Capacitated Vehicle Routing Problem Using Algebraic Harris Hawks Optimization Algorithm
Mohammad Sajid, Md Saquib Jawed, Shafiqul Abidin, Mohammad Shahid, Shakeel Ahamad, Jagendra Singh
Abstract
The capacitated vehicle routing problem (CVRP) is an NP-hard combinatorial optimization problem that plays a significant role in end distribution in smart logistics. The CVRP solution can be denoted as a permutation of given customers. The solutions in the continuous-valued swarm intelligence (SI) algorithms (i.e., particle swarm optimization, ant colony optimization, HHO, etc.) for permutation problems are represented as continuous-valued vectors. These continuous-valued vectors must be converted into permutations to compute the fitness values. However, there exist potentially infinite continuous-valued vectors corresponding to a single permutation due to cardinality reasons, thus inserting huge plateaus in the fitness landscape navigated by the underlying SI. An algebraic Harris hawks optimization (AHHO) algorithm is proposed for permutation-based CVRP to optimize the total traveled distance. The proposed AHHO algorithm is the algebraic version of Harris hawks optimization (HHO), and it simulates the hunting moves of Harris hawks in permutation-based solution space. The proposed AHHO employs a novel discrete version of Lévy flights based on Lévy distribution and local search operators. The performance of the proposed AHHO algorithm is estimated on 85 well-known CVRP benchmark instances. The proposed AHHO algorithm offers promising results compared to random-key HHO, hybrid firefly, and cuckoo search with Lévy flights algorithms.