Experiments on the Node, Edge, and Arc Routing Problem

The Node, Edge, and Arc Routing Problem (NEARP) was defined by Prins and Bouchenoua in 2004 along with the first benchmark called CBMix. The NEARP generalizes the classical Capacitated Vehicle Routing Problem (CVRP), the Capacitated Arc Routing Problem (CARP), and the General Routing Problem. It is also denoted the Mixed Capacitated General Routing Problem (MCGRP). The NEARP removes the strict and unwarranted dichotomy that previously existed in the literature between arc routing and node routing. In real applications, there are many cases where the pure node or arc routing models are not adequate. In fundamentally node-based routing applications such as newspaper delivery and communal waste management that have typically been modeled as arc routing problems in the literature, the number of points is often so large that demand aggregation is necessary. Aggregation heuristics will normally give a NEARP instance, possibly with side constraints. Hence, the NEARP is a scientifically challenging problem with high industrial relevance. In this report we present experiments with Spider, SINTEF’s industrial VRP solver, on the three NEARP benchmarks that have been published so far: CBMix, BHW, and DI-NEARP. Bach, Hasle, and Wøhlk have developed a combinatorial lower bound for the NEARP and defined the two latter benchmarks. Here, we present an experimental study with Spider on the three existing NEARP benchmarks. Upper and lower bounds are given for all instances. Three of the BHW instances have been solved to optimality. SINTEF has developed a web page for NEARP results on http://www.sintef.no/NEARP

Experiments on the Node, Edge, and Arc Routing Problem

-The Node, Edge, and Arc Routing Problem (NEARP) was defined by Prins and Bouchenoua in 2004 along with the first benchmark called CBMix. The NEARP generalizes the classical Capacitated Vehicle Routing Problem (CVRP), the Capacitated Arc Routing Problem (CARP), and the General Routing Problem. It is also denoted the Mixed Capacitated General Routing Problem (MCGRP). The NEARP removes the strict and unwarranted dichotomy that previously existed in the literature between arc routing and node routing. In real applications, there are many cases where the pure node or arc routing models are not adequate. In fundamentally node-based routing applications such as newspaper delivery and communal waste management that have typically been modeled as arc routing problems in the literature, the number of points is often so large that demand aggregation is necessary. Aggregation heuristics will normally give a NEARP instance, possibly with side constraints. Hence, the NEARP is a scientifically challenging problem with high industrial relevance. In this report we present experiments with Spider, SINTEF’s industrial VRP solver, on the three NEARP benchmarks that have been published so far: CBMix, BHW, and DI-NEARP. Bach, Hasle, and Wøhlk have developed a combinatorial lower bound for the NEARP and defined the two latter benchmarks. Here, we present an experimental study with Spider on the three existing NEARP benchmarks. Upper and lower bounds are given for all instances. Three of the BHW instances have been solved to optimality. SINTEF has developed a web page for NEARP results on http://www.sintef.no/NEARP

Optimal Orchestration of Virtual Network Functions

-The emergence of Network Functions Virtualization (NFV) is bringing a set of novel algorithmic challenges in the operation of communication networks. NFV introduces volatility in the management of network functions, which can be dynamically orchestrated, i.e., placed, resized, etc. Virtual Network Functions (VNFs) can belong to VNF chains, where nodes in a chain can serve multiple demands coming from the network edges. In this paper, we formally define the VNF placement and routing (VNF-PR) problem, proposing a versatile linear programming formulation that is able to accommodate specific features and constraints of NFV infrastructures, and that is substantially different from existing virtual network embedding formulations in the state of the art. We also design a math-heuristic able to scale with multiple objectives and large instances. By extensive simulations, we draw conclusions on the trade-off achievable between classical traffic engineering (TE) and NFV infrastructure efficiency goals, evaluating both Internet access and Virtual Private Network (VPN) demands. We do also quantitatively compare the performance of our VNF-PR heuristic with the classical Virtual Network Embedding (VNE) approach proposed for NFV orchestration, showing the computational differences, and how our approach can provide a more stable and closer-to-optimum solution

The two-echelon capacitated vehicle routing problem: models and math-based heuristics

Multiechelon distribution systems are quite common in supply-chain and logistics. They are used by public administrations in their transportation and traffic planning strategies, as well as by companies, to model own distribution systems. In the literature, most of the studies address issues relating to the movement of flows throughout the system from their origins to their final destinations. Another recent trend is to focus on the management of the vehicle fleets required to provide transportation among different echelons. The aim of this paper is twofold. First, it introduces the family of two-echelon vehicle routing problems (VRPs), a term that broadly covers such settings, where the delivery from one or more depots to customers is managed by routing and consolidating freight through intermediate depots. Second, it considers in detail the basic version of two-echelon VRPs, the two-echelon capacitated VRP, which is an extension of the classical VRP in which the delivery is compulsorily delivered through intermediate depots, named satellites. A mathematical model for two-echelon capacitated VRP, some valid inequalities, and two math-heuristics based on the model are presented. Computational results of up to 50 customers and four satellites show the effectiveness of the methods developed