Solving the p-hub Median Problem Under Intentional Disruptions Using Simulated Annealing

Hubs are special facilities designed to act as switching, transshipment and sorting points in various distribution systems. Since hub facilities concentrate and consolidate flows, disruptions at hubs could have large effects on the performance of a hub network. In this paper, we have formulated the multiple allocation p-hub median problem under intentional disruptions as a bi-level game model. In this model, the follower’s objective is to identify those hubs the loss of which would most diminish service efficiency. Moreover, the leader’s objective is to identify the set of hubs to locate in order to minimize expected transportation cost while taking normal and failure conditions into account. We have applied two algorithms based on simulated annealing to solve the defined problem. In addition, the algorithms have been calibrated using the Taguchi method. Computational experiments on different instances indicate that the proposed algorithms would be efficient in practice.     

Uncapacitated single allocation p-hub maximal covering problem

The hub location problem is to find a set of hub nodes on the network, where logistics transportation via the hubs is encouraged because of the cost or distance savings. Each node that has a specified amount of demands can be connected to one of p hubs. The uncapacitated single allocation p-hub maximal covering problem is to maximize the logistics covered, where the logistics of demand is said to be covered if the distance between two nodes is less than or equal to the specified range in consideration of the distance savings between hubs. The aim of our model is to locate the hub, and to allocate non-hub nodes to the located hub nodes; the hub can maximize the demand covered by deadline traveling time. It is presented an integer programming formulation for the new hub covering model, and a computational study based on several instances derived from the CAB (Civil Aeronautics Board) data set. Two heuristics, distance based allocation and volume based allocation methods, are suggested with a computational experiment on the CAB data set. Performances of heuristics are evaluated, and it is shown that good solutions are found in a relatively reasonable computation time for most of instances.     

Solving scalarized multi‐objective network flow problems using an interior point method

In this paper, we present a primal‐dual interior‐point algorithm to solve a class of multi‐objective network flow problems. More precisely, our algorithm is an extension of the single‐objective primal infeasible dual feasible inexact interior point method for multi‐objective linear network flow problems. Our algorithm is contrasted with standard interior point methods and experimental results on bi‐objective instances are reported. The multi‐objective instances are converted into single objective problems with the aid of an achievement function, which is particularly adequate for interactive decision‐making methods.     

Uncapacitated single and multiple allocation p-hub center problems

The hub median problem is to locate hub facilities in a network and to allocate non-hub nodes to hub nodes such that the total transportation cost is minimized. In the hub center problem, the main objective is one of minimizing the maximum distance/cost between origin destination pairs. In this paper, we study uncapacitated hub center problems with either single or multiple allocation. Both problems are proved to be NP-hard. We even show that the problem of finding an optimal single allocation with respect to a given set of hubs is already NP-hard. We present integer programming formulations for both problems and propose a branch-and-bound approach for solving the multiple allocation case. Numerical results are reported which show that the new formulations are superior to previous ones.     

Solving two-stage hybrid flow shop using climbing depth-bounded discrepancy search

This paper investigates how to adapt a discrepancy-based search method to solve two-stage hybrid flowshop scheduling problems in which each stage consists of several identical machines operating in parallel. The objective is to determine a schedule that minimizes the makespan. We present an adaptation of the Climbing Depth-bounded Discrepancy Search (CDDS) method based on Johnson’s rule and on dedicated lower bounds for the two-stage hybrid flow shop problem. We report the results of extensive computational experiments, which show that the proposed adaptation of the CDDS method solves instances in restrained CPU time and with high quality of makespan.     

A 2-phase algorithm for solving the single allocation p-hub center problem

The single allocation p-hub center problem is an NP-hard location–allocation problem which consists of locating hub facilities in a network and allocating non-hub nodes to hub nodes such that the maximum distance/cost between origin–destination pairs is minimized. In this paper we present an exact 2-phase algorithm where in the first phase we compute a set of potential optimal hub combinations using a shortest path based branch and bound. This is followed by an allocation phase using a reduced sized formulation which returns the optimal solution. In order to get a good upper bound for the branch and bound we developed a heuristic for the single allocation p-hub center problem based on an ant colony optimization approach. Numerical results on benchmark instances show that the new solution approach is superior over traditional MIP-solver like CPLEX. As a result we are able to provide new optimal solutions for larger problems than those reported previously in literature. We are able to solve problems consisting of up to 400 nodes in reasonable time. To the best of our knowledge these are the largest problems solved in the literature to date.     

Hub network design problem in the presence of disruptions

The main issue in p-hub median problem is locating hub facilities and allocating spokes to those hubs in order to minimize the total transportation cost. However hub facilities may fail occasionally due to some disruptions which could lead to excessive costs. One of the most effective ways to hedge against disruptions especially intentional disruptions is designing more reliable hub networks. In this paper, we formulate the multiple allocation p-hub median problem under intentional disruptions by a bi-level model with two objective functions at the upper level and a single objective at the lower level. In this model, the leader aims at identifying the location of hubs so that minimize normal and worst-case transportation costs. Worst-case scenario is modeled in the lower level where the follower’s objective is to identify the hubs that if lost, it would mostly increase the transportation cost. We develop two multi-objective metaheuristics based on simulated annealing and tabu search to solve the problem. Computational results indicate the viability and effectiveness of the proposed algorithms for exploring the non-dominated solutions.     

Real-time optimization flow control

In this paper, we propose a dynamic optimization approach to end-to-end flow control in data networks. The objective is to maximize the aggregate utilities of the data sources over soft transmission rate bounds and delay constraints. The network links and data sources are considered as processors of a distributed computational system that has a global objective function. The presented model works with different shapes of utility curves under the proposition of elastic data traffic. The approach relies on real-time observations of the delay as a measure of the data network congestion at the routers (network nodes). A primal–dual algorithm carried out by the data sources is used to solve the optimization problem in a decentralized manner. The calculated transmission rates are bounded and the sources are subjected to a maximum number of data packets that can be queued downstream of each transmission session. The algorithm solves for the rates without the access to any network global information while each source calculates its transmission rate that should maximize the global objective function. The calculated optimal rates conform to rate-to-queue proportionality. Finally, we present an extensive simulation results to demonstrate the reliability of the algorithm.     

A tabu-search based heuristic for the hub covering problem over incomplete hub networks

Hub location problems deal with finding the location of hub facilities and with the allocation of demand nodes to these located hub facilities. In this paper, we study the single allocation hub covering problem over incomplete hub networks and propose an integer programming formulation to this end. The aim of our model is to find the location of hubs, the hub links to be established between the located hubs, and the allocation of non-hub nodes to the located hub nodes such that the travel time between any origin–destination pair is within a given time bound. We present an efficient heuristic based on tabu search and test the performance of our heuristic on the CAB data set and on the Turkish network.     

Routing and scheduling decisions in the hierarchical hub location problem

Hubs are facilities that consolidate and disseminate flow in many-to-many distribution systems. The hub location problem considers decisions that include the locations of hubs in a network and the allocations of demand (non-hub) nodes to these hubs. We propose a hierarchical multimodal hub network structure, and based on this network, we define a hub covering problem with a service time bound. The hierarchical network consists of three layers in which we consider a ring-star-star (RSS) network. This multimodal network may have different types of vehicles in each layer. For the proposed problem, we present and strengthen a mathematical model with some variable fixing rules and valid inequalities. Also, we develop a heuristic solution algorithm based on the subgradient approach to solve the problem in more reasonable times. We conduct the computational analysis over the Turkish network and the CAB data sets.     

Lagrangian relaxation for maximum service in multicast routing with QoS constraints

In this paper, we propose a new variant of the Multicast Routing Problem called Maximum Service in Multicast Routing with Quality of Service constraints applied in the context of vehicular ad hoc networks, for which data must be sent from a root node to a set of terminal nodes. The use of all nodes is not mandatory and each connection between the root and a terminal aims to satisfy the quality of service according to the limits established for each metric. The objective is to maximize the number of serviced terminals according to the network's quality of service metrics. We present an integer programming formulation and four Lagrangian relaxations, to obtain good primal and dual bounds. We also develop a local search applied during the resolution of the Lagrangian relaxations. These methodologies were subjected to computational experiments with a set of 40 instances generated with characteristics of vehicular ad hoc networks. Statistical analyses were performed to compare the performance between methodologies, where the model achieved optimal values for 29 instances, and the Lagrangian relaxations rendered competitive bounds, especially for large instances.     

A hybrid Lagrangian genetic algorithm for the prize collecting Steiner tree problem

We consider the version of prize collecting Steiner tree problem (PCSTP) where each node of a given weighted graph is associated with a prize and where the objective is to find a minimum weight tree spanning a subset of nodes and collecting a total prize not less that a given quota Q.$Q.$ We present a lower bound and a genetic algorithm for the PCSTP. The lower bound is based on a Lagrangian decomposition of a minimum spanning tree formulation of the problem. The volume algorithm is used to solve the Lagrangian dual. The genetic algorithm incorporates several enhancements. In particular, it fully exploits both primal and dual information produced by Lagrangian decomposition. The proposed lower and upper bounds are assessed through computational experiments on randomly generated instances with up to 500 nodes and 5000 edges. For these instances, the proposed lower and upper bounds exhibit consistently a tight gap: in 76% of the cases the gap is strictly less than 2%.     

Exact and heuristic procedures for single machine scheduling with quadratic earliness and tardiness penalties

The present paper studies the single machine, no-idle-time scheduling problem with a weighted quadratic earliness and tardiness objective. We investigate the relationship between this problem and the assignment problem, and we derive two lower bounds and several heuristic procedures based on this relationship. Furthermore, the applicability of the time-indexed integer programming formulation is investigated. The results of a computational experiment on a set of randomly generated instances show (1) the high-quality results of the proposed heuristics, (2) the low optimality gap of one of the proposed lower bounds and (3) the applicability of the integer programming formulation to small and medium size cases of the problem.     

A heuristic-based branch and bound algorithm for unconstrained quadratic zero-one programming

In this paper we describe a branch and bound algorithm for solving the unconstrained quadratic 0–1 programming problem. The salient features of it are the use of quadratic programming heuristics in the transformation of subproblems and exploiting some classes of facets of the polytope related to the quadratic problem in deriving upper bounds on the objective function. We develop facet selection procedures that form a basis of the bound computation algorithm. We present computational experience on four series of randomly generated problems and 14 real instances of a quadratic problem arising in design automation. We remark that the same ideas can also be applied to some other combinatorial optimization problems.     

应对枢纽失效的轴辐式网络枢纽备份

为提高轴辐式网络可靠性,在初始枢纽失效时保持轴辐式网络正常运转,提出了一种轴辐式网络枢纽备份优化方法,给每一个枢纽点选择一个备份枢纽,使轴辐式网络初始成本和备份成本总和最优。首先,在轴辐式网络基本模型中引入枢纽备份变量,建立非线性规划扩展模型,通过变量代换的线性化方法,将扩展模型线性化,用数学求解器CPLEX求解轴辐式网络枢纽备份小规模问题。然后,增加轴辐式网络节点规模,设计遗传算法求解大规模轴辐式网络枢纽备份优化问题。最后,在CPLEX和遗传算法中,调整初始轴辐式网络成本和备份成本比例权重,分别得到初始成本、备份成本、枢纽选址与备份枢纽的精确解和优化解。算例实验得出初始轴辐式网络、备份枢纽以及目标函数最优值。实验结果表明,所提方法备份枢纽分担了初始枢纽的流量和容量,当初始枢纽失效时,备份枢纽可以承担初始枢纽的运输任务让轴辐式网络继续运转。该枢纽备份优化方法可应用于应急物流和物流网络安全管理方面。     

Lagrangian bounds for large‐scale multicommodity network design: a comparison between Volume and Bundle methods

The Bundle Method and the Volume Algorithm are among the most efficient techniques to obtain accurate Lagrangian dual bounds for hard combinatorial optimization problems. We propose here to compare their performance on very large scale Fixed‐Charge Multicommodity Capacitated Network Design problems. The motivation is not only the quality of the approximation of these bounds as a function of the computational time but also the ability to produce feasible primal solutions and thus to reduce the gap for very large instances for which optimal solutions are out of reach. Feasible solutions are obtained through the use of Lagrangian information in constructive and improving heuristic schemes. We show in particular that, if the Bundle implementation has provided great quality bounds in fewer iterations, the Volume Algorithm is able to reduce the gaps of the largest instances, taking profit of the low computational cost per iteration compared to the Bundle Method.     

A decomposition approach for the probabilistic maximal covering location-allocation problem

The maximal covering location problem (MCLP) maximizes the population that has a facility within a maximum travel distance or time. Numerous extensions have been proposed to enhance its applicability, like the probabilistic model for the maximum covering location-allocation with a constraint in waiting time or queue length for congested systems, with one or more servers per service center. This paper presents a solution procedure for that probabilistic model, considering one server per center, using a column generation and covering graph approaches. The computational tests report interesting results for network instances up to 818 vertices. The column generation results are competitive solving the instances in reasonable computational times, reaching optimality for some and providing good bounds for the difficult instances.     

Uplink scheduling for joint wireless orthogonal frequency and time division multiple access networks

In this paper, we present a deterministic resource allocation model for a hybrid uplink wireless orthogonal frequency and time division multiple access network. Since the input data of the model may be affected by uncertainty, we further consider a stochastic formulation of the problem which we transform into an equivalent deterministic binary second-order conic program (SOCP). Subsequently, we use this binary SOCP to derive an equivalent integer linear programming formulation. The proposed models are aimed at maximizing the total bandwidth channel capacity subject to user power and sub-carrier assignment constraints while simultaneously scheduling users in time. As such, the models are best suited for non-real-time applications where sub-channel multiuser diversity can be further exploited simultaneously in frequency and time domains. Finally, in view of the large execution times required by CPLEX to solve the proposed models, we propose a variable neighborhood search metaheuristic procedure. Our numerical results show tight bounds and near optimal solutions for most of the instances when compared to the optimal solution of the problem. Moreover, we obtain better feasible solutions than CPLEX in the stochastic case. Finally, these bounds are obtained at a very low computational cost.     

多分配枢纽站集覆盖问题的随机p- 鲁棒优化模型及算法

枢纽站选址是轴辐式网络优化设计的重要问题,枢纽站覆盖则是该问题的一个类型.考虑枢纽站建站成本和节点间运输距离的不确定性,结合随机优化和鲁棒优化方法,建立了完备轴辐式网络中多分配枢纽站集覆盖问题的随机-鲁棒优化模型;采用二进制编码,对量子粒子群算法进行改进,加入免疫思想,设计了免疫量子粒子群求解算法.最后通过算例对模型进行仿真计算,结果表明了该模型及算法的可行性和有效性.     

The multi-period incremental service facility location problem

In this paper we introduce the multi-period incremental service facility location problem where the goal is to set a number of new facilities over a finite time horizon so as to cover dynamically the demand of a given set of customers. We prove that the coefficient matrix of the allocation subproblem that results when fixing the set of facilities to open is totally unimodular. This allows to solve efficiently the Lagrangean problem that relaxes constraints requiring customers to be assigned to open facilities. We propose a solution approach that provides both lower and upper bounds by combining subgradient optimization to solve a Lagrangean dual with an ad hoc heuristic that uses information from the Lagrangean subproblem to generate feasible solutions. Numerical results obtained in the computational experiments show that the obtained solutions are very good. In general, we get very small percent gaps between upper and lower bounds with little computation effort.