Learning Whale Optimization Algorithm for Open Vehicle Routing Problem with Loading Constraints

This paper addresses the two-dimensional loading open vehicle routing problem with time window (2L-OVRPTW). We propose a learning whale optimization algorithm (LWOA) to minimize the total distance; an improved skyline filling algorithm (ISFA) is designed to solve the two-dimensional loading problem. In LWOA, the whale optimization algorithm is used to search the solution space and get the high-quality solution. Then, by learning and accumulating the block structure and customer location information in the high-quality solution individuals, a three-dimensional matrix is designed to guide the updating of the population. Finally, according to the problem characteristics, the local search method based on fleet and vehicle is designed and performed on the high-quality solution region. IFSA is used to optimize the optimal individual. The computational results show that the proposed algorithm can effectively solve 2L-OVRPTW.

Multi-depot open vehicle routing problem with fuzzy time windows

This paper presents one method and one hybrid genetic algorithm for multi-depot open vehicle routing problem with fuzzy time windows (MDOVRPFTW) without maximum time windows. For the method, the degree of customers’ willingness to accept goods (DCWAG) is firstly proposed, it’s one fuzzy vague and determines maximum time windows. Referring to methods to determine fuzzy membership function, the function between DCWAG and the starting service time is constructed. By setting an threshold for DCWAG, the starting service time that the threshold corresponds can be treated as the maximum time window, which meets the actual situation. The goal of the model is to minimize the total cost. For the algorithm, MDOVRPFTW without maximum time windows is an extension of the NP-hard problem, the hybrid genetic algorithm was designed, which is combination of genetic algorithm and Hungarian algorithm. When the hybrid genetic algorithm applied to one pharmaceutical logistics company in Beijing City, China, one optimal scheme is determined. Then the rationality and the stability of solutions by the hybrid genetic algorithm are proved. Finally, sensitivity analyses are performed to investigate the impact of someone factor on DCWAG and some suggestions are proposed.

A Modified Kruskal's Algorithm to Improve Genetic Search for Open Vehicle Routing Problem

This article has proposed a modified Kruskal's method to increase the efficiency of a genetic algorithm to determine the path of least distance starting from a central point to solve the open vehicle routing problem. In a vehicle routing problem, vehicles start from a central point and several customers placed in different locations to serve their demands and return to the central point. In the case of the open vehicle routing problem, the vehicles do not go back to the central point after serving the customers. The challenge is to reduce the number of vehicles used and the distance travelled simultaneously. The proposed method applies genetic algorithms to find the set of customers those are covered by a particular vehicle and the authors have applied the proposed modified Kruskal's method for local routing optimization. The results of the new method are analyzed in comparison with some of the evolutionary methods.