||We consider finding the near-optimized solution of logistic's vehicle routing problem includes grouping of customers and travelling salesman problem.|
We try to balance the number of customers for each vehicle. According to k-mean clustering algorithm, we add restrictions of the number of each cluster and conditions of distributing each customer to achieve our target.
After that, we want to find a near-shortest route passing through all the customers for each cluster. This problem is a travelling salesman problem, has been proved to be an NP-hard problem that exact solution should be got by exhaustion method or branch and bound method. Therefore, we use Diagonalize Complete Algorithm to construct a feasible Hamiltonian path, and then using 2-opt and Feiring algorithm to get a shorter path. Among these algorithm, if the number of cluster is n, then the computing of $2$-opt algorithm is O( n^2 ) and can not be parallelable, so we consider two different way to modify the algorithm to do parallel computing with MPI. That is, if we use p processes in MPI, then it can reducing the computing to O( n^2/p ).