Electronic Notes in Discrete Mathematics最新文献

Motivated by the perspective use in decomposition-based generic Mixed Integer Programming (MIP) solvers, we consider the problem of scoring Dantzig-Wolfe decomposition patterns. In particular, assuming to receive in input a MIP instance, we tackle the issue of estimating the tightness of the dual bound yielded by a particular decomposition of that MIP instance, and the computing time required to obtain such a dual bound, looking only at static features of the corresponding data matrices. We propose decomposition ranking methods. We also sketch and evaluate an architecture for an automatic data-driven detector of good decompositions.

The Green Vehicle Routing and Scheduling Problem (GVRSP) aims to minimize carbon Dioxide Emissions (CO₂) in logistics systems through better planning of deliveries made by a fleet of vehicles. In this paper, the GVRSP considers heterogeneous vehicles, time-varying traffic congestion, capacity constraints and the delivery can be fractionated. The GVRSP also allows vehicles to stop on arcs, so vehicle is allowed to travel an arc in multiple time periods. We present a mathematical formulation to describe the problem and a hybrid algorithm that combines the metaheuristic Iterated Local Search (ILS), the Random Variable Neighborhood Descent (RVND) procedure and an exact Set Covering model. The results obtained are compared with the state of the art and we show that the proposed approach has a strong performance.

In this paper we consider the scheduling problem of the curing process for a tire factory. The objective is to determine the minimum makespan in order to meet the demand requirements of different tires, restricted by the number of parts, molds and heaters and allowed combinations of mold-mold and mold-heater. We provide a mixed-integer linear programming (MILP) for the problem and two different rules or estimators for determining an upper bound value of the planning horizon, needed for solving the model. In order to evaluate the suggested estimators, we carry out some numerical experiments over ten different instances based on real data. From the results of these numerical experiments we can conclude that the tightness of estimators have a significant impact on the resolution time of the model.

The demand for network services, such as proxy or firewall, is ever increasing due to the massive diffusion of applications, both on computers and mobile devices. Virtual Network Functions allow to instantiate network services on clouds in a software based manner, thus allowing to dynamically provide services at a reasonable cost. In this work we consider the problem of placing Virtual Network Function instances (services) and routing the demands so as to guarantee that demands can reach the requested services. We discuss the complexity of a particular version of the Virtual Network Function placement and routing problem and the impact of the network topology on the problem complexity.

Let G = (V, E) be a connected graph of set of nodes V and set of edges E. Let T = (V_T, E_T), with V_T = V and E_T ⊆ E, be a spanning tree of G. With each edge e ∈ E there is associated a routing cost $c_e^R$ if e connects two internal nodes of T; or an access cost $c_e^A$, otherwise. The problem is to determine a spanning tree (tree-star) considering access and routing edge costs of minimum cost. We present two new formulations and a cutting-plane algorithm. One is based on a classical spanning tree model. The novelty relies on the way we capture access and routing edges depending on the internal nodes of the tree. The second model is completely new and is based on the concept of dicycle to represent routing edges as quadratic variables that are linearized accordingly to obtain a tree-star equivalent structure. Computational experiments performed on benchmark instances for models P_Flow and P_HR from the literature and for the new ones (P_ST and P_DC) indicate that this problem is very difficult to deal with. Only a very small number of instances was solved to optimality in a given time limit. Models P_DC and P_HR, improved with cutting-plane strategies, although they do not solve optimally almost instances, performed better for this problem, with the dicycle-based model presenting the smallest gaps for instances for which some feasible solution was found.

Traditional considerations related to dynamic stability constraint in the Container Loading Problem (CLP), such as boxes with insufficient lateral support, have proven to be inaccurate when compared with the results of dynamic simulations where the boxes are subjected to real world conditions. In response to this, two indicators for dynamic stability were introduced; the number of fallen boxes and the number of boxes likely to be damaged in case of acceleration. These indicators, however, have not yet been estimated using a mechanical approach.

An open source application (PackageCargo) was developed to calculate, visualize, and save efficient packing patterns to instances of the CLP, including a dynamic simulation environment to obtain performance indicators related the dynamic stability of such patterns. The physics engine used in the application is capable of trading accuracy for simulation speed, and is in most cases non-deterministic. Through PackageCargo we evaluated the accuracy of new dynamic stability metrics.

Additionally, a mechanical model that measures dynamic stability without the need to subject the packing pattern to a physics simulation was developed, based on a dynamic analysis of the forces and accelerations acting upon the boxes and using the kinetic parameters of the load such as mass distribution, coefficient of friction, and rigidity.

The integrated Train Timetabling and Stop Planning (TTSP) problem calls for determining the optimal timetables for a given set of trains, while choosing, for each train, the subset of stations where it will stop. Both the timetable and the stop plan are determined based on the passenger demand, i.e. on the number of passengers travelling between an origin and a destination stations. In this work, we study the Robust TTSP (RTTSP), where passenger demand is considered to be uncertain, as it is often the case in real practice. We propose an Integer Linear Programming (ILP) model for RTTSP based on Light Robustness, an effective technique introduced in [Fischetti, M., and M. Monaci, Light robustness In: Ahuja RK, Möhring RH, Zaroliagis CD (eds) Robust and online large-scale optimization. Lecture Notes in Computer Science 5868 (2009), 61–84. Springer, Berlin Heidelberg]. We test the proposed ILP model on real-world data of the Wuhan-Guangzhou high-speed railway corridor under different demand scenarios.

This paper investigates a drayage problem, which is motivated by a carrier providing door-to-door freight transportation services by trucks and containers. The trucks carry one or two containers to ship container loads from a port to importers and from exporters to the same port. The problem is modeled by a set covering formulation with integer variables. We propose a Price-and-Branch algorithm for this problem, in which the pricing problem is a pair of shortest path problems, one for each truck type, in a suitable graph. The algorithm can determine near-optimal solutions in a short time.

Delay-Constrained Routing (DCR) problems require to route a new flow in a computer network subject to worst-case end-to-end delay guarantees. The delay of a packet flow has three components, one of which is the “queueing delay”, that depends on the scheduling algorithm implemented by the routers of the network. When flows are not independent of each other, i.e., admitting a new flow changes the delay of the existing ones, admission control policies are necessary to ensure that existing flows do not become latency-unfeasible. It has been recently shown that admission control runs contrary to the usual objective function employed in these models, i.e., minimization of the reserved rates, significantly worsening network performance. In this paper we investigate the phenomenon and propose a heuristic way to overcome the problem.

The problem under study is the Minimum Broadcast Time (MBT). We are given a simple graph and a singleton that owns a message. The goal is to disseminate the message as soon as possible, where the communication takes place between neighboring-nodes in a selective fashion and each forwarding takes one time-slot. The MBT serves as an inspirational problem for the design of delay-sensitive forwarding schemes. Since the problem belongs to the $\mathrm{NP}$-Hard class, the literature offers heuristics, approximation algorithms and exact exponential-time solutions.

The contributions of this paper are two-fold. First, an ILP formulation for the problem is provided. Second, a competitive heuristic is developed. A fair comparison between TreeBlock and previous heuristics highlights the effectiveness of our proposal.