Best routes selection in multimodal networks using multi-objective genetic algorithm

In this study, we propose a bi-level multi-objective Taguchi genetic algorithm for a multimodal routing problem with time windows. The mathematic model is constructed, which is featured by two optimal objectives, multiple available transportation manners and different demanded delivery times. After thoroughly analyzing the characteristics of the formulated model, a corresponding bi-level multi-objective Taguchi genetic algorithm is designed to find the Pareto-optimal front. At the upper level, a genetic multi-objective algorithm simultaneously searches the Pareto-optimal front and provides the most feasible routing path choices for the lower level. After generalizing the matrices of costs and time in a multimodal transportation network, the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-shortest path algorithm is applied to providing some potential feasible paths. A multi-objective genetic algorithm is proposed at the lower level to determine the local optimal combination of transportation manners for these potential feasible paths. To make the genetic algorithm more robust, sounder and faster, the Taguchi (orthogonal) experimental design method is adopted in generating the initial population and the crossover operator. The case study shows that the proposed algorithm can effectively find the Pareto-optimal front solutions and offer series of transportation routes with best combinations of transportation manners. The shipper can easily select the required shipping schemes with specified demands.