Multi-objective Vehicle Routing Research Articles

A multi-objective vehicle routing and scheduling problem with uncertainty in customers’ request and priority

In this paper, a multi-objective vehicle routing and scheduling problem with uncertainty in priority and request of customers is presented. In the proposed model, a set of dynamic requests is received over time, and the planner does not have any information regarding their location and size until they arrive. Moreover, the routing model aims to satisfy different customers according to their specific time windows which were predefined by an expert as (being very important, important, casual or unimportant). This paper uses the proposed model as a multi-objective problem where the total required number of vehicles, the total distance travelled and the waiting time imposed on vehicles are minimized, and the total customers' satisfaction for service is maximized. An efficient framework for solving this model is designed and its performance is evaluated in different steps for various test problems generalized from Solomon's VRPTW benchmark problems. The various heuristics and improvement concepts incorporate local exploitation in the evolutionary search, and the concept of Pareto optimality for the multi-objective optimization is used in the proposed procedure. The computational experiments on data sets illustrate the efficiency and effectiveness of the proposed approach.

Cellular Ant Algorithm for the Multi-Objective Vehicle Routing Problem

Cellular Ant Algorithm for the Multi-Objective Vehicle Routing Problem

Multiobjective vehicle routing problem with fixed delivery and optional collections

We present an adaption on the formulation for the vehicle routing problem with fixed delivery and optional collections, in which the simultaneous minimization of route costs and of collection demands not fulfilled is considered. We also propose a multiobjective version of the iterated local search (MOILS). The performance of the MOILS is compared with the \(\epsilon \)-constrained (\(P_{\epsilon }\)) ILS, the NSGA-II and the indicator-based multi-objective local search methods in the solution of 14 problem instances containing between 50 and 199 customers plus the depot. The results indicate that the MOILS outperformed the other approaches, obtaining significantly better average values for coverage, hypervolume and cardinality.

Multiobjective Quantum Evolutionary Algorithm for the Vehicle Routing Problem with Customer Satisfaction

The multiobjective vehicle routing problem considering customer satisfaction (MVRPCS) involves the distribution of orders from several depots to a set of customers over a time window. This paper presents a self‐adaptive grid multi‐objective quantum evolutionary algorithm (MOQEA) for the MVRPCS, which takes into account customer satisfaction as well as travel costs. The degree of customer satisfaction is represented by proposing an improved fuzzy due‐time window, and the optimization problem is modeled as a mixed integer linear program. In the MOQEA, nondominated solution set is constructed by the Challenge Cup rules. Moreover, an adaptive grid is designed to achieve the diversity of solution sets; that is, the number of grids in each generation is not fixed but is automatically adjusted based on the distribution of the current generation of nondominated solution set. In the study, the MOQEA is evaluated by applying it to classical benchmark problems. Results of numerical simulation and comparison show that the established model is valid and the MOQEA is effective for MVRPCS.

A decomposition-based hierarchical optimization algorithm for hot rolling batch scheduling problem

In this paper, the hot rolling batch scheduling problem is formulated as a multi-objective vehicle routing problem with double time windows model, in which the first time window deals with the surface grade constraint and the second one is for the linkage modes. In view of the complexity of the proposed model and the priority of considered objectives in practical production, a decomposition-based hierarchical optimization algorithm is proposed to solve the model. Firstly, the model is decomposed into two sub-problems: vehicle routing problem with time windows (VRPTW) and single vehicle routing problem with time windows (SVRPTW). Secondly, MACS-VRPTW is used to optimize the VRPTW sub-problem, in which the first objective is prior to the second one. Then, dynamic programming and genetic algorithm are used to optimize the SVRPTW sub-problem so as to reach a higher hot charge temperature. Experimental results based on the practical production instances have indicated that the proposed model and algorithm are effective and efficient.

Multi-objective vehicle routing problem with time windows using goal programming and genetic algorithm

This paper presents a new model and solution for multi-objective vehicle routing problem with time windows (VRPTW) using goal programming and genetic algorithm that in which decision maker specifies optimistic aspiration levels to the objectives and deviations from those aspirations are minimized. VRPTW involves the routing of a set of vehicles with limited capacity from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. This paper uses a direct interpretation of the VRPTW as a multi-objective problem where both the total required fleet size and total traveling distance are minimized while capacity and time windows constraints are secured. The present work aims at using a goal programming approach for the formulation of the problem and an adapted efficient genetic algorithm to solve it. In the genetic algorithm various heuristics incorporate local exploitation in the evolutionary search and the concept of Pareto optimality for the multi-objective optimization. Moreover part of initial population is initialized randomly and part is initialized using Push Forward Insertion Heuristic and λ-interchange mechanism. The algorithm is applied to solve the benchmark Solomon's 56 VRPTW 100-customer instances. Results show that the suggested approach is quiet effective, as it provides solutions that are competitive with the best known in the literature.

Multi-objective vehicle routing problems

Routing problems, such as the traveling salesman problem and the vehicle routing problem, are widely studied both because of their classic academic appeal and their numerous real-life applications. Similarly, the field of multi-objective optimization is attracting more and more attention, notably because it offers new opportunities for defining problems. This article surveys the existing research related to multi-objective optimization in routing problems. It examines routing problems in terms of their definitions, their objectives, and the multi-objective algorithms proposed for solving them.

A self-tuning heuristic for a multi-objective vehicle routing problem

In this study, a heuristic free from parameter tuning is introduced to solve the vehicle routing problem (VRP) with two conflicting objectives. The problem which has been presented is the designing of optimal routes: minimizing both the number of vehicles and the maximum route length. This problem, even in the case of its single objective form, is NP-hard. The proposed self-tuning heuristic (STH) is based on local search and has two parameters which are updated dynamically throughout the search process. The most important advantage of the algorithm is the application convenience for the end-users. STH is tested on the instances of a multi-objective problem in school bus routing and classical vehicle routing. Computational experiments, when compared with the prior approaches proposed for the multi-objective routing of school buses problem, confirm the effectiveness of STH. STH also finds high-quality solutions for multi-objective VRPs.

Solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation

This paper considers the routing of vehicles with limited capacity from a central depot to a set of geographically dispersed customers where actual demand is revealed only when the vehicle arrives at the customer. The solution to this vehicle routing problem with stochastic demand (VRPSD) involves the optimization of complete routing schedules with minimum travel distance, driver remuneration, and number of vehicles, subject to a number of constraints such as time windows and vehicle capacity. To solve such a multiobjective and multi-modal combinatorial optimization problem, this paper presents a multiobjective evolutionary algorithm that incorporates two VRPSD-specific heuristics for local exploitation and a route simulation method to evaluate the fitness of solutions. A new way of assessing the quality of solutions to the VRPSD on top of comparing their expected costs is also proposed. It is shown that the algorithm is capable of finding useful tradeoff solutions for the VRPSD and the solutions are robust to the stochastic nature of the problem. The developed algorithm is further validated on a few VRPSD instances adapted from Solomon’s vehicle routing problem with time windows (VRPTW) benchmark problems.

Discussion of “Multiobjective Vehicle Routing and Scheduling Problem with Time Window Constraints in Hazardous Material Transportation” by Qiang Meng, Der-Horng Lee, and Ruey Long Cheu

A discussion of an article with the aforementioned article, published in this journal (Volume 131, No. 9, September 2005), is presented. The discussers agree with the importance of modeling time window constraints in routing and scheduling hazardous material transportation. They present some alternative suggestions regarding the quantification of accident rates, population exposure and trade-off between objectives that may lead to better decision-making.

Multiobjective Vehicle Routing and Scheduling Problem with Time Window Constraints in Hazardous Material Transportation

This paper proposes a novel vehicle routing and scheduling problem in transporting hazardous materials for networks with multiple time-varying attributes. It actually aims to identify all nondominated time-varying paths with departure times at the origin and waiting times at intermediate nodes along these paths for a given pair of origin and destination, subject to three kinds of practical constraints: Limited operational time period, and service, and waiting time window constraints at a node. Based on the assumption of linear waiting attributes at a node, the proposed problem can be equivalently transformed into a static multiobjective shortest path problem in an acyclic network reconstructed by the space-time network technique. An efficient dynamic programming method is then developed. In addition, two numerical examples and a case study are carried out to demonstrate the methodology proposed in this paper.

納期に対する満足度を考慮した多目的配送計画に関する研究 : Hybrid GAを用いたパレート最適集合の生成

In this paper, we proposed a hybrid genetic algorithm (Hybrid GA) approach to a multi-objective vehicle routing problem (MVRP). The objective functions considered in this MVRP are (1). to minimize the number of vehicles used, (2). to minimize the total traveling distance for vehicles, (3). to minimize the total waiting time for vehicles, and (4). to maximize the grade of customer satisfaction with due-time. With respect to customer satisfaction with due-time, we used the concept of fuzzy due-time because it can describe customers' preference with service time better than crisped expression of satisfaction with 0 and 1. To handle such multi-objectivity, a set of Pareto optimal solutions are searched by Hybrid GA. Among Pareto optimal solutions, we furthermore targeted at compromise solutions whose objective functions take almost intermediate values each, in order to produce realistic routing plans for vehicles. In the proposed algorithm, a local search procedure is applied to each solution at each generation for efficient search of solutions. The computational results show that the proposed algorithm is efficient for solving MVRP.

Multicriteria pickup and delivery problem with transfer opportunity

In this research, we develop a multiobjective vehicle routing and scheduling heuristic for a pickup and delivery problem. The problem contains time window, advanced request, multi-vehicle and many-to-many transport. In addition, the fleet size is not predetermined, and customers are allowed to transfer between vehicles. The objectives of scheduling are to minimize vehicle expense, tardiness and travel time. We propose a concurrent scheduling approach, which allocates customers to more than one vehicle and assigns more than one customer to a vehicle at a time. It differs from the usual concurrent approach in three aspects: (i) it uses the look-ahead strategy to construct miniroute; (ii) it adopts the head/tail, head, and tail integration techniques; and (iii) it allows interactivity. The procedure takes full advantage of due time and travel time information and is implemented through a computer program. It is a one-phase heuristic that can be reiterated when necessary. We provide detailed programming procedures and present the computational results of the proposed algorithm through the real data.

A multiobjective vehicle routing problem with soft time windows: the case of a public library distribution system

Over the years, the central focus of vehicle routing problems has been the construction of minimum cost delivery routes, i.e. the creation of spatial utilities without considering temporal aspects. In many public service organizations, however, the minimum cost route without time windows can lead to poor customer service due to its ignorance of delivery deadlines. On the other hand, the most timely route may excessively lengthen vehicle travel distance, thereby increasing the total distribution cost. Consequently, the public distribution system calls for a new vehicle routing model that both considers time windows and analyzes the tradeoff between time and cost. This paper develops such a model and verifies its practical usefulness by applying it to the case of a public library distribution system in the Columbus, Ohio metropolitan area.