弹性轨道磁悬浮控制系统模型降阶研究

在磁悬浮控制系统中,常常忽略轨道的弹性来设计控制算法。在这种控制算法作用下,当轨道刚度较小时,系统容易产生振动。为解决该问题,可以将轨道弹性加入悬浮模型,然后设计控制算法。考虑轨道弹性之后,悬浮系统的模型会比较复杂,控制算法难以在工程实现。为此,采用Hankel范数近似法对考虑轨道弹性后的模型进行降阶,并且在降阶模型的基础上设计控制算法,解决了轨道弹性引发的系统振动问题。并且,这种方法容易在工程中实现。文章最后利用仿真结果验证了降阶方法的可行性。     

Schedule design for liner services under vessel speed reduction incentive programs

Gas and particulate emissions from ship transportation have been increasing in recent years. In order to mitigate ship emissions near coastal areas, voluntary vessel speed reduction incentive programs (VSRIPs) were put in place by a number of ports. This paper studies a schedule design problem faced by liner shipping companies under VSRIPs. It proposes a mixed-integer nonlinear mathematical model for the minimization of the total cost, consisting of fuel cost, as well as operating cost, minus dockage refunds. The model balances three determinants, that is, the compliance of VSRIPs, the speed limit (the maximum physical speed of ships and the upper speed limit imposed by VSRIPs), and the limited number of ships. An enumerative algorithm and a piecewise-linear approximation algorithm are developed, based on some properties of the nonlinear model. The efficiency of the proposed algorithms is validated through extensive computational experiments.     

Approximation algorithms for general one‐warehouse multi‐retailer systems

Logistical planning problems are complicated in practice because planners have to deal with the challenges of demand planning and supply replenishment, while taking into account the issues of (i) inventory perishability and storage charges, (ii) management of backlog and/or lost sales, and (iii) cost saving opportunities due to economies of scale in order replenishment and transportation. It is therefore not surprising that many logistical planning problems are computationally difficult, and finding a good solution to these problems necessitates the development of many ad hoc algorithmic procedures to address various features of the planning problems. In this article, we identify simple conditions and structural properties associated with these logistical planning problems in which the warehouse is managed as a cross‐docking facility. Despite the nonlinear cost structures in the problems, we show that a solution that is within ε‐optimality can be obtained by solving a related piece‐wise linear concave cost multi‐commodity network flow problem. An immediate consequence of this result is that certain classes of logistical planning problems can be approximated by a factor of (1 + ε) in polynomial time. This significantly improves upon the results found in literature for these classes of problems. We also show that the piece‐wise linear concave cost network flow problem can be approximated to within a logarithmic factor via a large scale linear programming relaxation. We use polymatroidal constraints to capture the piece‐wise concavity feature of the cost functions. This gives rise to a unified and generic LP‐based approach for a large class of complicated logistical planning problems. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Scheduling parallel machines with inclusive processing set restrictions

We consider the problem of assigning a set of jobs to different parallel machines of the same processing speed, where each job is compatible to only a subset of those machines. The machines can be linearly ordered such that a higher‐indexed machine can process all those jobs that a lower‐indexed machine can process. The objective is to minimize the makespan of the schedule. This problem is motivated by industrial applications such as cargo handling by cranes with nonidentical weight capacities, computer processor scheduling with memory constraints, and grades of service provision by parallel servers. We develop an efficient algorithm for this problem with a worst‐case performance ratio of + ε, where ε is a positive constant which may be set arbitrarily close to zero. We also present a polynomial time approximation scheme for this problem, which answers an open question in the literature. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

A stochastic approximation algorithm to compute bid prices for joint capacity allocation and overbooking over an airline network

In this article, we develop a stochastic approximation algorithm to find good bid price policies for the joint capacity allocation and overbooking problem over an airline network. Our approach is based on visualizing the total expected profit as a function of the bid prices and searching for a good set of bid prices by using the stochastic gradients of the total expected profit function. We show that the total expected profit function that we use is differentiable with respect to the bid prices and derive a simple expression that can be used to compute its stochastic gradients. We show that the iterates of our stochastic approximation algorithm converge to a stationary point of the total expected profit function with probability 1. Our computational experiments indicate that the bid prices computed by our approach perform significantly better than those computed by standard benchmark strategies and the performance of our approach is relatively insensitive to the frequency with which we recompute the bid prices over the planning horizon. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Annealing adaptive search,cross‐entropy,and stochastic approximation in global optimization

The Annealing Adaptive Search (AAS) algorithm for global optimization searches the solution space by sampling from a sequence of Boltzmann distributions. For a class of optimization problems, it has been shown that the complexity of AAS increases at most linearly in the problem dimension. However, despite its desirable property, sampling from a Boltzmann distribution at each iteration of the algorithm remains a practical challenge. Prior work to address this issue has focused on embedding Markov chain‐based sampling techniques within the AAS framework. In this article, based on ideas from the recent Cross‐Entropy method and Model Reference Adaptive Search, we propose an algorithm, called Model‐based Annealing Random Search (MARS), that complements prior work by sampling solutions from a sequence of surrogate distributions that iteratively approximate the target Boltzmann distributions. We establish a novel connection between MARS and the well‐known Stochastic Approximation method. By exploiting this connection, we prove the global convergence of MARS and characterize its asymptotic convergence rate behavior. Our empirical results indicate promising performance of the algorithm in comparison with some of the existing methods. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

The knapsack problem with a minimum filling constraint

We study a knapsack problem with an additional minimum filling constraint, such that the total weight of selected items cannot be less than a given threshold. The problem has several applications in shipping, e‐commerce, and transportation service procurement. When the threshold equals the knapsack capacity, even finding a feasible solution to the problem is NP‐hard. Therefore, we consider the case when the ratio α of threshold to capacity is less than 1. For this case, we develop an approximation scheme that returns a feasible solution with a total profit not less than (1 ‐ ε) times the total profit of an optimal solution for any ε > 0, and with a running time polynomial in the number of items, 1/ε, and 1/(1‐α). © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Efficient algorithms for flexible job shop scheduling with parallel machines

Job shop scheduling with a bank of machines in parallel is important from both theoretical and practical points of view. Herein we focus on the scheduling problem of minimizing the makespan in a flexible two-center job shop. The first center consists of one machine and the second has k parallel machines. An easy-to-perform approximate algorithm for minimizing the makespan with one-unit-time operations in the first center and k-unit-time operations in the second center is proposed. The algorithm has the absolute worst-case error bound of k − 1 , and thus for k = 1 it is optimal. Importantly, it runs in linear time and its error bound is independent of the number of jobs to be processed. Moreover, the algorithm can be modified to give an optimal schedule for k = 2 .     

Signal‐to‐interference‐plus‐noise ratio estimation for wireless communication systems: Methods and analysis

The Signal‐to‐Interference‐plus‐Noise Ratio (SINR) is an important metric of wireless communication link quality. SINR estimates have several important applications. These include optimizing the transmit power level for a target quality of service, assisting with handoff decisions and dynamically adapting the data rate for wireless Internet applications. Accurate SINR estimation provides for both a more efficient system and a higher user‐perceived quality of service. In this paper, we develop new SINR estimators and compare their mean squared error (MSE) performance. We show that our new estimators dominate estimators that have previously appeared in the literature with respect to MSE. The sequence of transmitted bits in wireless communication systems consists of both pilot bits (which are known both to the transmitter and receiver) and user bits (which are known only by the transmitter). The SINR estimators we consider alternatively depend exclusively on pilot bits, exclusively on user bits, or simultaneously use both pilot and user bits. In addition, we consider estimators that utilize smoothing and feedback mechanisms. Smoothed estimators are motivated by the fact that the interference component of the SINR changes relatively slowly with time, typically with the addition or departure of a user to the system. Feedback estimators are motivated by the fact that receivers typically decode bits correctly with a very high probability, and therefore user bits can be thought of as quasipilot bits. For each estimator discussed, we derive an exact or approximate formula for its MSE. Satterthwaite approximations, noncentral F distributions (singly and doubly) and distribution theory of quadratic forms are the key statistical tools used in developing the MSE formulas. In the case of approximate MSE formulas, we validate their accuracy using simulation techniques. The approximate MSE formulas, of interest in their own right for comparing the quality of the estimators, are also used for optimally combining estimators. In particular, we derive optimal weights for linearly combining an estimator based on pilot bits with an estimator based on user bits. The optimal weights depend on the MSE of the two estimators being combined, and thus the accurate approximate MSE formulas can conveniently be used. The optimal weights also depend on the unknown SINR, and therefore need to be estimated in order to construct a useable combined estimator. The impact on the MSE of the combined estimator due to estimating the weights is examined. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Balancing perfectly periodic service schedules: An application from recycling and waste management

A national recycling and waste management company provides periodic services to its customers from over 160 service centers. The services are performed periodically in units of weeks over a planning horizon. The number of truck‐hours allocated to this effort is determined by the maximum weekly workload during the planning horizon. Therefore, minimizing the maximum weekly workload results in minimum operating expenses. The perfectly periodic service scheduling (PPSS) problem is defined based on the practices of the company. It is shown that the PPSS problem is strongly NP‐hard. Attempts to solve large instances by using an integer programming formulation are unsuccessful. Therefore, greedy BestFit heuristics with three different sorting schemes are designed and tested for six real‐world PPSS instances and 80 randomly generated data files. The heuristics provide effective solutions that are within 2% of optimality on average. When the best found BestFit schedules are compared with the existing schedules, it is shown that operational costs are reduced by 18% on average. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 160–171, 2012