Analysis of Swarm Intelligence Algorithms Used for Solving Vehicle Routing Problems

A Vehicle Routing Problem (VRP) is a Non-Polynomial Hard Category (NP-hard) problem in which the best set of routes for a convoy of vehicles is traversed to deliver goods or services to a known set of customers. In VRP, some constraints are added to improve performance. Some variations of VRP are Capacitated Vehicle Routing Problem (CVRP), Vehicle Routing Problem with Stochastic Demands (VRPSD), Vehicle Routing Problem with Time Window (VRPTW), Dynamic Vehicle Routing Problem (DVRP), and Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD) where vehicle and routes have multiple constraints. Swarm intelligence is a well-used approach to solve VRPs. Moreover, different hybrid combinations of global and local optimization techniques are also used to optimize the said problem. In this research, an attempt is made to solve CVRP with VRPSD by using two different hybridized population-based approaches, that is, the Cuckoo Search Algorithm (CSA) and Particle Swarm Optimization (PSO). The experiments showed the accuracy of the improved CVRP that is superior to one obtained by using other classical versions and better than the results achieved by comparable algorithms. Besides, this improved algorithm can also improve search efficiency.

A general heuristic for vehicle routing problems

In the present PhD thesis, a collection of vehicle routing problems is examined and solved. These problems are aimed at producing the highest quality routes for performing various transportation operations. They frequently arise in practical applications of Logistics, and therefore, are of great importance both from the theoretical and commercial perspectives. For this reason, vehicle routing problems have attracted the attention of researchers from various fields of science, namely Operations Research, Mathematics, Computing Science, and Management Science. Vehicle routing problem variants belong to the category of NP-hard combinatorial optimization problems, thus they are very complex to be solved. Specifically, exact mathematical algorithms cannot optimally solve practical, large-scale routing problems within reasonable computational times. For this reason, researchers focused their interest in developing heuristic algorithms which are problem-specific methodologies aimed at determining good solutions, not necessarily the optimal ones, within limited computational times. Later, researchers introduced a new generation of approximate algorithms called metaheuristics which are able to produce higher quality solutions compared to the ones obtained by classical heuristics. Metaheuristics are intelligent strategies which incorporate low-level heuristic methods into algorithmic frameworks which are aimed at effectively exploring the solution search space. The basic attribute of metaheuristic strategies is that their behaviour does not depend on the special characteristics of the examined problem. Thus, they provide great flexibility of being applied for dealing with problems of diversified characteristics. The present PhD thesis proposes a collection of innovative metaheuristic methodologies for effectively tackling various problems of the vehicle routing literature. In methodological terms, a strategy for reducing the computational complexity of local search-based methods is introduced. Various metaheuristic schemes based on the aforementioned strategy are presented. The proposed complexity reduction strategy can be employed for dealing with very large-scale applications of vehicle routing problems. In addition, it can be used for efficiently applying rich and complex local search operators. It can also drastically accelerate the application of local search methods which are the most common algorithmic feature of commercial vehicle routing software packages. Moreover, the present thesis introduces several hybrid approaches which combine the powers of more than one metaheuristic method. In specific, two hybrid schemes are proposed which jointly employ the rationale of Tabu Search and Guided Local Search. Furthermore, an innovative metaheuristic mechanism which coordinates the performance of local search methods is introduced and analyzed. This mechanism is called Promises and exhibits a considerably robust behaviour, as it does not include any algorithmic parameters. Finally, various original methodological schemes are proposed, for tackling vehicle routing problems integrated with additional loading constraints. These schemes involve hybrid metaheuristic methods for dealing with the routing requirements operating in parallel with packing heuristic methods aimed at determining feasible packing arrangements for the transported products. The abovementioned algorithms are applied to deal with several vehicle routing variants. Specifically the following models are solved: (a) the classical Capacitated Vehicle Routing Problem, (b) the Open Vehicle Routing Problem, (c) the Vehicle Routing Problem with Backhauls, (d) the Vehicle Routing Problem with Simultaneous Pick-ups and Deliveries, (e) the Undirected Capacitated Arc Routing Problem with Profits, (f) the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints, and (g) the Capacitated Vehicle Routing Problem with Three-Dimensional Loading Constraints. The proposed algorithms were evaluated by being applied on benchmark instances for all the aforementioned models. They exhibited fine performance by improving most of the best known solutions of the literature. Finally, in the present PhD thesis, a new vehicle routing problem integrated with additional loading constraints is introduced, formulated and solved. This new problem models applications of transporting palletized products, and generalizes every integrated routing-packing model of the literature. To solve this introduced vehicle routing problem, an implementation of the Promises mechanism is proposed which operates in parallel with a bundle of 144 three-dimensional packing heuristics aimed at determining feasible loading structures for the transported products onto the vehicle pallets.

Urban development can compromise open space and many valued ecosystem functions such as biological diversity, forest carbon sequestration, and clean water. To maximize the protection of open space and ecosystems, community planners and conservation organizations can take preemptive action either by purchasing land before it is developed or by providing incentives to landowners not to sell their land for development. In either case, the parcels must be prioritized for retention. While a significant body of literature addresses this need for prioritization, optimal reserve selection models do not account for land-price feedback effects that arise in markets where open space conservation competes with development. In competitive land markets, conservation acquisitions can affect land prices either by increasing demand, and thereby shifting the competitive equilibrium, or by inducing amenity premiums. People are willing to pay more for lots that are adjacent to reserves. These price effects can lead to increased development outside of the reserves and unintended loss of open space and valued ecosystem functions. In “Dynamic Reserve Selection: Optimal Land Retention with Land-Price Feedbacks,” S. F. Tóth, R. G. Haight, and L. W. Rogers fill this gap by formulating a linear-integer programming model with adaptive cost coefficients that are endogenous to the parcel acquisition decisions. They show that it is not always optimal to buy as much land for conservation as possible early on in the land retention effort. Buying fewer, smaller but more expensive parcels that have high conservation value and higher risk of development appears to be optimal in many market scenarios. They also show that failure to account for these price effects can lead to significant losses in biological conservation. In the paper “Parameterized Supply Function Bidding: Equilibrium and Efficiency,” R. Johari and J. Tsitsiklis explore a fundamental trade-off in designing markets. The authors consider markets where firms compete to supply a good through a market mechanism. On one hand, sufficient flexibility must be granted to firms in declaring their supply functions to ensure that they can approximately declare their costs. On the other hand, as the strategic flexibility granted to firms increases, their temptation to misdeclare their cost increases as well. Indeed, while in principle arbitrary supply functions allow firms to declare all marginal cost information, in theory and practice we find that such strategic flexibility only encourages the exercise of market power. Indeed, such a phenomenon has been seen in various energy markets around the world. The authors shed light on this trade-off by studying a parameterized class of supply functions that allow firms enough flexibility to communicate information about their production cost, yet not enough flexibility to enable them to exercise market power and cripple the performance of the overall market. In other words, by partially restricting the range of possible supply functions firms can declare, the authors' mechanism design controls “gaming”; nevertheless, they demonstrate the resulting market-clearing mechanism is nearly efficient. Their analysis lends credence to the hypothesis that restricting the strategy space granted to firms can often improve allocative efficiency. A good partial flexible process structure has been proven to be an effective tool to match (random) demand and capacity in both manufacturing and service industries. While most existing literature focuses on discussing the average performance of flexible structures, other interesting questions are: How to design a good partial flexible process structure that performs close to full flexibility in all cases? Could a flexible structure designed by popular guidelines also perform well in the worst case? In “Process Flexibility Revisited: The Graph Expander and Its Applications,” M. C. Chou, G. A. Chua, C.-P. Teo, and H. Zheng study the worst-case performance of the flexible structure design problem under a more general setting, which considers a general class of objective functions. They propose a concept “Ψ-expander” (0 < Ψ ≤ 1), a variant from graph expander, to design partial flexible process structure, and they show that a 1-expander structure performs as well as full flexibility structure in all scenarios. A simple heuristic to design flexile structures in general nonsymmetric systems is developed based on this concept. Using numerical examples studied in previous literature, the structures designed by the heuristic performed favorably compared to other popular flexible structures. In customer service systems, such as call centers or hospital emergency departments, waiting customers are often unable to estimate their own delay. A long wait, coupled with feelings of uncertainty about the length of that wait, leads to poor service evaluation. For system managers, making delay announcements is a relatively inexpensive way of reducing customer uncertainty about delays, thereby improving customer satisfaction with the service provided. In “Wait-Time Predictors for Customer Service Systems with Time-Varying Demand and Capacity,” R. Ibrahim and W. Whitt investigate alternative ways to predict, in real time, the delay of an arriving customer in a service system with customer abandonment and time-varying demand and capacity. These delay predictions may be used to make delay announcements. The authors propose new, simple, and effective ways to generate better delay predictions in many-server queues with a time-varying arrival rate, a time-varying number of servers, and customer abandonment. Because a new project entails enormous uncertainty, it's advisable not to “bet the firm” on the new project. Instead, run a small-scale experiment before making an irreversible investment in project-specific assets. As the experiment proceeds, the likelihood of the project's success is slowly revealed; eventually the firm makes an expansion or an exit (abandonment) decision based on the profitability of the pilot project observed to date. According to real options theory, the decision criterion becomes more stringent (the decision rule requires stronger evidence before action) as uncertainty in the profitability increases, but it is not obvious if this means that it should take longer for the firm to make this decision when there is an increase in the uncertainty of the project's success. In “Acquisition of Project-Specific Assets with Bayesian Updating,” H. D. Kwon and S. A. Lippman examined this issue in a model with project-specific assets and a (pilot) project that is either highly profitable or unprofitable. While noise in the project's profit stream makes it impossible to determine the project's profitability, the firm takes a Bayesian approach to update its belief based on the observed profit stream. The authors show that the expected time it takes to make an expansion or an exit decision is not monotone in the uncertainty. Therefore, stringent expansion/exit criteria do not necessarily imply a long time to make a decision. The results have practical implications for firms faced with expansion via investment in project-specific assets or abandonment of the pilot project because the rules/policy for deciding when to expand and when to abandon are determined in advance, before psychological pressures mount. Moreover, in deciding whether or not to launch the pilot project, it is important to know how increases in uncertainty impact the time until the expansion/abandonment decision is made. Seasonal influenza (flu) is a major public health concern, and the first line of defense is the flu shot. Antigenic drifts and the high rate of influenza transmission require annual updates to the flu shot composition. The World Health Organization recommends which flu strains to include in the annual vaccine based on surveillance and epidemiological analysis. Thus far, the design and timing of the flu shot have been made in an ad hoc manner. In “Optimizing the Societal Benefits of the Annual Influenza Vaccine: A Stochastic Programming Approach,” O. Y. Özaltın, O. A. Prokopyev, A. J. Schaefer, and M. S. Roberts propose a multistage stochastic mixed-integer program to identify an optimal annual flu shot design. They calibrate their model with real-life data and incorporate risk sensitivity using mean-risk objective functions. The results provide valuable insights for pressing policy issues. Dynamic pricing, where price is adjusted over time to match supply with demand, has long been adopted in various industries. Though advanced information technologies further facilitate price changes, the costs of price adjustment prevail and sometimes could be quite significant. In “Integration of Inventory and Pricing Decisions with Costly Price Adjustments,” X. Chen, S. X. Zhou, and Y. Chen develop a stochastic, dynamic inventory system with price adjustment costs, which consist of both fixed and variable parts. To provide effective strategies for firms to manage inventory and set selling price of such systems, they characterize the optimal policies for two special scenarios: one with inventory carryover and no fixed price-change costs and the other with fixed price-change costs but no inventory carryover. For the general system, a heuristic is developed, and its effectiveness is demonstrated numerically. Deterministic fluid models can provide useful first-order approximations for the performance of stochastic queuing models of large service systems, because they des

Vehicle Routing Problem (VRP) is addressed to a class of problems for determining a set of vehicle routes, in which each vehicle departs from a given depot, serves a given set of customers, and returns back to the same depot. On the other hand, simultaneous delivery and pickup problems have drawn much attention in the past few years due to its high usage in real world cases. This study, therefore, considered a Vehicle Routing Problem with Time Windows and Simultaneous Delivery and Pickup (VRPTWSDP) and formulated it into a mixed binary integer programming. Due to the NP-hard nature of this problem, we proposed a variant of Particle Swarm Optimization (PSO) to solve VRPTWSDP. Moreover, in this paper we improve the basic PSO approach to solve the several variants of VRP including Vehicle Routing Problem with Time Windows and Simultaneous Delivery and Pickup (VRPTWSDP), Vehicle Routing Problem with Time Windows (VRPTW), Capacitated Vehicle Routing Problem (CVRP) as well as Open Vehicle Routing Problem (OVRP). In proposed algorithm, called Improved Particle Swarm Optimization (IPSO), we use some removal and insertion techniques and also combine PSO with Simulated Annealing (SA) to improve the searching ability of PSO and maintain the diversity of solutions. It is worth mentioning that these algorithms help to achieve a trade-off between exploration and exploitation abilities and converge to the global solution. Finally, for evaluating and analyzing the proposed solution algorithm, extensive computational tests on a class of popular benchmark instances, clearly show the high effectiveness of the proposed solution algorithm.

Optimization of capacitated vehicle routing problem with alternative delivery, pick-up and time windows: A modified hybrid approach

The distribution of goods to a set of geographically dispersed customers is a common problem faced by carrier companies, well-known as the Vehicle Routing Problem (VRP). The VRP consists of finding an optimal set of routes that minimizes total travel times for a given number of vehicles with a fixed capacity. Given the demand of each customer and a depot, the optimal set of routes should adhere to the following conditions: ?? Each customer is visited exactly once by exactly one vehicle. ?? All vehicle routes start and end at the depot. ?? Every route has a total demand not exceeding the vehicle capacity. The travel times between any two potential locations are given as input to the problem. Consequently, the total travel is computed by summing up the travel time over the chosen routes. In reality, carrier companies are faced with a number of other issues not conveyed in the VRP. The research in this thesis introduces a number of realistic variants of the VRP. These variants consider the VRP as a core component and incorporate additional features. By definition the VRP is NP-hard. Throughout the years a vast amount of research was aimed at developing both exact and heuristic solution procedures. Building on this established literature, solution procedures are developed to fit the variants proposed in this thesis. The standard VRP considers that the travel time between any pair of locations is constant throughout the day. However, congestion is present in most road networks. Considering traffic congestion results in time-dependent travel times, where the travel time between two location depends not only on the distance between them but also on the time of day one chooses to traverse this distance. Time-dependent travel times are considered in Chapters 2 and 3 of this thesis. Thus, in these Chapters we incorporate the time dimension into the VRP. The standard VRP does not take into account any customer service aspect. The customers are presumed to be available to receive their goods upon arrival of the vehicles. However, a number of carrier companies quote their expected arrival time to their customers. We introduce the concept of self-imposed time windows (SITW). SITW reflect the fact that the carrier company decides on when to visit the customer and communicates this to the customer. Once a time window is quoted to a customer the carrier company strives to provide service within this time window. SITW differ from time windows in the widely studied VRP with time windows (VRPTW), as the latter are exogenous constraints. In Chapters 4 and 5 SITW are endogenous decisions in stochastic environments. Thus, in addition to the sequencings decisions required by the VRP further timing decisions are needed. This thesis extends the VRP in two major dimensions: time-dependent travel times and self-imposed time windows. In reality carrier companies are faced with various uncertainties. The presented models incorporated some of these uncertainties by addressing three stochastic aspects: (I) In Chapter 3 stochastic service times are considered. (II) In Chapter 4, stochasticity in travel time is modeled to describes variability caused by random events such as car accidents or vehicle break down. (III) Finally, in Chapter 5 the objective was to construct a long term plan for providing consistent service to reoccurring customers. Stochasticity in this thesis is treated in an a priori manner. The plan, consisting of routes and timing decisions where necessary, is determined beforehand and is not modified according to the realization of the random events. Chapter 2 addresses environmental concerns by studying CO2 emissions in a timedependent vehicle routing problem environment. In addition to the decisions required for the assignment and scheduling of customers to vehicles, the vehicle speed limit is considered. The emissions per kilometer as a function of speed, is a function with a unique minimum speed v*. However, we show that limiting vehicle speed to this v* might be sub-optimal, in terms of total emissions. We adapted a Tabu search procedure for the proposed model. Furthermore, upper and lower bounds on the total amount of emissions that may be saved are presented. Quantifying the tradeoff between minimizing travel time as opposed to CO2 emissions is an important contribution. Another important contribution lies in incorporating fuel costs in the optimization. As fuel costs are correlated with CO2 emissions, Chapter 2 shows that even in today’s cost structure limiting vehicle speeds is beneficial. Chapter 3 defines the perturbed time-dependent VRP (P-TDVRP) model which is designed to handle unexpected delays at the various customer locations. A solution method that combines disruptions in a Tabu Search procedure is proposed. In Chapter 3 we identify situations capable of absorbing delays. i.e. where inserting a delay will lead to an increase in travel time that is less than the delay length itself. Based on this, assumptions with respect to the solution structure of P-TDVRP are formulated and validated. Furthermore, most experiments showed that the additional travel time required by the P-TDVRP, when compared to the travel time required by the TDVRP, was justified. In Chapter 4 the notion of self imposed time windows is defined and embedded in the VRP-SITW model. The objective of this problem is to minimize delay costs (caused by late arrivals at customers) as well as traveling time. The problem is optimized under various disruptions in travel times. The basic mechanism of dealing with these disruptions is allocating time buffers throughout the routes. Thus, additional timing decisions are taken. The time buffers attempt to reduce potential damage of disruptions. The solution approach combines a linear programming model with a local search heuristic. In Chapter 4, two main types of experiments were conducted: one compares the VRP with VRP-SITW while the other compares VRPTW with VRPSITW. The first set of experiments assessed the increase in operational costs caused by incorporating SITW in the VRP. The second set of experiments enabled evaluating the savings in operational costs by using flexible time windows, when compared to the VRPTW. Chapter 5 extends the customer service dimension by considering the consistent vehicle routing problem. Consistency is defined by having the same driver visiting the same customers at roughly the same time. As such, two main dimensions of consistency are identified in the literature, driver- and temporal consistency. In Chapter 5, driver consistency is imposed by having the same driver visit the same customers. Furthermore, we impose temporal consistency by SITW. A stochastic programming formulation is presented for the consistent VRP with stochastic customers. An exact solution method is proposed by adapting the 0-1 integer L- shaped algorithm to the problem. The method was able to solve the majority of test instances to optimality.

In today’s challenging sector of logistics and transportation, companies, seek to adapt software which leads to efficient solutions at an acceptable cost. Conventional routing software is developed to solve vehicle routing problem and help managers and planners in decision making. Simultaneously, specific constraints and different VRP (Vehicle Routing Problem) variants are considered each time, such as the Capacitated, the Multi Depot and the Pickup and Delivery VRP. However, the last few years the need for more reliable deliveries and better customer services arose. In addition, reducing travel distance, travel cost and environmental impact are important factors encountered in urban freight transportation. Therefore, routing software needs to take into account multiple constraints. Such constraints are traffic congestion, speed limits, transportation regulations and restricted zones. These constraints affect mainly Time dependent VRP, VRP with Time Windows, Dynamic VRP and Green VRP. Data collection and processing are essential in routing software for solving these variants and offering the best solution. The methods for solving these problems, along with technological achievements, including cloud computing, can lead to efficient, easily adaptable routing software. Such software solutions can eventually render companies with complex transportation and logistics problems, competitive. The scope of this paper is to describe the concept and methodological approach for the development of such a routing and scheduling system, operating in a cloud environment. The definition of its requirements and the development of the system is the main purpose of an ongoing research project, being in its first stages of system’s analysis and design.

The last-mile delivery problem is one of the most complex and resource-intensive aspects of modern logistics, especially within the growing e-commerce sector. As online shopping continues to expand, companies are under immense pressure to deliver goods more quickly, efficiently, and at lower costs, all while meeting the demands of increasingly time-sensitive customers. This has created a need for innovative solutions that can tackle challenges related to dynamic traffic patterns, fluctuating customer preferences, and operational constraints such as vehicle capacities and delivery windows. In response to these challenges, this paper explores the application of predictive analytics as a tool for optimizing last-mile delivery routes in real-time.The study begins by identifying the core challenges inherent in last-mile logistics, particularly in the U.S. e-commerce landscape, where the cost of last-mile delivery can represent up to 53% of total shipping costs. With traffic congestion, unpredictable customer availability, and delivery time constraints posing significant hurdles, conventional static route planning models often fall short. In this paper, predictive analytics is proposed as a solution to these challenges, utilizing real-time data to inform more efficient routing decisions. By processing vast amounts of real-time traffic data, customer preferences, and delivery constraints, predictive models can offer a more flexible and responsive approach to last-mile delivery.The research then presents a comprehensive literature review of existing route optimization methods, such as the traditional Vehicle Routing Problem (VRP) and its extensions, including VRP with Time Windows (VRPTW), Dynamic VRP (DVRP), and Capacitated VRP (CVRP). While these models have proven useful, their limitations are exposed when faced with real-time operational complexities in the e-commerce sector. Therefore, this study introduces an advanced dynamic routing model that integrates machine learning algorithms—such as decision trees and neural networks—with traditional VRP frameworks. These machine learning models, trained on historical data, are capable of predicting future traffic patterns, customer behavior, and delivery time windows.A case study is conducted using data from U.S.-based e-commerce companies to demonstrate the practical application of predictive analytics in optimizing last-mile delivery. The case study outlines how predictive models are used to dynamically adjust delivery routes based on real-time conditions, leading to significant improvements in efficiency, cost savings, and customer satisfaction. Key performance indicators such as delivery times, fuel consumption, and vehicle utilization are examined before and after the implementation of the predictive models, with the results showing a reduction in delivery time by 20% and fuel costs by 15%, alongside improved on-time delivery rates.The paper concludes by presenting the proposed dynamic route optimization model as a solution that combines the flexibility and responsiveness of predictive analytics with the robust framework of traditional VRP models. Through the integration of machine learning, real-time data processing, and dynamic routing, the model is shown to significantly improve last-mile delivery efficiency. This study's findings highlight the potential for predictive analytics to revolutionize the logistics industry, particularly in the high-demand e-commerce sector, where quick and reliable delivery is paramount. The research suggests that as e-commerce continues to grow, predictive analytics will play an increasingly critical role in ensuring that last-mile delivery is both cost-effective and responsive to the evolving needs of consumers.

The internet development access is really very fast and change all aspects for life activities include buying and selling transactions of goods or services that can arrange online or also called e-commerce which courier service influence. The courier basic operational is logistics of a supply chain. Transportation is a vital component in logistics management because it becomes the largest cost component in its activities that is about 50-60% of the total logistics costs. The purpose of this study is to find out what kind of vehicle routing problem (VRP) is used for courier service so can be used as reference for further research. Collect and selection process found 40 science journals for analyse. There has been a lot of research about the shortest route problem for courier service or can also called city logistics with VRP which the optimum solution obtained with heuristic and metaheuristic algorithm. Result found VRP type often used for courier service are dynamic VRP (DVRP) and VRP with time window (VRPTW) or can merging both dynamic VRP with time window (DVRPTW).

In this research, author reviews references related to the topic of multi-criterion (goal programming, multiple objective linear and nonlinear programming, bi-criterion programming, Multi-Attribute Decision-Making, Compromise Programming, Surrogate Worth Trade-off Method) and various versions of vehicle routing problem (VRP), Multi-Depot VRP (MDVRP), VRP with time windows (VRPWTW), Stochastic VRP (SVRP), Capacitated VRP (CVRP), Fuzzy VRP (FVRP), Location VRP (LVRP), Backhauling VRP(BHVRP), Facility Location VRP (FLVRP), and Inventory control VRP (ICVRP). Although VRP is a research area with rich research works and powerful researchers, only 81 articles are found that relate various vehicle routing type problems with various multiple objectives techniques. This author found that there is no research done in some areas of VRP (i.e., FVRP, ICVRP, LRP and CVRP). It is interesting to see that this research area was completely unattractive to master students (with zero research reported) and somewhat attractive to doctoral students (with 6 researches reported). Among the many multi-criterion programming techniques available, only three of them (goal programming, bi-criterion programming, linear and nonlinear multi-objective programming) are being employed to solve the problem.

The vehicle routing problem (VRP) is an important problem occurring in many distribution systems, which is also defined as a family of different versions such as the capacitated vehicle routing problem (CVRP) and the vehicle routing problem with time windows (VRPTW). The ant colony optimization (ACO) is a metaheuristic for combinatorial optimization problems, and the max-min ant system (MMAS) is a variation of ACO. This paper surveys on the research on the modified MMAS algorithm for solving the CVRP and VRPTW. First, this paper introduces the CVRP and VRPTW, and the basic principles of the ACO. Then, the modified MMAS algorithm and its application to the solution of the VRP and of its variations are presented in this paper. Results of empirical simulation using the well-known benchmark CVRP and VRPTW problems have shown that the method proposed in this paper performs highly competitive in terms of solution quality.

Improving generalization of neural Vehicle Routing Problem solvers through the lens of model architecture.

Vehicle routing problems constitute the core of many operations research efforts. Early studies introduced tailor-made solutions for each variant of a vehicle routing problem, but unified frameworks have emerged more recently. These approaches typically generalise across many vehicle routing problems and implement a method for tackling the generalised problem. In line with this, this research proposes a generic method for solving several fixed fleet vehicle routing problems - capacitated vehicle routing, open vehicle routing, vehicle routing with soft and hard time windows, open vehicle routing with soft and hard time windows, and time-dependent vehicle routing with soft and hard time windows - by transforming them into a time-dependent vehicle routing problem with soft time windows, solved by a variable neighbourhood search using a unique parameter setting, regardless of the original problem. Computational tests using standard benchmark instances from prior literature show that genericity does not come at the expense of solution quality. Moreover, the algorithm yields competitive results and some new best known solutions are obtained for the vehicle routing problem with soft time windows, the open vehicle routing problem with hard time windows, and time-dependent vehicle routing problem with hard time windows.

Vehicle routing problems constitute the core of many operations research efforts. Early studies introduced tailor-made solutions for each variant of a vehicle routing problem, but unified frameworks have emerged more recently. These approaches typically generalise across many vehicle routing problems and implement a method for tackling the generalised problem. In line with this, this research proposes a generic method for solving several fixed fleet vehicle routing problems - capacitated vehicle routing, open vehicle routing, vehicle routing with soft and hard time windows, open vehicle routing with soft and hard time windows, and time-dependent vehicle routing with soft and hard time windows - by transforming them into a time-dependent vehicle routing problem with soft time windows, solved by a variable neighbourhood search using a unique parameter setting, regardless of the original problem. Computational tests using standard benchmark instances from prior literature show that genericity does not come at the expense of solution quality. Moreover, the algorithm yields competitive results and some new best known solutions are obtained for the vehicle routing problem with soft time windows, the open vehicle routing problem with hard time windows, and time-dependent vehicle routing problem with hard time windows.