Rich vehicle routing problems: From a taxonomy to a definition

Over the last years, several variants of multi-constrained Vehicle Routing Problems (VRPs) have been studied, forming a class of problems known as Rich Vehicle Routing Problems (RVRPs). The purpose of the paper is twofold: (i) to provide a comprehensive and relevant taxonomy for the RVRP literature and (ii) to propose an elaborate definition of RVRPs. To this end, selected papers addressing various cases are classified using the proposed taxonomy. Once the articles have been classified, a cluster analysis based on two discriminating criteria is performed and leads to the definition of RVRPs.     

Survivable routing and spectrum allocation algorithm based on p-cycle protection in elastic optical networks

With the number of large capacity applications in core network increasing, the bandwidth requirement of optical connections in conventional Wavelength Division Multiplexing (WDM) networks keeps enhancing, so that the Orthogonal Frequency Division Multiplexing (OFDM) technology is adopted to provide higher spectrum efficiency and flexibility in the future elastic optical networks. Meanwhile, survivability in the conventional WDM optical networks has been widely studied as an important issue to ensure the service continuity. However, survivability in OFDM-based elastic optical networks is more challenging than that in conventional WDM optical networks because each fiber usually carries even more connections. Therefore, it is necessary to study the new lightpath protection algorithm in elastic optical networks. Since p-cycle protection scheme has short restoration time and simple protection switching procedure, in this paper, we study the static Survivable p-Cycle Routing and Spectrum Allocation (SC-RSA) problem with providing an Integer Linear Programming (ILP) formulation. Since RSA is a NP-hard problem, we propose a new heuristic algorithm called Elastic p-Cycle Protection (ECP) to tolerate the single-fiber link failure. For each demand, ECP scheme can compute highly-efficient p-cycles to provide protection for all of the on-cycle links and the straddling links. We also consider the load balancing and choose the proper working path for each demand. Simulation results show that the proposed ECP scheme achieves better performances than traditional single-line-rate survivable schemes.     

A multi-start algorithm for a balanced real-world Open Vehicle Routing Problem

The aim of this paper is to solve a real-world problem proposed by an international company operating in Spain and modeled as a variant of the Open Vehicle Routing Problem in which the makespan, i.e., the maximum time spent on the vehicle by one person, must be minimized. A competitive multi-start algorithm, able to obtain high quality solutions within reasonable computing time is proposed. The effectiveness of the algorithm is analyzed through computational testing on a set of 19 school-bus routing benchmark problems from the literature, and on 9 hard real-world problem instances.     

Efficiently navigating a random Delaunay triangulation

Planar graph navigation is an important problem with significant implications to both point location in geometric data structures and routing in networks. However, whilst a number of algorithms and existence proofs have been proposed, very little analysis is available for the properties of the paths generated and the computational resources required to generate them under a random distribution hypothesis for the input. In this paper we analyse a new deterministic planar navigation algorithm with constant spanning ratio (w.r.t the Euclidean distance) which follows vertex adjacencies in the Delaunay triangulation. We call this strategy cone walk. We prove that given n uniform points in a smooth convex domain of unit area, and for any start point z and query point q; cone walk applied to z and q will access at most sites with complexity with probability tending to 1 as n goes to infinity. We additionally show that in this model, cone walk is ‐memoryless with high probability for any pair of start and query point in the domain, for any positive ξ. We take special care throughout to ensure our bounds are valid even when the query points are arbitrarily close to the border. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 95–136, 2016     

用于解决大规模波长路由光网中路由和波长分配问题的新启发式算法

本文提出了一种新的启发式算法,它将路由和波长分配问题分解为两个子问题分别进行优化求解,并以最小化波长需求作为目标函数。在不同通信负荷的情况下,我们以NSF网为例,分析了波长通道(WP)和虚波长通道(VWP)路由方案之间在波长需求方面的差别。同时还研究了网络波长重用度的问题。数值结果表明所提出的算法可有效地应用于大规模波长路由光网。     

Min–Max vs. Min–Sum Vehicle Routing: A worst-case analysis

The classical objective function of the Vehicle Routing Problem (VRP) is to minimize the total distance traveled by all vehicles (Min–Sum). In several situations, such as disaster relief efforts, computer networks, and workload balance, the minimization of the longest route (Min–Max) is a better objective function. In this paper, we compare the optimal solution of several variants of the Min–Sum and the Min–Max VRP, from the worst-case point of view. Our aim is two-fold. First, we seek to motivate the design of heuristic, metaheuristic, and matheuristic algorithms for the Min–Max VRP, as even the optimal solution of the classical Min–Sum VRP can be very poor if used to solve the Min–Max VRP. Second, we aim to show that the Min–Max approach should be adopted only when it is well-justified, because the corresponding total distance can be very large with respect to the one obtained by optimally solving the classical Min–Sum VRP.     

An extension of labeling techniques for finding shortest path trees

Label setting techniques are all based on Dijkstra’s condition of always scanning the node with the minimum label, which guarantees that each node will be scanned exactly once; while this condition is sufficient it is not necessary. In this paper, we discuss less restrictive conditions that allow the scanning of a node that does not have the minimum label, yet still maintaining sufficiency in scanning each node exactly once; various potential shortest path schemes are discussed, based on these conditions. Two approaches, a label setting and a flexible hybrid one are designed and implemented. The performance of the algorithms is assessed both theoretically and computationally. For comparative analysis purposes, three additional shortest path algorithms – the commonly cited in the literature – are coded and tested. The results indicate that the approaches that rely on the less restrictive optimality conditions perform substantially better for a wide range of network topologies.     

Multi-objective evacuation routing in transportation networks

In this paper, the optimal design and analysis of evacuation routes in transportation networks is examined. An methodology for optimal egress route assignment is suggested. An integer programming (IP) formulation for optimal route assignment is presented, which utilizes M/G/c/c state dependent queueing models to cope with congestion and time delays on road links. M/G/c/c simulation software is used to evaluate performance measures of the evacuation plan: clearance time, total travelled distance and blocking probabilities. Extensive experimental results are included.     

无线传感器网络多跳路由协议研究

目的：无线传感器网络发展迅速,但传感器的高能耗问题成为制约其发展的主要瓶颈,高效节能的路由协议设计成为研究热点。方法：针对目前无线传感器网络常用的LEACH路由协议存在的簇首能耗过分集中、簇首分布不均衡问题,提出了改进的路由协议EEACRA,在总结、分析LEACH路由协议现有问题的基础上,给出了EEACRA路由协议的簇首选取门限值、簇首位置调整算法和基于能量代价最小的簇间多跳路由算法的实现方法,同时给出了具体的实现EEACRA协议的工作流程和关键算法。在MATLAB环境下对LEACH路由协议和EEACRA路由协议进行了仿真,对比了不同能耗降低措施对网络能耗降低的贡献。结果：仿真结果表明EEACRA路由协议的网络稳定期较LEACH路由协议有较大的改善。结论：证明了改进的路由协议EEACRA可以有效地提高网络的稳定期。     

A novel algorithm to integrate synchronous digital hierarchy networks into Optical Transport Network using mixed line rates

In this era of high data transfer speeds and new age technologies, Optical Transport Network (OTN) along with its newly introduced Optical Transport Hierarchy (OTH) has provided a lease of life to legacy low rate networks. It has provided a common backbone for multiple data rates to coexist on same fiber along with the enhanced transmission reach. The cost effective Optical Transport Network design has always been a complex issue due to the presence of multiple variables like number of fibers on each link, available data rates on each fiber, the wavelength count, transmission reach at each data rate, etc. In this paper an Integer Linear Programming (ILP) model has been presented to solve Routing problem for Synchronous Digital Hierarchy (SDH) over OTN over DWDM design. Optical Transport Hierarchy (OTH) has been used to integrate heterogenous SDH/SONET operating at different rates (STM-16, STM-64 and STM-256) into a single network supporting mixed line rates. These rates can coexist in a same fiber but each rate carries different cost with it. The objective function aims at finding the least cost routing solution by looking at different tradeoffs between the Capital Expenditure and the operational expenditure. Certainly different variables like the number of fibers and wavelengths, transmission reach, etc. are a factor in it. A mechanism has been put to monitor the Bit Error Rate (BER) levels as well. For evaluating the ILP model, 18 Node 38 Link European Optical Network was considered as the reference model and two ordering techniques, namely, full ILP and highest rate first (HRF) were used for deriving the results. The ILP model was designed with minimum of decision variables so in spite of big reference network it converges much faster. Under the given conditions, full ILP gave least cost network whereas HRF ordering took least time for ILP to converge.