Bilevel Optimization for On-Demand Multimodal Transit Systems

This study explores the design of an On-Demand Multimodal Transit System (ODMTS) that includes segmented mode switching models that decide whether potential riders adopt the new ODMTS or stay with their personal vehicles. It is motivated by the desire of transit agencies to design their network by taking into account both existing and latent demand, as quality of service improves. The paper presents a bilevel optimization where the leader problem designs the network and each rider has a follower problem to decide her best route through the ODMTS. The bilevel model is solved by a decomposition algorithm that combines traditional Benders cuts with combinatorial cuts to ensure the consistency of mode choices by the leader and follower problems. The approach is evaluated on a case study using historical data from Ann Arbor, Michigan, and a user choice model based on the income levels of the potential transit riders

Waste processing facility location problem by stochastic programming: Models and solutions

The paper deals with the so-called waste processing facility location problem (FLP), which asks for establishing a set of operational waste processing units, optimal against the total expected cost. We minimize the waste management (WM) expenditure of the waste producers, which is derived from the related waste processing, transportation, and investment costs. We use a stochastic programming approach in recognition of the inherent uncertainties in this area. Two relevant models are presented and discussed in the paper. Initially, we extend the common transportation network flow model with on-and-off waste-processing capacities in selected nodes, representing the facility location. Subsequently, we model the randomly-varying production of waste by a scenario-based two-stage stochastic integer linear program. Finally, we employ selected pricing ideas from revenue management to model the behavior of the waste producers, who we assume to be environmentally friendly. The modeling ideas are illustrated on an example of limited size solved in GAMS. Computations on larger instances were realized with traditional and heuristic algorithms, implemented within MATLAB. © Springer Nature Switzerland AG 2019

Analysis of road network pattern considering population distribution and central business district.

This paper proposes a road network growing model with the consideration of population distribution and central business district (CBD) attraction. In the model, the relative neighborhood graph (RNG) is introduced as the connection mechanism to capture the haracteristics of road network topology. The simulation experiment is set up to illustrate the effects of population distribution and CBD attraction on the characteristics of road network. Moreover, several topological attributes of road network is evaluated by using coverage, circuitness, treeness and total length in the experiment. Finally, the suggested model is verified in the simulation of China and Beijing Highway networks

Optimizing constrained subtrees of trees

Given a tree G = (V, E) and a weight function defined on subsets of its nodes, we consider two associated problems. The first, called the ''rooted subtree problem'', is to find a maximum weight subtree, with a specified root, from a given set of subtrees. The second problem, called ''the subtree packing problem'', is to find a maximum weight packing of node disjoint subtrees chosen from a given set of subtrees, where the value of each subtree may depend on its root. We show that the complexity status of both problems is related, and that the subtree packing problem is polynomial if and only if each rooted subtree problem is polynomial, In addition we show that the convex hulls of the feasible solutions to both problems are related: the convex hull of solutions to the packing problem is given by ''pasting together'' the convex hulls of the rooted subtree problems. We examine in detail the case where the set of feasible subtrees rooted at node i consists of all subtrees with at most k nodes, For this case we derive valid inequalities, and specify the convex hull when k less than or equal to 4

Multicommodity Capacitated Network Design

This paper presents a comprehensive survey of models and algorithms for multicommodity capacitated network design problems, which are mostly encountered in telecommunications and transportation network planning. These problems are important not only due to the major relevance of their applications, but also because they pose considerable modeling and algorithmic challenges. We present a general arc-based model, describe useful alternative formulations and survey the literature on simplex-based cutting plane and Lagrangian relaxation approaches. We then focus on our own contributions that develop and compare several relaxation methods for a particular case of this model, the fixed-charge problem. These methods are based on Lagrangian relaxation and nondifferentiable optimization techniques, namely, the subgradient and bundle approaches. Our experimental results, while very encouraging, indicate that solving effciently these diffcult problems requires a judicious combination of cutting planes, Lagrangian relaxation methods and sophisticated heuristics. In addition, due to their inherent decomposition properties, these techniques can be adapted to parallel computing environments, which is highly desirable in order to solve realistically sized instances

Mathematical programming models for traffic engineering in Ethernet networks implementing the multiple spanning tree protocol

The Multiple Spanning Tree Protocol (MSTP), used in Ethernet networks, maintains a set of spanning trees that are used for routing the demands in the network. Each spanning tree is allocated to a pre-defined set of demands. In this paper we present two mixed integer programming models for the Traffic Engineering problem of optimally designing a network implementing MSTP, such that link utilization is minimized. This is the first approach that focuses on using exact methods to solve this problem. We present tests in order to compare the two formulations, in terms of formulation strength and computing time. © 2014 Springer International Publishing.SCOPUS: cp.kinfo:eu-repo/semantics/publishe