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

Application of a Modified ACO Algorithm for Optimizing Routes and Externality Effect of Solid Waste Management

To improve solid waste management and maintain its sustainability, it is important to reduce both the solid waste operational cost which includes the monetary value of distances covered and the externality effects of solid waste management. Therefore, this paper presents an application of a modified Ant Colony System algorithm to a bi-objective model for solid waste management in the Shama District in the Western Region of Ghana. The objective is to optimize route lengths and externality effects of solid waste management. Data on route lengths and population of communities along the routes were collected from 20 communities in the Shama Distric. Externality effect was measured by considering the population of the communities along the routes, the cost of treating a common cold subject to the assumption of two percent of the population being affected by the externality effect. The implemented algorithm has demonstrated the bi-objective optimal solution of route length (km) and externality effect (GHS) of (11, 2100) achievable on the path , which respectively represents a path linking the following communities: Aboadze, Abuesi Assorko Essaman, Beposo, Bosomdo and Fawomanye. There is therefore the need to ensure that the communities involved are linked with good roads

A robust solving strategy for the vehicle routing problem with multiple depots and multiple objectives

This document presents the development of a robust solving strategy for the Vehicle Routing Problem with Multiple Depots and Multiple Objectives (MO-MDVRP). The problem tackeled in this work is the problem to minimize the total cost and the load imbalance in vehicle routing plan for distribution of goods. This thesis presents a MILP mathematical model and a solution strategy based on a Hybrid Multi- Objective Scatter Search Algorithm. Several experiments using simulated instances were run proving that the proposed method is quite robust, this is shown in execution times (less than 4 minutes for an instance with 8 depots and 300 customers); also, the proposed method showed good results compared to the results found with the MILP model for small instances (up to 20 clients and 2 depots).MaestríaMagister en Ingeniería Industria

Sustainable distribution system design: a two-phase DoE-guided meta-heuristic solution approach for a three-echelon bi-objective AHP-integrated location-routing model

This article introduces a sustainable integrated bi-objective location-routing model, its two-phase solution approach and an analysis procedure for the distribution side of three-echelon logistics networks. The mixed-integer programming model captures several real-world factors by introducing an additional objective function and a set of new constraints in the model that outbound logistics channels find difficult to reconcile. The sustainable model minimises CO2 emissions from transportation and total costs incurred in facilities and the transportation channels. Design of Experiment (DoE) is integrated to the meta-heuristic based optimiser to solve the model in two phases. The DoE-guided solution approach enables the optimiser to offer the best stable solution space by taking out solutions with poor design features from the space and refining the feasible solutions using a convergence algorithm thereby selecting the realistic results. Several alternative solution scenarios are obtained by prioritising and ranking the realistic solution sets through a multi-attribute decision analysis tool, Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The robust model provides the decision maker the ability to take decisions on sustainable open alternative optimal routes. The outcomes of this research provide theoretical and methodological contributions, in terms of integrated bi-objective location-routing model and its two-phase DoE-guided meta-heuristic solution approach, for the distribution side of three-echelon logistics networks

A Many-objective Ant Colony Optimization applied to the Traveling Salesman Problem

Evolutionary algorithms present performance drawbacks when applied to Many-objective Optimization Problems (MaOPs). In this work, a novel approach based on Ant Colony Optimization theory (ACO), denominated ACO λ base-p algorithm, is proposed in order to handle Manyobjective instances of the well-known Traveling Salesman Problem (TSP). The proposed algorithm was applied to several Many-objective TSP instances, verifying the quality of the experimental results using the Hypervolume metric. A comparison with other state-of-the-art Multi Objective ACO algorithms as MAS, M3AS and MOACS as well as NSGA2 evolutionary algorithm was made, verifying that the best experimental results were obtained when the proposed algorithm was used, proving a good applicability to MaOPs.Facultad de Informátic

A Many-objective Ant Colony Optimization applied to the Traveling Salesman Problem

Evolutionary algorithms present performance drawbacks when applied to Many-objective Optimization Problems (MaOPs). In this work, a novel approach based on Ant Colony Optimization theory (ACO), denominated ACO λ base-p algorithm, is proposed in order to handle Manyobjective instances of the well-known Traveling Salesman Problem (TSP). The proposed algorithm was applied to several Many-objective TSP instances, verifying the quality of the experimental results using the Hypervolume metric. A comparison with other state-of-the-art Multi Objective ACO algorithms as MAS, M3AS and MOACS as well as NSGA2 evolutionary algorithm was made, verifying that the best experimental results were obtained when the proposed algorithm was used, proving a good applicability to MaOPs.Facultad de Informátic

Ant colony optimization based simulation of 3d automatic hose/pipe routing

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis focuses on applying one of the rapidly growing non-deterministic optimization algorithms, the ant colony algorithm, for simulating automatic hose/pipe routing with several conflicting objectives. Within the thesis, methods have been developed and applied to single objective hose routing, multi-objective hose routing and multi-hose routing. The use of simulation and optimization in engineering design has been widely applied in all fields of engineering as the computational capabilities of computers has increased and improved. As a result of this, the application of non-deterministic optimization techniques such as genetic algorithms, simulated annealing algorithms, ant colony algorithms, etc. has increased dramatically resulting in vast improvements in the design process. Initially, two versions of ant colony algorithms have been developed based on, respectively, a random network and a grid network for a single objective (minimizing the length of the hoses) and avoiding obstacles in the CAD model. While applying ant colony algorithms for the simulation of hose routing, two modifications have been proposed for reducing the size of the search space and avoiding the stagnation problem. Hose routing problems often consist of several conflicting or trade-off objectives. In classical approaches, in many cases, multiple objectives are aggregated into one single objective function and optimization is then treated as a single-objective optimization problem. In this thesis two versions of ant colony algorithms are presented for multihose routing with two conflicting objectives: minimizing the total length of the hoses and maximizing the total shared length (bundle length). In this case the two objectives are aggregated into a single objective. The current state-of-the-art approach for handling multi-objective design problems is to employ the concept of Pareto optimality. Within this thesis a new Pareto-based general purpose ant colony algorithm (PSACO) is proposed and applied to a multi-objective hose routing problem that consists of the following objectives: total length of the hoses between the start and the end locations, number of bends, and angles of bends. The proposed method is capable of handling any number of objectives and uses a single pheromone matrix for all the objectives. The domination concept is used for updating the pheromone matrix. Among the currently available multi-objective ant colony optimization (MOACO) algorithms, P-ACO generates very good solutions in the central part of the Pareto front and hence the proposed algorithm is compared with P-ACO. A new term is added to the random proportional rule of both of the algorithms (PSACO and P-ACO) to attract ants towards edges that make angles close to the pre-specified angles of bends. A refinement algorithm is also suggested for searching an acceptable solution after the completion of searching the entire search space. For all of the simulations, the STL format (tessellated format) for the obstacles is used in the algorithm instead of the original shapes of the obstacles. This STL format is passed to the C++ library RAPID for collision detection. As a result of using this format, the algorithms can handle freeform obstacles and the algorithms are not restricted to a particular software package