Vehicle Capacity Constraints Research Articles

Alleviating bus bunching via modular vehicles

The notorious phenomenon of bus bunching prevailing in uncontrolled bus systems produces irregular headways and downgrades the level of service by increasing passengers’ expected waiting time. Modular autonomous vehicles (MAVs), due to their ability to split and merge en route, have the potential to help both late and early buses recover from schedule deviation while providing continuous service. In this paper, we propose a novel bus bunching alleviation strategy for MAV-aided transit systems. We first consider a soft vehicle capacity constraint and establish a continuum approximation (CA) model (Model I) to capture the system dynamics intertwined with the MAV splitting and merging operations, and then establish an infinite-horizon stochastic optimization model to determine the optimal splitting and merging strategy. To capture the reality that passengers may fail to board an overcrowded bus, we propose a second model (Model II) by extending Model I to accommodate a hard vehicle capacity constraint. Based on the characteristics of the problem, we develop a customized deep Q-network (DQN) algorithm with multiple relay buffers and a penalized ruin state applicable for both models to optimize the strategy for each MAV. Numerical results show that the strategy obtained via the DQN algorithm is an effective bunch-proof strategy and has a better performance than the myopic strategy for MAV-aided systems and the two-way-looking strategy for conventional bus systems. Sensitivity analyses are also conducted to examine the effectiveness and benefits of the proposed strategy across different operation scenarios.

Logistics vehicle routing optimisation with synchronised transfer

This paper presents a synchronized transfer strategy in which operators can schedule logistics vehicles among employees and arrange the transfer of commodities. The transfer time consists of the vehicle waiting time and commodity transition time. By adopting the strategy, logistics vehicles can visit fewer communities, resulting in savings in transportation cost under ensuring punctual delivery. An integer programming model based on a space-time-state network is proposed to describe the complex transfer process. To simplify the model, time window and vehicle capacity constraints are embedded into the network. The alternating direction method of multipliers (ADMM) is designed to solve the model. In the ADMM-based solution framework, the original model can be converted into a series of shortest-path searching subproblems and iteratively solved using a dynamic programming (DP) algorithm. Our computational results show that the proposed model and algorithm are efficient and competitive.

Determination of the Distribution Route for Bottled Drinking Water Using Sweep Algorithm and Saving Algorithm

The route determination by the heuristic way in the Vehicle Routing Problem (VRP) is an approach to distribution with the goal of minimizing distribution routes, assuming that vehicle routes must depart from and return to the central facility by finding the shortest or fastest route. The heuristic methods used include the sweep method and saving matrix for the grouping phase, while the improvement phase for each formed cluster utilizes the intra-route insertion algorithm. The results show that the heuristic approach indicates that the saving method produces shorter travel distances compared to the sweep method. For the characteristics of this data, the saving method may be better in handling vehicle capacity constraints. The choice between the saving method and the sweep method depends heavily on factors such as the distance between consumers, the number of distribution points, and vehicle capacity constraints.

Smart Waste Collection Based on Vehicle Routing Optimization: Case of Casablanca City

Morocco has implemented circular economy principles in their waste management program to close or rehabilitate all existing landfills. However, the waste collection and transportation process remain highly inefficient and costly, contributing to a substantial environmental footprint for waste collection operations. The inefficiencies in the current waste management system highlight the need for innovative solutions to optimize collection processes and minimize environmental impact. This study responds to this imperative by proposing the use of smart bin technology combined with a vehicle routing problem tool. The integration of these technologies aims to develop an intelligent solution for appropriate waste collection, limiting container pickup only when necessary, and optimizing waste collection routes. Our approach considers several factors, including the fill level of each container, time windows, vehicle capacity, and tour completion constraints. By addressing these key factors, the system seeks to revolutionize waste management practices, improving the efficiency and effectiveness of waste collection.

A co-evolutionary genetic algorithm with knowledge transfer for multi-objective capacitated vehicle routing problems

The capacitated vehicle routing problem (CVRP) aims to find the routes that minimize transportation costs. However, in real-world applications, the equitable workload is essential for the drivers and logistics companies. For assigning an appropriate load for each vehicle, this paper formulates the CVRP with workload balancing as a multi-objective optimization problem (MO-CVRP). The goal is to simultaneously minimize the total length of routes and the variance of loads assigned to each vehicle. Although several multi-objective evolutionary algorithms (MOEAs) have been proposed for the MO-CVRP, they often suffer from slow convergence speeds due to the complexity of the search space, which hinders the identification of clear search directions. To address this issue, the knowledge transfer method is introduced that can leverage search experiences from related problems to expedite the solution process of the current problem. Specifically, a co-evolutionary genetic algorithm with knowledge transfer is proposed, where a simplified version of the traveling salesman problem (TSP) by disregarding the vehicle capacity constraint is utilized to facilitate the quick solution of the original MO-CVRP. To enable information interaction between these two problems, the widely used denoising autoencoder is adopted to construct a transformation relation between solutions from the TSP to the MO-CVRP. Additionally, an adaptive migration strategy is proposed to adaptively select the migration methods and an improved split operator strategy is designed to ensure the feasibility of the solutions. The proposed algorithm is compared with four state-of-the-art MOEAs on MO-CVRP test sets with different scales. Experimental results show that the proposed algorithm exhibits faster convergence speed and achieves solutions with superior convergence.

An improved particle swarm optimization with particle refactor operator for perishable food delivery problems by electric vehicles

ABSTRACT The increasing demand for perishable food and the popularity of electric vehicles have promoted the integration research of perishable food delivery services and electric vehicles. Aiming at minimizing the total delivery cost, a new model is formulated for perishable food delivery problems by electric vehicles (PFDP-EV), which considers vehicle capacity constraints, travel time constraints, time window constraints, and so on. An improved particle swarm optimization with particle refactor operator (IPSO-PRO) is developed to solve the proposed model. For the IPSO-PRO, a particle refactor operator is designed to help reconstruct the unqualified particles, and an elite selection strategy and an adaptive weighted strategy are used to improve the performance. Then, extensive efforts are conducted to verify the proposed method. First, the parameters of IPSO-PRO are tuned based on the Taguchi method. Second, small-scale, medium-scale, and large-scale perishable food delivery instances (19 instances) are simulated to evaluate the performance, and the results show that IPSO-PRO achieves the best average gap of 0%. Finally, based on a simulation case, the result and sensitivity analysis are conducted to reveal insightful management insights, which provides decision support for perishable food delivery problems.

Multi-depot vehicle scheduling with multiple vehicle types on overlapped bus routes

In China, overlapped routes from multiple bus lines are widespread. Some buses are overcrowded while others have few passengers. The goal of this study is to reduce onboard passenger crowding without wasting bus capacity. This paper examines an extended multiple-depot vehicle scheduling problem (VSP) with multiple vehicle types. First, a bi-objective integer programming model was created. The trade-off between operating cost and passenger travel cost was established and the crowding cost due to different vehicle sizes was especially considered. Then, the capacity restraint incremental assignment algorithm and a vehicle scheduling method with multiple vehicle types were developed to find Pareto-optimal solutions that considered vehicle capacity constraints. Finally, the proposed methodology was validated using a real-world transit network in Beijing, China. The optimization results from about 1.18 million bus card swiping records show that our model and solution algorithm can effectively reduce the passenger crowding cost and avoid the waste of transport capacity.

Route efficiency implications of time windows and vehicle capacities in first- and last-mile logistics

In this paper, we analyze the route efficiency effects that emerge from combining realistically constrained first-mile pickup and last-mile delivery operations into joint vehicle routes. Specifically, we examine (i) the individual effect of discrete, non-overlapping time window constraints; (ii) the individual effect of vehicle capacity constraints; and (iii) the joint impact of both constraint types on local route efficiency gains due to the integration of pickup and delivery operations. Extending the existent literature on continuum approximation of route distances, we propose closed-form adjustment factors which accurately capture these non-trivial route efficiency effects. To derive the adjustment factors, we conduct extensive numerical experiments and apply a novel hybrid data analysis approach which combines exploratory data analysis with symbolic regression. Our analysis suggests that these real-world constraints affect the optimal stop sequence and diminish or even eliminate the expected efficiency gains from integrating first- and last-mile operations. The proposed adjustment factors are particularly relevant for the optimal strategic design and operational planning of modern, industrial-scale distribution networks in light of growing and increasingly fragmented e-commerce volumes and a high cost pressure on the logistics industry. They help researchers and practitioners to efficiently quantify the expected benefits from integrating pickup and delivery operations, and to assess under which circumstances such an integration is (not) desirable.

Nature-Inspired Optimal Route Network Design for Shared Autonomous Vehicles

Emerging forms of shared mobility call for new vehicle routing models that take into account vehicle sharing, ride sharing and autonomous vehicle fleets. This study deals with the design of an optimal route network for autonomous vehicles, considering both vehicle sharing and ride sharing. The problem is modeled as a one-to-many-to-one vehicle routing problem with vehicle capacity and range constraints. An ant colony optimization algorithm is applied to the problem in order to construct a set of routes that satisfies user requests under operational constraints. Results show that the algorithm is able to produce solutions in relatively short computational times, while exploiting the possibility of ride sharing to reduce operating costs. Results also underline the potential of exploiting shared autonomous vehicles in the context of a taxi service for booking trips through electronic reservation systems.

Shuttle Bus Timetable Adjustment in Response to Behind-Schedule Commuter Railway Disturbance

Shuttle bus connection is a valid technique to handle unplanned problems and promote sustainable transportation. The study describes tools that facilitate the shuttle bus timetable adjustment responding to a disturbance resulting from behind-schedule trains on a commuter railway. This behind-schedule disturbance is divided in four stages allowing for different delay ranges. The problem and its solution involve different elements, such as shuttle bus route selection, stop location, and timetable adjustment. We propose a nonlinear integer programming model, in which the objective function is based on the waiting, travelling, and walking costs for passengers as well as the operation cost of the route chosen. Vehicle capacity constraints and precise passengers’ waiting times are considered. A genetic algorithm and a simulated annealing algorithm combined with a priori decomposition are used to derive an efficient solution. A case study of a shuttle bus serving the Jinshan Railway in Shanghai, China, is tested to validate that, compared to the no-planning timetable, the total cost of the optimized timetable is reduced by 7.6%, especially including a dramatic reduction in the cost of passenger waiting time by 49.1%.

Local Optima Network Analysis of Multi-Attribute Vehicle Routing Problems

Multi-Attribute Vehicle Routing Problems (MAVRP) are variants of Vehicle Routing Problems (VRP) in which, besides the original constraint on vehicle capacity present in Capacitated Vehicle Routing Problem (CVRP), other attributes that model diverse real-life system characteristics are present. Among the most common attributes studied in the literature are vehicle capacity and route duration constraints. The influence of these restrictions on the overall structure of the problem and the performance of local search algorithms used to solve it has yet to be well known. This paper aims to explain the impact of constraints present in different variants of VRP through the alterations of the structure of the underlying search space that they cause. We focus on Local Optima Network Analysis (LONA) for multiple Traveling Salesman Problem (m-TSP) and VRP with vehicle capacity (CVRP), route duration (DVRP), and both (DCVRP) constraints. We present results that indicate that measures obtained for a sample of local optima provide valuable information on the behavior of the landscape under modifications in the problem’s constraints. Additionally, we use the LONA measures to explain the difficulty of VRP instances for solving by local search algorithms.

Evolutionary algorithm based approach for solving transportation problems in normal and pandemic scenario

In recent times, COVID-19 pandemic has posed certain challenges to transportation companies due to the restrictions imposed by different countries during the lockdown. These restrictions cause delay and/ or reduction in the number of trips of vehicles, especially, to the regions with higher restrictions. In a pandemic scenario, regions are categorized into different groups based on the levels of restrictions imposed on the movement of vehicles based on the number of active cases (i.e., number of people infected by COVID-19), number of deaths, population, number of COVID-19 hospitals, etc. The aim of this study is to formulate and solve a fixed-charge transportation problem (FCTP) during this pandemic scenario and to obtain transportation scheme with minimum transportation cost in minimum number of trips of vehicles moving between regions with higher levels of restrictions. For this, a penalty is imposed in the objective function based on the category of the region(s) where the origin and destination are situated. However, reduction in the number of trips of vehicles may increase the transportation cost to unrealistic bounds and so, to keep the transportation cost within limits, a constraint is imposed on the proposed model. To solve the problem, the Genetic Algorithm (GA) has been modified accordingly. For this purpose, we have designed a new crossover operator and a new mutation operator to handle multiple trips and capacity constraints of vehicles. For numerical illustration, in this study, we have solved five example problems considering three levels of restrictions, for which the datasets are generated artificially. To show the effectiveness of the constraint imposed for reducing the transportation cost, the same example problems are then solved without the constraint and the results are analyzed. A comparison of results with existing algorithms proves that our algorithm is effective. Finally, some future research directions are discussed.

A Vehicle Routing Problem With Option for Outsourcing and Time-Dependent Travel Time

This paper studies the time-dependent vehicle routing problem with private fleet and common carriers (TDVRPPC), which provides an option to outsource the customer requests and considers real-world time-dependent travel times. The problem is commonly seen in the transportation and logistics industries as it considers the impact of changing traffic conditions on travel times, maximum working hour regulations as well as vehicle capacity constraints. The time-dependent travel time is modeled as a piecewise linear function, based on which a mixed integer programming model is proposed for the TDVRPPC. To solve this NP-hard problem, we customize a hybrid algorithm to harness an adaptive large neighborhood search algorithm for exploration and a tabu search for the exploitation of the search. Through constraint relaxation, dynamic and coordinated adjustment of diversification and intensification strengths of the hybridized procedures, as well as an effective segment-based evaluation method, the proposed algorithm performs well on newly generated test instances for the TDVRPPC and on benchmark instances for the simplified vehicle routing problem with private fleet and common carriers (VRPPC).

Equity‐oriented vehicle routing optimization for catering distribution services with timeliness requirements

The rapid development in the catering services and urban logistics industries has significantly promoted the prosperity of business-to-consumer (B2C) e-commerce urban logistics distribution, which is gaining increasing interest from food producers, distribution platforms, and consumers. Unlike traditional logistics supply chains, catering distribution services have strong timeliness and consideration of delivery delay. Traditional distribution platforms usually group commodities by their origins or destinations and then transport each group with one logistics vehicle. However, for a logistics distribution area with limited commodities, the vehicle capacity cannot be fully utilized if one vehicle can only transport commodities with the same origin or destination. Therefore, a mixed-load strategy is proposed in which commodities with different origins or destinations in a distribution area could be transported by the same vehicle to improve vehicle capacity utilization. A mixed-load strategy would further cause delivery sequencing problems, leading to different delivery delays for customers. This study proposed an equity-oriented vehicle routing problem for food distribution services with timeliness requirements considering a mixed-loading strategy and vehicle capacity constraints. For the above problem, a multi-commodity flow optimization model was constructed for the equity-oriented vehicle routing problem and a mixed-load strategy based on a time-discretized space-time-state network representation. An augmented Lagrangian relaxation approach was utilized to reformulate the original model and thus effectively solve the proposed model. Furthermore, the augmented Lagrangian model was decomposed and linearized into a series of shortest path searching subproblems and iteratively solved by a dynamic programming algorithm using an alternating direction method of multipliers (ADMM)-based solution framework. Finally, the proposed model and solution approaches were tested on numerous networks.

Vehicle dispatching plan for minimizing passenger waiting time in a corridor with buses of different sizes: Model formulation and solution approaches

Urban public transportation agencies sometimes have to operate mixing vehicles of different sizes on their routes, due to resource limitations or historical reasons. Services with different passenger-carrying capacities are provided to passengers during a mixed-fleet operation. A fundamental question arising here is how to optimally deploy a given fleet of different bus sizes to provide services that minimize passenger waiting time. We formulate a mixed-fleet vehicle dispatching problem as a Mixed-Integer Nonlinear Programming (MINLP) model to optimize dispatching schemes (dispatching orders and times) when a given set of buses of different sizes are available to serve demand along a route. The objective is to minimize the average passenger waiting time under time-dependent demand volumes. Stochastic travel times between stops and vehicle capacity constraints (i.e., introducing extra waiting time due to denied boarding) are explicitly modeled. A Simulated Annealing (SA) algorithm coupled with a Monte Carlo simulation framework is developed to solve large real-world instances in the presence of stochastic travel times. Results show that, in addition to dispatching headway, bus dispatching sequence can strongly affect waiting times under a mixed-fleet operation. Indeed, with an optimal dispatching sequence, a more accurate adjustment of supply to demand is possible in accordance with time-dependent demand conditions, and the total savings in waiting time are mainly driven by a further reduction in the number of passengers left behind. The optimality of uneven dispatching headways stems from two elements: having a mixed fleet and having localized peaks on demand that make buses run full.

Two-Sided Matching on Comprehensive Transportation Network Emergency Vehicles’ Allocation

In emergency rescue, the allocation of comprehensive transportation network emergency vehicles often affects the efficiency of the whole rescue process. In the context of disasters, this paper researches the one-to-many two-sided matching problem between the emergency vehicles and the materials to be transported. Firstly, based on the needs of both parties involved in the matching, the satisfaction evaluation systems are constructed; with the goal of maximizing the weighted satisfaction of the affected areas and vehicles, the optimization model of the materials and emergency vehicles matching is established; then, an improved National Intern Matching Program (NIMP) algorithm is designed to solve the model, which is based on the k: 1 experimental pairing and updating ideas, and can take into account the capacity and destination constraints of vehicles in the matching process. Finally, through the calculation of an example, the matching scheme can make the satisfaction of material transportation reach 0.7392, and the simulation analysis proves that the scheme keeps certain stability in risky conditions.

Flying taxis revived: Can Urban air mobility reduce road congestion?

Many metropolitan regions are investigating Urban Air Mobility (UAM) as a new transport mode for medium distance intra-regional trips. In this paper, an agent-based travel demand model was developed to simulate UAM demand for the region surrounding Munich, Germany. Special attention was given to mode choice, vertiport access and egress, airport trips, and UAM vehicle capacity constraints. Under base conditions, the model predicts a rather small mode share for UAM of 0.61%. The results show that in a metropolitan area with well-developed road and transit networks, traveling by UAM does not save much time. This is particularly true if access and egress trips to and from vertiports are included, as well as wait times, security checks and boarding times. The model shows that there is no reduction in vehicle kilometers traveled by car due to the modal shift to UAM. In fact, if access and egress trips to the vertiports are included, the total vehicle-kilometers traveled by car increases by 0.3%. Therefore, UAM is not found to alleviate congestion, but at most may serve selected markets, such as emergency vehicles or longer trips between remote areas where other transport networks are not as well developed. Keywords uam, Transport modelling, Mobility, Mode choice model

A modified coronavirus herd immunity optimizer for capacitated vehicle routing problem

Capacitated Vehicle routing problem is NP-hard scheduling problem in which the main concern is to find the best routes with minimum cost for a number of vehicles serving a number of scattered customers under some vehicle capacity constraint. Due to the complex nature of the capacitated vehicle routing problem, metaheuristic optimization algorithms are widely used for tackling this type of challenge. Coronavirus Herd Immunity Optimizer (CHIO) is a recent metaheuristic population-based algorithm that mimics the COVID-19 herd immunity treatment strategy. In this paper, CHIO is modified for capacitated vehicle routing problem. The modifications for CHIO are accomplished by modifying its operators to preserve the solution feasibility for this type of vehicle routing problems. To evaluate the modified CHIO, two sets of data sets are used: the first data set has ten Synthetic CVRP models while the second is an ABEFMP data set which has 27 instances with different models. Moreover, the results achieved by modified CHIO are compared against the results of other 13 well-regarded algorithms. For the first data set, the modified CHIO is able to gain the same results as the other comparative methods in two out of ten instances and acceptable results in the rest. For the second and the more complicated data sets, the modified CHIO is able to achieve very competitive results and ranked the first for 8 instances out of 27. In a nutshell, the modified CHIO is able to efficiently solve the capacitated vehicle routing problem and can be utilized for other routing problems in the future such as multiple travelling salesman problem.

STUDI ALGORITMA IGVNS, ALGORITMA GVNS, DAN ALGORITMA ABC PADA MULTIPLE TRIP VEHICLE ROUTING PROBLEM (MTVRP)

The Multiple Trip Vehicle Routing Problem (MTVRP) is one of the VRP variants with vehicle capacity constraints, and the limited number of vehicles allows each vehicle to distribute more than one route so as to minimize the number of vehicles used. The algorithm used in this study is the Improved General Variable Neighborhood Search (IGVNS) algorithm. The IGVNS algorithm is a hybrid between the GVNS algorithm and the VNS algorithm. The calculation results of the IGVNS algorithm will be compared with the GVNS algorithm and the ABC algorithm. The main stages of the IGVNS and GVNS algorithms are initial solution formation, perturbation, and solution improvement. The main stages of the ABC algorithm are initialization, solution improvement and optimization. Based on manual calculations using 8 points, the ABC algorithm produces a distance of 86 km and a service time of 1.47 hours, the GVNS algorithm produces a distance of 80 km and a service time of 1.37 hours, the IGVNS algorithm produces a distance of 79 km and service time is 1.35 hours. Based on one example of the ABC algorithm, the calculation solution using the IGVNS algorithm shows more optimal results. Based on the results of parameter testing, the v max parameter affects the calculation results, that is the greater the v max value, the more optimal the resulting solution. While the a max parameter does not affect the calculation results because it shows constant results in two successive iterations carried out.

Time-dependent transit fare optimization with elastic and spatially distributed demand

Motivated by the lack of microeconomic models that optimize time-dependent transit fares based on realistic demand formulations, this paper presents a microeconomic model for the design of a time-dependent transit pricing scheme considering elastic and spatiotemporally distributed demand. To model the spatial distribution of demand, a transit line with multiple origin–destination pairs is considered. To model the cyclical demand fluctuations, transit operations in one day are divided into multiple time periods. In the proposed model we optimize fares, headway, vehicle capacity, and maximum fleet size, with the objective of maximizing social welfare, subject to fleet size and vehicle capacity constraints. We find time-dependent pricing could avoid cross-subsidization among travelers in different time periods. Under both pricing schemes, the time-dependent headways satisfy the same optimality condition: the total rider waiting cost equals the total fixed cost on the supplier side. We also demonstrate that both resource constraints (vehicle capacity and fleet size) can be binding in multiple time periods, unlike the usual assumption in the literature that resource constraints are binding only in the period with the highest demand. Two extensions (considering a financial constraint and a variable roundtrip time) are also investigated. The developed models can be used to facilitate the design of time-dependent pricing schemes for practical applications.