A Radial Hybrid Estimation of Distribution Algorithm for the Vehicle Routing Problem with Time Windows

Abstract

The vehicle routing environment has been widely studied under different approaches. It is due to its practical characteristic that makes its research interesting. Therefore, the vehicle-scheduling problem continues being attracted to develop new evolutionary algorithms. In this paper, we propose a new estimation of distribution algorithm coupled with a radial probability function. The aforementioned radial function comes from the hydrogen element. Continuous values, for the solution representation, are used in this research. Each value represents the distance, in picometers, between the electron and the core of the hydrogen atom. The representation, elected in this research, is suitable to integrate the radial probability distribution as a probability model. This approach is proposed in order to build a competitive estimation of distribution algorithm for the vehicle routing problem with time windows. The key point is to exploit the radial probability distribution to construct offspring, and to tackle the inconvenient of the estimation of distribution algorithms, i.e., lack of diversity of the solutions and poor ability of exploitation. In addition, this paper omits to use permutation-based representation as other recent estimation of distribution algorithms. Various instances and numerical experiments are presented to illustrate, and to validate this novel research. The results, obtained from this research, permits to conclude that using radial probability distributions is an emerging field to develop new and efficient EDAs.