Line planning with user-optimal route choice

We consider the problem of designing lines in a public transport system, where we include user-optimal route choice. The model we develop ensures that there is enough capacity present for every passenger to travel on a shortest route. We present two different integer programming formulations for this problem, and discuss exact solution approaches. To solve large-scale line planning instances, we also implemented a genetic solution algorithms. We test our algorithms in computational experiments using randomly generated instances along realistic data, as well as a realistic instance modeling the German long-distance network. We examine the advantages and disadvantages of using such user-optimal solutions, and show that our algorithms sufficiently scale with instance size to be used for practical purposes

Survey on Ten Years of Multi-Depot Vehicle Routing Problems: Mathematical Models, Solution Methods and Real-Life Applications

A crucial practical issue encountered in logistics management is the circulation of final products from depots to end-user customers. When routing and scheduling systems are improved, they will not only improve customer satisfaction but also increase the capacity to serve a large number of customers minimizing time. On the assumption that there is only one depot, the key issue of distribution is generally identified and formulated as VRP standing for Vehicle Routing Problem. In case, a company having more than one depot, the suggested VRP is most unlikely to work out. In view of resolving this limitation and proposing alternatives, VRP with multiple depots and multi-depot MDVRP have been a focus of this paper. Carrying out a comprehensive analytical literature survey of past ten years on cost-effective Multi-Depot Vehicle Routing is the main aim of this research. Therefore, the current status of the MDVRP along with its future developments is reviewed at length in the paper

An integrated assignment, routing, and speed model for roadway mobility and transportation with environmental, efficiency, and service goals

Managing all the mobility and transportation services with autonomous vehicles for users of a smart city requires determining the assignment of the vehicles to the users and their routing in conjunction with their speed. Such decisions must ensure low emission, efficiency, and high service quality by also considering the impact on traffic congestion caused by other vehicles in the transportation network. In this paper, we first propose an abstract trilevel multi-objective formulation architecture to model all vehicle routing problems with assignment, routing, and speed decision variables and conflicting objective functions. Such an architecture guides the development of subproblems, relaxations, and solution methods. We also propose a way of integrating the various urban transportation services by introducing a constraint on the speed variables that takes into account the traffic volume caused across the different services. Based on the formulation architecture, we introduce a (bilevel) problem where assignment and routing are at the upper level and speed is at the lower level. To address the challenge of dealing with routing problems on urban road networks, we develop an algorithm that alternates between the assignment-routing problem on an auxiliary complete graph and the speed optimization problem on the original non-complete graph. The computational experiments show the effectiveness of the proposed approach in determining approximate Pareto fronts among the conflicting objectives

A parametric integer programming algorithm for bilevel mixed integer programs

We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and mixed integer bilevel problems. For the mixed integer case where the leader's variables are continuous, our algorithm also detects whether the infimum cost fails to be attained, a difficulty that has been identified but not directly addressed in the literature. In this case it yields a ``better than fully polynomial time'' approximation scheme with running time polynomial in the logarithm of the relative precision. For the pure integer case where the leader's variables are integer, and hence optimal solutions are guaranteed to exist, we present two algorithms which run in polynomial time when the total number of variables is fixed.Comment: 11 page

A bilevel approach for compensation and routing decisions in last-mile delivery

In last-mile delivery logistics, peer-to-peer logistic platforms play an important role in connecting senders, customers, and independent carriers to fulfill delivery requests. Since the carriers are not under the platform's control, the platform has to anticipate their reactions, while deciding how to allocate the delivery operations. Indeed, carriers' decisions largely affect the platform's revenue. In this paper, we model this problem using bilevel programming. At the upper level, the platform decides how to assign the orders to the carriers; at the lower level, each carrier solves a profitable tour problem to determine which offered requests to accept, based on her own profit maximization. Possibly, the platform can influence carriers' decisions by determining also the compensation paid for each accepted request. The two considered settings result in two different formulations: the bilevel profitable tour problem with fixed compensation margins and with margin decisions, respectively. For each of them, we propose single-level reformulations and alternative formulations where the lower-level routing variables are projected out. A branch-and-cut algorithm is proposed to solve the bilevel models, with a tailored warm-start heuristic used to speed up the solution process. Extensive computational tests are performed to compare the proposed formulations and analyze solution characteristics

On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

Optimal Design of Signal Controlled Road Networks Using Differential Evolution Optimization Algorithm

This study proposes a traffic congestion minimization model in which the traffic signal setting optimization is performed through a combined simulation-optimization model. In this model, the TRANSYT traffic simulation software is combined with Differential Evolution (DE) optimization algorithm, which is based on the natural selection paradigm. In this context, the EQuilibrium Network Design (EQND) problem is formulated as a bilevel programming problem in which the upper level is the minimization of the total network performance index. In the lower level, the traffic assignment problem, which represents the route choice behavior of the road users, is solved using the Path Flow Estimator (PFE) as a stochastic user equilibrium assessment. The solution of the bilevel EQND problem is carried out by the proposed Differential Evolution and TRANSYT with PFE, the so-called DETRANSPFE model, on a well-known signal controlled test network. Performance of the proposed model is compared to that of two previous works where the EQND problem has been solved by Genetic-Algorithms- (GAs-) and Harmony-Search- (HS-) based models. Results show that the DETRANSPFE model outperforms the GA- and HS-based models in terms of the network performance index and the computational time required

CoBRA: A Coevolutionary Meta-heuristic for Bi-level Optimization

This article presents CoBRA, a new parallel coevolutionary algorithm for bi-level optimization. CoBRA is based on a coevolutionary scheme to solve bi-level optimization problems. It handles population-based meta-heuristics on each level, each one cooperating with the other to provide solutions for the overall problem. Moreover, in order to evaluate the relevance of CoBRA against more classical approaches, a new performance assessment methodology, based on rationality, is introduced. An experimental analysis is conducted on a bi-level distribution planning problem, where multiple manufacturing plants deliver items to depots, and where a distribution company controls several depots and distributes items from depots to retailers. The experimental results reveal significant enhancements with respect to a more classical approach, based on a hierarchical scheme.Cet article présente CoBRA, un nouvel algorithme paralléle et coévolutionnaire pour l'optimisation bi-niveau. CoBRA se base sur un modèle coévolutionnaire pour faire face aux problèmes d'optimisation bi-niveau. Il manipule une méta-heuristique à base de population sur chaque niveau, chacune coopérant avec l'autre de manière à garder une vue générale sur le problème complet. De plus, afin d'étudier la pertinence de CoBRA par rapport aux approches plus classique, une nouvelle méthodologie, basée sur la rationalité est introduite. Est conduite ensuite une étude expérimentale sur un problème bi-niveau de distribution-production, dans lequel des usines contrôlées par une entreprise produisent des marchandises pour des dépôts, et une autre entreprise contrôlant les dépôts se charge de livrer les marchandises à des clients. Cet article se conclut sur l'observation d'un réel gain de performance par rapport à une approche plus classique, basée sur un modèle hiérarchique