A hybrid genetic algorithm with an adaptive diversity control technique for the homogeneous and heterogeneous dial-a-ride problem

Dial-a-Ride Problem (DARP) is one of the classic routing problems with pairing and precedence constraints. Due to these types of constraints, it is quite challenging to design an efficient evolutionary algorithm for solving this problem. In this paper, a genetic algorithm in combination with a variable neighborhood descent procedure is suggested to solve the DARP. This algorithm, which is called Hybrid Genetic Algorithm (HGA), is independent of any repairing procedure or user-defined penalty factors. Instead, it uses the constraint dominance principle with respect to the number of unserved requests. Our algorithm employs an adaptive population management technique which takes into account not only the quality of solutions but also their contribution in the diversity level. To do so efficiently, this population management technique utilizes a simple arc-based representation for the DARP solutions. A route-based crossover procedure known as Route Exchange Crossover is used in the HGA. This crossover method is thoroughly compared with five other crossover techniques including a new one called Block Exchange Crossover. The HGA produces competitive solutions in comparison with the state-of-the-art methods for tackling the DARP and Heterogeneous DARP (H-DARP). It obtains the optimal solutions of all the small and medium size standard instances of the DARP and finds new best results for two large ones with unknown optimal solutions. Moreover, for 12 out of 24 new instances of the H-DARP, the best known solutions are improved using the HGA.