem, which seeks journeys combining schedule-based transportation (buses,
trains) with unrestricted modes (walking, driving), is even harder, relying on
approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4,
previously published by Microsoft Research. This work was mostly done while
the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at
Microsoft Research Silicon Valle
Ant colony optimization and its application to the vehicle routing problem with pickups and deliveries
Ant Colony Optimization (ACO) is a population-based metaheuristic that can be used to find approximate solutions to difficult optimization problems. It was first introduced for solving the Traveling Salesperson Problem. Since then many implementations of ACO have been proposed for a variety of combinatorial optimization. In this chapter, ACO is applied to the Vehicle Routing Problem with Pickup and Delivery (VRPPD). VRPPD determines a set of vehicle routes originating and ending at a single depot and visiting all customers exactly once. The vehicles are not only required to deliver goods but also to pick up some goods from the customers. The objective is to minimize the total distance traversed. The chapter first provides an overview of ACO approach and presents several implementations to various combinatorial optimization problems. Next, VRPPD is described and the related literature is reviewed, Then, an ACO approach for VRPPD is discussed. The approach proposes a new visibility function which attempts to capture the “delivery” and “pickup” nature of the problem. The performance of the approach is tested using well-known benchmark problems from the literature
Building Blocks for Mapping Services
Mapping services are ubiquitous on the Internet. These services enjoy a considerable user base. But it is often overlooked that providing a service on a global scale with virtually millions of users has been the playground of an oligopoly of a select few service providers are able to do so. Unfortunately, the literature on these solutions is more than scarce. This thesis adds a number of building blocks to the literature that explain how to design and implement a number of features
The Dynamic Multi-objective Multi-vehicle Covering Tour Problem
This work introduces a new routing problem called the Dynamic Multi-Objective Multi-vehicle Covering Tour Problem (DMOMCTP). The DMOMCTPs is a combinatorial optimization problem that represents the problem of routing multiple vehicles to survey an area in which unpredictable target nodes may appear during execution. The formulation includes multiple objectives that include minimizing the cost of the combined tour cost, minimizing the longest tour cost, minimizing the distance to nodes to be covered and maximizing the distance to hazardous nodes. This study adapts several existing algorithms to the problem with several operator and solution encoding variations. The efficacy of this set of solvers is measured against six problem instances created from existing Traveling Salesman Problem instances which represent several real countries. The results indicate that repair operators, variable length solution encodings and variable-length operators obtain a better approximation of the true Pareto front
Quantum-Assisted Solution Paths for the Capacitated Vehicle Routing Problem
Many relevant problems in industrial settings result in NP-hard optimization
problems, such as the Capacitated Vehicle Routing Problem (CVRP) or its reduced
variant, the Travelling Salesperson Problem (TSP). Even with today's most
powerful classical algorithms, the CVRP is challenging to solve classically.
Quantum computing may offer a way to improve the time to solution, although the
question remains open as to whether Noisy Intermediate-Scale Quantum (NISQ)
devices can achieve a practical advantage compared to classical heuristics. The
most prominent algorithms proposed to solve combinatorial optimization problems
in the NISQ era are the Quantum Approximate Optimization Algorithm (QAOA) and
the more general Variational Quantum Eigensolver (VQE). However, implementing
them in a way that reliably provides high-quality solutions is challenging,
even for toy examples. In this work, we discuss decomposition and formulation
aspects of the CVRP and propose an application-driven way to measure solution
quality. Considering current hardware constraints, we reduce the CVRP to a
clustering phase and a set of TSPs. For the TSP, we extensively test both QAOA
and VQE and investigate the influence of various hyperparameters, such as the
classical optimizer choice and strength of constraint penalization. Results of
QAOA are generally of limited quality because the algorithm does not reach the
energy threshold for feasible TSP solutions, even when considering various
extensions such as recursive, warm-start and constraint-preserving mixer QAOA.
On the other hand, the VQE reaches the energy threshold and shows a better
performance. Our work outlines the obstacles to quantum-assisted solutions for
real-world optimization problems and proposes perspectives on how to overcome
them.Comment: Submitted to the IEEE for possible publicatio
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