Heuristic methods for vehicle routing problem with time windows

This paper documents our investigation into various heuristic methods to solve the vehicle routing problem with time windows (VRPTW) to near optimal solutions. The objective of the VRPTW is to serve a number of customers within predefined time windows at minimum cost (in terms of distance travelled), without violating the capacity and total trip time constraints for each vehicle. Combinatorial optimisation problems of this kind are non-polynomial-hard (NP-hard) and are best solved by heuristics. The heuristics we are exploring here are mainly third-generation artificial intelligent (AI) algorithms, namely simulated annealing (SA), Tabu search (TS) and genetic algorithm (GA). Based on the original SA theory proposed by Kirkpatrick and the work by Thangiah, we update the cooling scheme and develop a fast and efficient SA heuristic. One of the variants of Glover's TS, strict Tabu, is evaluated and first used for VRPTW, with the help of both recency and frequency measures. Our GA implementation, unlike Thangiah's genetic sectoring heuristic, uses intuitive integer string representation and incorporates several new crossover operations and other advanced techniques such as hybrid hill-climbing and adaptive mutation scheme. We applied each of the heuristics developed to Solomon's 56 VRPTW 100-customer instances, and yielded 18 solutions better than or equivalent to the best solution ever published for these problems. This paper is also among the first to document the implementation of all the three advanced AI methods for VRPTW, together with their comprehensive results.     

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.     

A reactive MILP approach to the multidepot heterogeneous fleet vehicle routing problem with time windows

The time‐window‐constrained vehicle routing problem (VRPTW) is a well‐known combinatorial problem. Its goal is to discover the best set of routes for a vehicle fleet in order to service a given number of customers at minimum cost. Vehicle capacity, maximum service time and time‐window constraints must be satisfied. Most proposed VRPTW optimizing approaches intend to discover the best or a near‐optimal solution at once. Improvement methods are old strategies that apply heuristics to insert customers into tours and/or rearrange nodes to obtain better routes. They are performed until no further improvement is achieved. Little research has been focused on model‐based reactive approaches seeking a better solution by exploring a small solution space around the current solution. This work presents a new model‐based improvement methodology for the multi‐depot heterogeneous‐fleet VRPTW problem to enhance an initial solution through solving a series of MILP mathematical problems that allow exchanges of nodes among tours and node reordering on every route. By restricting the range of improvement options, the problem size can be bounded and a limited number of binary variables is required for real‐world problems. The improvement formulation is based on a continuous time‐domain representation that handles assignment and sequencing decisions through different sets of binary variables and uses the notion of a generalized predecessor instead of a direct predecessor. Several types of VRPTW problems have been efficiently solved.     

基于带时间窗口车辆路径问题的蚁群算法

带时间窗口的车辆路径问题（VRPTW）是一个NP-Complete优化问题。VRPTW的主要目标在于利用最少的车辆数以及最短的行程来服务客户，客户有固定的需求和被服务的时间限制。基于该问题提出了一种并行多蚁群算（PMACS-VRFTW）：首先利用QUICK-ACS生成初始解，然后利用ACS-VEI和ACS-TIME分别优化车辆数和行程距离。试验表明，所提出的算法基于Solomon的VRPTW基准实例获得了很好的结果。     

Modeling rolling batch planning as vehicle routing problem with time windows

This paper considers the rolling batch planning problem of grouping and sequencing a given set of slabs into several rolling units in iron and steel industry. The existing mathematical methods often used for the problem are traveling salesman problem (TSP) and vehicle routing problem (VRP), but these methods are not precise, because the position limitation of some slabs in a rolling unit scheduling is not considered. Therefore we suggest a new model, vehicle routing problem with time window (VRPTW) to describe the rolling batch planning problem, in which the position limitation of slabs are quantified as the time constraints. Several solution methods including the genetic algorithm are presented for solving the problem and the computational results show that the genetic algorithm is superior to other methods.In this paper, the vehicle routing problem with time window (VRPTW) of combinational optimization is used to analyze and model the rolling batch planning problem. Genetic algorithm and heuristic are used to solve the problem. Simulation results based on the actual production data show that this model is precise and the genetic algorithm based method is very promising.     

Design of an improved quantum-inspired evolutionary algorithm for a transportation problem in logistics systems

Logistics faces great challenges in vehicle schedule problem. Intelligence Technologies need to be developed for solving the transportation problem. This paper proposes an improved Quantum-Inspired Evolutionary Algorithm (IQEA), which is a hybrid algorithm of Quantum-Inspired Evolutionary Algorithm (QEA) and greed heuristics. It extends the standard QEA by combining its principles with some heuristics methods. The proposed algorithm has also been applied to optimize a problem which may happen in real life. The problem can be categorized as a vehicle routing problem with time windows (VRPTW), which means the problem has many common characteristics that VRPTW has, but more constraints need to be considered. The basic idea of the proposed IQEA is to embed a greed heuristic method into the standard QEA for the optimal recombination of consignment subsequences. The consignment sequence is the order to arrange the vehicles for the transportation of the consignments. The consignment subsequences are generated by cutting the whole consignment sequence according to the values of quantum bits. The computational result of the simulation problem shows that IQEA is feasible in achieving a relatively optimal solution. The implementation of an optimized schedule can save much more cost than the initial schedule. It provides a promising, innovative approach for solving VRPTW and improves QEA for solving complexity problems with a number of constraints.     

A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows

In this paper, we present an effective memetic algorithm for the vehicle routing problem with time windows (VRPTW). The paper builds upon an existing edge assembly crossover (EAX) developed for the capacitated VRP. The adjustments of the EAX operator and the introduction of a novel penalty function to eliminate violations of the time window constraint as well as the capacity constraint from offspring solutions generated by the EAX operator have proven essential to the heuristic's performance. Experimental results on Solomon's and Gehring and Homberger benchmarks demonstrate that our algorithm outperforms previous approaches and is able to improve 184 best-known solutions out of 356 instances.     

基于遗传算法求解带时间窗的车辆路由问题

提出一种改进的遗传算法，用于求解带时间窗的车辆路由问题．在算法中采用了直观的自然数缟码机制、三复本锦标赛的选择方法和改进的启发式交叉算子，实验表明该方法用于求解带时间窗的车辆路由问题的有效性．     

VNS methods for home care routing and scheduling problem with temporal dependencies,and multiple structures and specialties

The need for optimization in the Home Care Service is becoming more and more legitimate in the face of the increase of demand and cost all over the world. Recently, many researchers in the Operation Research community have been attracted by this issue, which presents interesting aspects related to the vehicle routing problems. In this paper, we consider a new variant called the vehicle routing problem with time windows, temporal dependencies (synchronization, precedence, and disjunction), multi‐structures, and multispecialties problem (VRPTW‐TD‐2MS). This new variant is an extension of the vehicle routing problems with time windows and synchronization constraints (VRPTW‐S) that is well‐studied in literature. We present a Mixed Integer Programming method, and propose three Variable Neighborhood Search approaches. Extensive experiments show the effectiveness and efficiency of the General Variable Neighborhood Search with Ejection Chains‐based local search for solving VRPTW‐TD‐2MS and VRPTW‐S.     

Waste collection vehicle routing problem with time windows

In this paper, we address a real life waste collection vehicle routing problem with time windows (VRPTW) with consideration of multiple disposal trips and drivers’ lunch breaks. Solomon's well-known insertion algorithm is extended for the problem. While minimizing the number of vehicles and total traveling time is the major objective of vehicle routing problems in the literature, here we also consider the route compactness and workload balancing of a solution since they are very important aspects in practical applications. In order to improve the route compactness and workload balancing, a capacitated clustering-based waste collection VRPTW algorithm is developed. The proposed algorithms have been successfully implemented and deployed for the real life waste collection problems at Waste Management, Inc. A set of waste collection VRPTW benchmark problems is also presented in this paper.Waste collection problems are frequently considered as arc routing problems without time windows. However, that point of view can be applied only to residential waste collection problems. In the waste collection industry, there are three major areas: commercial waste collection, residential waste collection and roll-on-roll-off. In this paper, we mainly focus on the commercial waste collection problem. The problem can be characterized as a variant of VRPTW since commercial waste collection stops may have time windows. The major variation from a standard VRPTW is due to disposal operations and driver's lunch break. When a vehicle is full, it needs to go to one of the disposal facilities (landfill or transfer station). Each vehicle can, and typically does, make multiple disposal trips per day. The purpose of this paper is to introduce the waste collection VRPTW, benchmark problem sets, and a solution approach for the problem. The proposed algorithms have been successfully implemented and deployed for the real life waste collection problems of Waste Management, the leading provider of comprehensive waste management services in North America with nearly 26,000 collection and transfer vehicles.