Workload Equity in Vehicle Routing Problems: A Survey and Analysis

Over the past two decades, equity aspects have been considered in a growing number of models and methods for vehicle routing problems (VRPs). Equity concerns most often relate to fairly allocating workloads and to balancing the utilization of resources, and many practical applications have been reported in the literature. However, there has been only limited discussion about how workload equity should be modeled in VRPs, and various measures for optimizing such objectives have been proposed and implemented without a critical evaluation of their respective merits and consequences. This article addresses this gap with an analysis of classical and alternative equity functions for biobjective VRP models. In our survey, we review and categorize the existing literature on equitable VRPs. In the analysis, we identify a set of axiomatic properties that an ideal equity measure should satisfy, collect six common measures, and point out important connections between their properties and those of the resulting Pareto-optimal solutions. To gauge the extent of these implications, we also conduct a numerical study on small biobjective VRP instances solvable to optimality. Our study reveals two undesirable consequences when optimizing equity with nonmonotonic functions: Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all tours are TSP optimal, Pareto-optimal solutions can be workload inconsistent, i.e. composed of tours whose workloads are all equal to or longer than those of other Pareto-optimal solutions. We show that the extent of these phenomena should not be underestimated. The results of our biobjective analysis are valid also for weighted sum, constraint-based, or single-objective models. Based on this analysis, we conclude that monotonic equity functions are more appropriate for certain types of VRP models, and suggest promising avenues for further research.Comment: Accepted Manuscrip

Joint multicast routing and channel assignment in multiradio multichannel wireless mesh networks using tabu search

Copyright @ 2009 IEEE Computer SocietyThis paper proposes a tabu search (TS) based optimization approach to search a minimum-interference multicast tree which satisfies the end-to-end delay constraint and optimizes the usage of the scarce radio network resource in wireless mesh networks. The path-oriented encoding method is adopted and each candidate solution is represented by a tree data structure (i.e., a set of paths). Since we expect the multicast trees on which the minimum-interference channel assignment can be produced, a fitness function that returns the total channel conflict is devised. The techniques for controlling the tabu search procedure are well developed. A simple yet effective channel assignment algorithm is proposed to reduce the channel conflict. Simulation results show that the proposed TS multicast algorithm can produce the multicast trees which have better performance in terms of both the total channel conflict and the tree cost than that of a well known multicast algorithm in wireless mesh networks.This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1

A Computational Study of Genetic Crossover Operators for Multi-Objective Vehicle Routing Problem with Soft Time Windows

The article describes an investigation of the effectiveness of genetic algorithms for multi-objective combinatorial optimization (MOCO) by presenting an application for the vehicle routing problem with soft time windows. The work is motivated by the question, if and how the problem structure influences the effectiveness of different configurations of the genetic algorithm. Computational results are presented for different classes of vehicle routing problems, varying in their coverage with time windows, time window size, distribution and number of customers. The results are compared with a simple, but effective local search approach for multi-objective combinatorial optimization problems

Issues in the Scalability of Gate-level Morphogenetic Evolvable Hardware

Traditional approaches to evolvable hardware (EHW), in which the field programmable gate array (FPGA) configuration is directly encoded, have not scaled well with increasing circuit and FPGA complexity. To overcome this there have been moves towards encoding a growth process, known as morphogenesis. Using a morphogenetic approach, has shown success in scaling gate-level EHW for a signal routing problem, however, when faced with a evolving a one-bit full adder, unforseen difficulties were encountered. In this paper, we provide a measurement of EHW problem difficulty that takes into account the salient features of the problem, and when combined with a measure of feedback from the fitness function, we are able to estimate whether or not a given EHW problem is likely to be able to be solved successfully by our morphogenetic approach. Using these measurements we are also able to give an indication of the scalability of morphogenesis when applied to EHW

Joint multicast routing and channel assignment in multiradio multichannel wireless mesh networks using simulated annealing

This is the post-print version of the article - Copyright @ 2008 Springer-VerlagThis paper proposes a simulated annealing (SA) algorithm based optimization approach to search a minimum-interference multicast tree which satisfies the end-to-end delay constraint and optimizes the usage of the scarce radio network resource in wireless mesh networks. In the proposed SA multicast algorithm, the path-oriented encoding method is adopted and each candidate solution is represented by a tree data structure (i.e., a set of paths). Since we anticipate the multicast trees on which the minimum-interference channel assignment can be produced, a fitness function that returns the total channel conflict is devised. The techniques for controlling the annealing process are well developed. A simple yet effective channel assignment algorithm is proposed to reduce the channel conflict. Simulation results show that the proposed SA based multicast algorithm can produce the multicast trees which have better performance in terms of both the total channel conflict and the tree cost than that of a well known multicast algorithm in wireless mesh networks.This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1