Improved artificial bee colony algorithm for vehicle routing problem with time windows.

The Vehicle Routing Problem with Time Windows (VRPTW) consists of a homogenous set of vehicles and a set of customer located in a city. In VRPTW all the vehicles starts from the depot visit the customer and end at the depot. Each customer is visited exactly by one vehicle within the specified time window. The objective is to minimize the number of vehicles and total distance travelled simultaneously. This represents the multiobjective Vehicle Routing Problem with Time Windows. The proposed work consists of Hybrid Genetic Search with Diversity Control using the Genetic Algorithm for solving the VRPTW. The Pareto approach is used for finding the set of optimal solutions for achieving the multiobjective. The crossover operator is used for exchanging the best routes, which have shortest distance. Two mutation operators such as relocation mutation operator and split mutation operator were used in this application. In this, it accounts penalty for an infeasible solutions with respect to time-window and duration constrains. The computations are performed using the instances which are obtained from the VRPLIB.

Vehicle Routing Problem with Time Windows (VRPTW) is a constrained NP-hard problem that designs the least cost routes from one depot to a set of geographically scattered points. Most of traditional techniques are difficult to solve this kind of problem. In this paper, we explored the validity of another swarm-intelligence-based model-Bacterial Foraging Optimization (BFO) for VRPTW solving. Original BFO, BFO with linear decreasing chemotaxis step (BFO-LDC) and BFO with non-linear decreasing chemotaxis step (BFO-NDC) are used to obtain the best solutions of a given VRPTW problem, respectively. The experimental results demonstrated that the proposed BFO algorithms have the potential to solve Vehicle Routing Problem with Time Windows (VRPTW) with rapid convergence rate and the good result accuracy.

A parallel memetic algorithm for the NP-hard vehicle routing problem with time windows (VRPTW) is proposed. The algorithm consists of components which are executed as parallel processes. A process runs either a heuristic algorithm or a hybrid of a genetic algorithm and some local refinement procedures. In order to improve the results, processes co-operate periodically using a novel randomized scheme. During each phase of co-operation processes exploit their best solutions found so far. The purpose of the work is to devise the parallel memetic algorithm which determines the VRPTW solutions of the highest possible quality. The experiments on Gehring and Homberger's (GH) benchmarking tests show that the algorithm achieves very good results. By making use of it the best-known solutions to 171 out of 300 GH tests were improved.

Path optimization is a critical issue in vehicle routing problems (VRPs). This study tends to solve a VRP with time windows (VRPTW), which is an important version of VRP. Its principal objective is to find out the minimum cost routes to serve the customers within service time intervals, by a fleet of vehicles having confined capacity. An improved ant colony optimization (ACO) is applied to the problem, which uses a new pheromone reset and update function to enhance the route searching and a 2-opt method to improve the optimized path. The proposed ACO is tested on standard benchmarks of VRPTW. The results verifies the effectiveness of the algorithm and confirms it as better path optimizing method for VRPTW, in comparison to the traditional ACO and other heuristics.

‘Route balance’ is the difference between the longest and the shortest among all the route lengths. The route balance is frequently considered in a vehicle routing problem (VRP) for balancing the distance travelled among delivery vehicles. This is a common practice since in VRPs there are no time elements. However, in recent years, some research works have considered route balance in a vehicle routing problem with time windows (VRPTW). As there are more time elements in VRPTW, this paper refutes that route balance is sufficient for VRPTW by simultaneously optimising makespan and workload imbalance using ‘total time balance’ instead of route balance. On the other hand, ‘total time balance’ is the difference between the longest total time taken and the shortest total time taken among delivery vehicles. As such, makespan is the longest total time taken among vehicles. Total time taken for a vehicle is the sum of vehicle run time, waiting time and service time. In order to demonstrate the importance of using total time balance instead of route balance on VRPTW, three different multi-objective VRPTW models, namely, (1) only with general VRPTW objectives (i.e. ‘total distance travelled’ by all vehicles and ‘total number of vehicles’ used), (2) general VRPTW objectives with route balance and (3) general VRPTW objectives with total time balance are developed and solved by fitness aggregated genetic algorithm (FAGA) for 36 Solomon’s benchmark instances. By comparison of the makespan produced by the FAGA between the three cases, the importance of using total time balance instead of route balance on multi-objective VRPTW is demonstrated. Also, the makespan produced by the FAGA for the third case, i.e. general VRPTW objectives with total time balance is compared with the makespan produced by fitness aggregated differential evolution (FADE). By comparing makespan with statistical testing between FAGA and FADE, the outperformance of FAGA over FADE is verified. To check the practicality of the total time balance on multi-objective VRPTW, an instance with real time windows is also solved for the three cases by the FAGA and its makespan are compared and reported.

The Improved Artificial Bee Colony (IABC) algorithm is a variant of the well-known Artificial Bee Colony (ABC) algorithm. In IABC, a new initialization approach and a new search mechanism were added to the ABC for avoiding local optimums and a better convergence speed. New parameters were added for the new search mechanism. Specified values of these newly added parameters have a direct impact on the performance of the IABC algorithm. For better performance of the algorithm, parameter values should be subjected to change from problem to problem and also need to be updated during the run of the algorithm. In this paper, two novel parameter control methods and related algorithms have been developed in order to increase the performance of the IABC algorithm for large scale optimization problems. One of them is an adaptive parameter control which updates parameter values according to the feedback coming from the search process during the run of the algorithm. In the second method, the management of the parameter values is left to the algorithm itself, which is called self-adaptive parameter control. The adaptive IABC algorithms were examined and compared to other ABC variants and state-of-the-art algorithms on a benchmark functions suite. Through the analysis of the results of the experiments, the adaptive IABC algorithms outperformed almost all ABC variants and gave competitive results with state-of-the-art algorithms from the literature.

In the field of operations research, the vehicle routing problem with time windows (VRPTW) has been widely studied because it is extensively used in practical applications. Real-life situations discussed in the relevant research include time windows and vehicle capabilities. Among the constraints in a VRPTW, the practical consideration of the fairness of drivers’ performance bonuses has seldom been discussed in the literature. However, the shortest routes and balanced performance bonuses for all sales drivers are usually in conflict. To balance the bonuses awarded to all drivers, an auction bidding approach was developed to address this practical consideration. The fairness of performance bonuses was considered in the proposed mathematical model. The nearest urgent candidate heuristic used in the auction bidding approach determined the auction price of the sales drivers. The proposed algorithm both achieved a performance bonus balance and planned the shortest route for each driver. To evaluate the performance of the auction bidding approach, several test instances were generated based on VRPTW benchmark data instances. This study also involved sensitivity and scenario analyses to assess the effect of the algorithm’s parameters on the solutions. The results show that the proposed approach efficiently obtained the optimal routes and satisfied the practical concerns in the VRPTW.

In a preceding study, authors critically analysed the functional behaviour of Artificial Bee Colony (ABC) algorithm in view of some of its reported search limitations and offered directions for performance improvements. Accordingly, an improved ABC (IABC) algorithm is proposed with inclusion of three features: (1) dynamic update of probability values of food sources after every successful new search under the onlooker bees operator, (2) Allocation of variable ‘effective limit’ to each food source based upon its food quality instead of global fixed ‘limit’ and (3) insulation of best-so-far solution from scout bee operator. The additional features render substantial improvements in search abilities of ABC algorithm. The experiments with classical and CEC’2014 benchmark test functions confirm the supremacy of IABC algorithm over basic ABC algorithm as well as some of its variants and other evolutionary algorithms. Notably, the IABC algorithm does not introduce any new control parameter or hybridization with any other operator and maintains almost same level of computational complexity.

The vehicle routing problem with time windows (VRPTW) which has both capacity and time constraints is an extension of vehicle routing problem (VRP). The problem is solved by optimizing routes for the vehicles so as to meet all given constraints as well as to minimize travelling distance and number of vehicles. This paper proposes to analyze a multi objective evolutionary algorithm (MOEA) that incorporates Various heuristics for local exploitation in the evolutionary search and the concept of pareto’s optimality to solve multi objective optimization in VRPTW. In this paper we model VRPTW as a modified version specialized for a multi objective context, using Evolutionary Algorithm to get a set of pareto optimal solutions considering three objectives, the number of vehicles, the total travel distance and the total delivery time at the same time. This new approach is validated with very good results and the comparison is performed on a standard benchmark problems showing that the algorithm outperforms highly competitive results compared with previously published studies.

A hybrid tabu search algorithm, which generates initial solution by genetic algorithm, is proposed here to solve the vehicle routing problems with time windows (VRPTW). Experimental result shows that this algorithm is better than the other known algorithms.

This paper addresses the problem of delivering continuously deteriorating agri-fresh produce from a wholesaler to a number of retailers, within specific time windows. The prime objective is to decide the routes in such a way that the overall cost incurred in transportation, deterioration and penalty is minimised. To model these conflicting objectives a mathematical modelling approach is proposed. The Vehicle Routing Problem with Time Windows (VRPTW) is a Non-deterministic Polynomial-time hard (NP-hard) problem, without considering the business constraints, and becomes computationally prohibitive with the increase in number of retailers. To solve the VRPTW within feasible time limits, Artificial Immune System (AIS)-based solution methodology is proposed. The algorithm is tested on real-life instances generated from Azadpur wholesale market, New Delhi (India). An experiment is performed on the same problems with other algorithms, such as Genetic Algorithm (GA) and Simulated Annealing (SA), to compare the effectiveness and efficiency of the proposed approach. It is found from the quality of solution and rate of convergence that AIS performed better compared to the other applied approaches.

Crowd animation is a new and continuous challenge in computer animation. In tradition, crowd animation can be realized by key frame technology, and animators should set every character’s expression, action, motion, and behavior. Therefore animators’ workload by hand will increase tremendously with characters growing, which lead to difficult to realize crowd animation for low efficiency and poor global controllability, especially in path planning by appointing a target position for each individuals. In order to overcome these, an improved artificial bee colony (IM-ABC) algorithm is proposed to apply on the path planning of crowd animation. The IM-ABC is fit to simulate the crowd motion in animation based on the following two merits over the others in crowd animation. One is the rule of role transformation, which can make the rapid convergence of the result and avoid getting trapped in the local optima. The other is the realization of multi-object optimization in the process of iteration, which reaches the uniformly distributed result of swarm motion and especially fits to realize the path plan. In this paper, we simply reviews classical ABC algorithm proposed by Karaboga at the beginning. Then, in order to speed the convergence and make individuals generate paths more realistic and natural, some measures are taken to modify the classical ABC (called IM-ABC) algorithm, which include initializing colony based on chaos sequence, selfadaptively selecting the follower bees, and adaptively controlling parameters, etc. After the experiments of benchmark functions, the results confirm that the IM-ABC have better performance than the classical ABC algorithm and others. Finally, the IM-ABC algorithm is used for path planning to generate the route from the initial to the destination without collision. Through simulation experiments based on four motion models it is showed that this method can succeed generating the optimum paths with efficiency, intelligence, and natural features.

In order to improve the accuracy of the artificial bee colony algorithm (ABC) on vehicle routing problem with time window (VRPTW), This paper makes the following improvements to the ABC. Three kinds of neighborhood search methods are introduced. In the leader bee and follower bee search stage, the single search mode is changed into a three-way search method, which improves the optimization depth of the algorithm. Multiple neighborhood searches of new food sources generated by the scouter bee is conducted and proceeding to the next iteration has enhanced the survival of new food sources and increased the diversity of populations. The global optimal solution is recorded by setting and updating the bulletin board. Simulation experiments show that the improved discrete ABC algorithm has obvious advantages in solving large-scale VRPTW. Therefore, the improved discrete ABC algorithm has great potential and application value in solving VRPTW.

In this paper, the vehicle routing problem with time windows (VRPTW) was considered, and a mixed integer programming mathematic model of VRPTW was proposed in detail. Meantime, an improved ant colony algorithm (IACA) was proposed to overcome the shortcomings of premature convergence and slow convergence of conventional ant colony algorithm (ACA). The experiment results showed that the IACA can solve VRPTW effectively.

Vehicle routing problem with time windows (VRPTW) is a practical and complex vehicle routing problem (VRP) which is faced by thousands of companies in logistics and transportation. Usually, VRP is solved by traditional heuristic algorithms. Recently, deep learning models under the reinforcement learning (RL) framework have been proposed to solve variants of VRP. In our study, we propose to use the hierarchical RL to find an optimal policy for generating optimal routes in VRPTW. The hierarchical RL structure includes a low level which generates feasible solutions and a high level which further searches for an optimal solution. Experimental results show that the proposed hierarchical RL model outperforms the non-hierarchical RL model and the heuristic algorithms Google OR-Tools. The proposed model also shows generalization capability in three different scenarios: varied time window constraints, from small-scale to large-scale problems, and generalization across different datasets. The flexible framework of hierarchical RL can also be applied to solve other complex VRPs with multiple objectives.