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

Evolutionary population dynamics and multi-objective optimisation problems

Griffith Sciences, School of Information and Communication TechnologyFull Tex

Global convexity in the bi-criteria Traveling Salesman problem

This work studies the solution space topology of the Traveling Salesman Problem or TSP, as a bi-objective optimization problem. The concepts of category and range of a solution are introduced for the first time in this analysis. These concepts relate each solution of a population to a Pareto set, presenting a more rigorous theoretical framework than previous works studying global convexity for the multi-objective TSP. The conjecture of a globally convex structure for the solution space of the bi-criteria TSP is confirmed with the results presented in this work. This may support successful applications using state of the art metaheuristics based on Ant Colony or Evolutionary Computation.IFIP International Conference on Artificial Intelligence in Theory and Practice - Evolutionary ComputationRed de Universidades con Carreras en Informática (RedUNCI

Global convexity in the bi-criteria Traveling Salesman problem

This work studies the solution space topology of the Traveling Salesman Problem or TSP, as a bi-objective optimization problem. The concepts of category and range of a solution are introduced for the first time in this analysis. These concepts relate each solution of a population to a Pareto set, presenting a more rigorous theoretical framework than previous works studying global convexity for the multi-objective TSP. The conjecture of a globally convex structure for the solution space of the bi-criteria TSP is confirmed with the results presented in this work. This may support successful applications using state of the art metaheuristics based on Ant Colony or Evolutionary Computation.IFIP International Conference on Artificial Intelligence in Theory and Practice - Evolutionary ComputationRed de Universidades con Carreras en Informática (RedUNCI

Multi-objective ant colony optimization for the twin-screw configuration problem

The Twin-Screw Configuration Problem (TSCP) consists in identifying the best location of a set of available screw elements along a screw shaft. Due to its combinatorial nature, it can be seen as a sequencing problem. In addition, different conflicting objectives may have to be considered when defining a screw configuration and, thus, it is usually tackled as a multi-objective optimization problem. In this research, a multi-objective ant colony optimization (MOACO) algorithm was adapted to deal with the TSCP. The influence of different parameters of the MOACO algorithm was studied and its performance was compared with that of a previously proposed multi-objective evolutionary algorithm and a two-phase local search algorithm. The experimental results showed that MOACO algorithms have a significant potential for solving the TSCP.This work has been supported by the Portuguese Fundacao para a Ciencia e Tecnologia under PhD grant SFRH/BD/21921/2005. Thomas Stutzle acknowledges support of the Belgian F.R.S-FNRS of which he is a research associate, the E-SWARM project, funded by an ERC Advanced Grant, and by the Meta-X project, funded by the Scientific Research Directorate of the French Community of Belgium

A Perturbed Self-organizing Multiobjective Evolutionary Algorithm to solve Multiobjective TSP

Travelling Salesman Problem (TSP) is a very important NP-Hard problem getting focused more on these days. Having improvement on TSP, right now consider the multi-objective TSP (MOTSP), broadened occurrence of travelling salesman problem. Since TSP is NP-hard issue MOTSP is additionally a NP-hard issue. There are a lot of algorithms and methods to solve the MOTSP among which Multiobjective evolutionary algorithm based on decomposition is appropriate to solve it nowadays. This work presents a new algorithm which combines the Data Perturbation, Self-Organizing Map (SOM) and MOEA/D to solve the problem of MOTSP, named Perturbed Self-Organizing multiobjective Evolutionary Algorithm (P-SMEA). In P-SMEA Self-Organizing Map (SOM) is used extract neighborhood relationship information and with MOEA/D subproblems are generated and solved simultaneously to obtain the optimal solution. Data Perturbation is applied to avoid the local optima. So by using the P-SMEA, MOTSP can be handled efficiently. The experimental results show that P-SMEA outperforms MOEA/D and SMEA on a set of test instances