Abstract
The natural behaviour of the honeybee has attracted the attention of researchers in recent years and several algorithms have been developed that mimic swarm behaviour to solve optimisation problems. This paper introduces an artificial bee colony (ABC) algorithm for the vehicle routing problem with time windows (VRPTW). A Modified ABC algorithm is proposed to improve the solution quality of the original ABC. The high exploration ability of the ABC slows-down its convergence speed, which may due to the mechanism used by scout bees in replacing abandoned (unimproved) solutions with new ones. In the Modified ABC a list of abandoned solutions is used by the scout bees to memorise the abandoned solutions, then the scout bees select a solution from the list based on roulette wheel selection and replace by a new solution with random routs selected from the best solution. The performance of the Modified ABC is evaluated on Solomon benchmark datasets and compared with the original ABC. The computational results demonstrate that the Modified ABC outperforms the original ABC also produce good solutions when compared with the best-known results in the literature. Computational investigations show that the proposed algorithm is a good and promising approach for the VRPTW.
Highlights
Many real transportation logistics and distribution problems can be expressed as a vehicle routing problem, where the objective is to plan a route with minimum cost while serving a set of customers with known demands
Overall comparison indicates that our Modified artificial bee colony (ABC) algorithm is able to obtain the best results in comparison to state-of-the-art approaches, as represented by reducing the distance travelled, which is the main objective of the vehicle routing problem with time windows (VRPTW)
A statistical test is executed to examine if there is any significant difference between the ABC and the Modified ABC algorithms with the significance interval 95 % (α = 0.05)
Summary
Many real transportation logistics and distribution problems can be expressed as a vehicle routing problem, where the objective is to plan a route with minimum cost while serving a set of customers with known demands. The ABC algorithm works based on local communication between three groups of bees (scouts, employed and onlookers) and between each other about their environment, which contributes to the collective intelligence of the bee colony (Karaboga 2005). Solomon (1987) proposes the formulation of the VRPTW, Solomon’s benchmark has 56 instances with 100 customers must be served by a predefined number of vehicles. If the solution cannot be improved in a predefined number of iterations (defined as a parameter called limit), the employed bee becomes a scout bee in order to explore a new solution. In this paper we propose an improved version of the ABC algorithm, where a list of abandoned solutions is defined (abnd_lst: extendable abandoned list) so that the scout bees can memorise the solutions that exceed the maximum number of trials (limit). Group RC mixes the customers distribution in the instances R and C
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