We prove a result concerning objective functions that can be used to obtain eÆcient and balanced solutions to the multi-commodity network ow problem. This type of solution is of interest when routing traÆc in the Internet. A particular case of the result proved here (see Corollary 2 below) was stated without proof in a previous paper. Objective Functions for Balance in TraÆc Engineering? Juan A...

We address the problem of optimal multi-agent path finding (MAPF) in this paper. The task is to find a set of actions for each agent in know terrain so that each agent arrives to its desired destination from a given starting position. Agents are not allowed to collide with each other along their paths. Furthermore, a solution that minimizes the total time is required. In this paper we study sea...

Markovian network equilibrium generalizes the classical Wardrop in games. At a equilibrium, each player of game solves Markov decision process instead shortest path problem. We propose two novel extensions by considering (1) variable demand, which offers players quitting option, and (2) multi-commodity flow, allows to have heterogeneous ending time. further develop dynamic-programming-based ite...

This paper documents the formalization of Appia's problem onto the integer program framework, and the multi-commodity problem. We also present our thoughts on possible future work in formalization.

The fixed-charge Capacitated Multi-commodity Network Design (CMND) is a well-known problem of both practical and theoretical significance. Network design models represent a wide variety of planning and operation management issues in transportation telecommunication, logistics, production and distribution. In this paper, Ant Colony Optimization (ACO) based neighborhoods are proposed for CMND pro...

Bike sharing systems (BSSs) offer a mobility service whereby public bikes, located at different stations across an urban area, are available for shared use. An important point is that the distribution of rides between stations is not uniformly distributed and certain stations fill up or empty over time. These empty and full stations lead to demand for bikes and return boxes that cannot be fulfi...

This paper proposes a new heuristicmethod for the logistics network design and planning problem based on linear relaxation and DC (difference of convex functions) programming. We consider a multi-period, multi-echelon,multi-commodity andmulti-product problemdefined as a large scalemixed integer linear programming (MILP) model. The method is experimented on data sets of various size. The numeric...