A Discrete Hybrid Invasive Weed Optimization Algorithm for the Capacitated Vehicle Routing Problem

Abstract The capacitated vehicle routing problem (CVRP) has been proved to be NP complete problem. The CVRP is not just a purely academic construct, it has many applications in practice. In this work, a discrete invasive weed optimization algorithm (DIWO) is proposed to solve the capacitated vehicle routing problem. Adaptive mutation and crossover in the genetic operation process are introduced to ensure the diversity of the algorithm and prevent it from falling into a local optimal solution with premature convergence. We use real matrix encoding and construct a discretization process for the subgeneration in the parent generation region. An improved 2-Opt and exchange operations structure based on the property of the problem is proposed to construct the two-stage hybrid variable-domain search method, strengthening the capacity of the local and global search ability of the algorithms. Comparing the experimental simulation and the algorithm with literature for different scale benchmarks proves that the DIWO algorithm is simple, efficient, adaptable, and robust for discrete combinatorial optimization problems.