Planning a Capacitated Road Network with Flexible Travel Times: A Genetic Algorithm

Abstract

We are concerned with a capacitated location-multi allocation-routing problem in a road network with flexible travel times. It is assumed that all links are two-way and capacities of the server nodes and arcs for accepting of population are limited. The aim of our work is to find numbers and locations of server nodes, allocation of the existing population in existing demand nodes on the network to the servers and the allocation of existing population in each node to different routes to determine the decided server for each member so that total transportation time is minimized. Here, two basic concepts are considered: multi allocation and flexible travel times. The concept of multi allocation arises from the possibility of allocating the existing population in a demand node to more than one server node. Also, flexible travel times concentrate on impact of traveling population on the times of links simultaneously, that is, depending on how the population is distributed on the network, the travel times on links may be increased. So, to have the least increase in the time of each link, it is necessary to decide upon the distribution of population in the network. We formulate the proposed problem as a mixed-integer nonlinear programming model and then present a genetic algorithm (GA) for solving large problems Finally, we make two sets of numerical experiments and analyze the obtained results by LINGO solver and GA. Numerical results show the proposed GA to be highly efficient.