PD反馈特征结构配置在最优控制问题中的应用

考虑了二阶线性系统的比例微分(PD)反馈特征结构配置问题以及其在最优控制问题中的应用。基于比例微分特征结构配置参数化方法,将二阶线性系统的最优控制问题转化为一个便于求解的有约束条件的极小值问题,并给出了相应的求解算法。三自由度质量弹簧阻尼系统算例及其仿真结果表明所提算法简单、有效。     

二次型极小化问题的迭代算法

在新的控制条件下,证明了二次型极小化问题的迭代算法的有效性,所得结果改进了徐洪坤关于二次型优化的最新结果。     

A competitive genetic algorithm for resource-constrained project scheduling

In this paper we consider the resource-constrained project scheduling problem (RCPSP) with makespan minimization as objective. We propose a new genetic algorithm approach to solve this problem. Subsequently, we compare it to two genetic algorithm concepts from the literature. While our approach makes use of a permutation based genetic encoding that contains problem-specific knowledge, the other two procedures employ a priority value based and a priority rule based representation, respectively. Then we present the results of our thorough computational study for which standard sets of project instances have been used. The outcome reveals that our procedure is the most promising genetic algorithm to solve the RCPSP. Finally, we show that our genetic algorithm yields better results than several heuristic procedures presented in the literature. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 733–750, 1998     

Variations on a cutting plane method for solving concave minimization problems with linear constraints

A cutting plane method for solving concave minimization problems with linear constraints has been advanced by Tui. The principle behind this cutting plane has been applied to integer programming by Balas, Young, Glover, and others under the name of convexity cuts. This paper relates the question of finiteness of Tui's method to the so-called generalized lattice point problem of mathematical programming and gives a sufficient condition for terminating Tui's method. The paper then presents several branch-and-bound algorithms for solving concave minimization problems with linear constraints with the Tui cut as the basis for the algorithm. Finally, some computational experience is reported for the fixed-charge transportation problem.     

A finite descent theory for linear programming,piecewise linear convex minimization,and the linear complementarity problem

A descent algorithm simultaneously capable of solving linear programming, piecewise linear convex minimization, and the linear complementarity problem is developed. Conditions are given under which a solution can be found in a finite number of iterations using the geometry of the problem. A computer algorithm is developed and test problems are solved by both this method and Lemke's algorithm. Current results indicate a decrease in the number of cells visited but an increase in the total number of pivots needed to solve the problem.     

Multiproduct dynamic lot-sizing model with coordinated replenishments

In this article we consider a multiproduct dynamic lot-sizing model. In addition to a separate setup cost for each product ordered, a joint setup cost is incurred when at least one product is ordered. We formulate the model as a concave minimization problem over a compact polyhedral set and present a finite branch and bound algorithm for finding an optimal ordering schedule. Superiority of the branch and bound algorithm to the existing exact procedures is demonstrated. We report computational experience with problems whose dimensions render the existing procedures computationally infeasible.     

An exact algorithm for the batch sequencing problem in a two-machine flow shop with limited buffer

This paper deals with the problem of makespan minimization in a flow shop with two machines when the input buffer of the second machine can only host a limited number of parts. Here we analyze the problem in the context of batch processing, i.e., when identical parts must be processed consecutively. We propose an exact branch-and-bound algorithm, in which the bounds exploit the batching nature of the problem. Extensive computational results show the effectiveness of the approach, and allow us to compare it with a previous heuristic approach. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 141–164, 1998     

Scheduling parallel dedicated machines with the speeding‐up resource

We consider a problem of scheduling jobs on m parallel machines. The machines are dedicated, i.e., for each job the processing machine is known in advance. We mainly concentrate on the model in which at any time there is one unit of an additional resource. Any job may be assigned the resource and this reduces its processing time. A job that is given the resource uses it at each time of its processing. No two jobs are allowed to use the resource simultaneously. The objective is to minimize the makespan. We prove that the two‐machine problem is NP‐hard in the ordinary sense, describe a pseudopolynomial dynamic programming algorithm and convert it into an FPTAS. For the problem with an arbitrary number of machines we present an algorithm with a worst‐case ratio close to 3/2, and close to 3, if a job can be given several units of the resource. For the problem with a fixed number of machines we give a PTAS. Virtually all algorithms rely on a certain variant of the linear knapsack problem (maximization, minimization, multiple‐choice, bicriteria). © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Least-absolute-value estimators for one-way and two-way tables

This paper concerns itself with the problem of estimating the parameters of one-way and two-way classification models by minimization of the sum of the absolute deviations of the regression function from the observed points. The one-way model reduces to obtaining a set of medians from which optimal parameters can be obtained by simple arithmetic manipulations. The two-way model is transformed into a specially structured linear programming problem, and two algorithms are presented to solve this problem. The occurrence of alternative optimal solutions in both models is discussed, and numerical examples are presented.     

Capacity improvement,penalties, and the fixed charge transportation problem

Capacity improvement and conditional penalties are two computational aides for fathoming subproblems in a branch‐and‐bound procedure. In this paper, we apply these techniques to the fixed charge transportation problem (FCTP) and show how relaxations of the FCTP subproblems can be posed as concave minimization problems (rather than LP relaxations). Using the concave relaxations, we propose a new conditional penalty and three new types of capacity improvement techniques for the FCTP. Based on computational experiments using a standard set of FCTP test problems, the new capacity improvement and penalty techniques are responsible for a three‐fold reduction in the CPU time for the branch‐and‐bound algorithm and nearly a tenfold reduction in the number of subproblems that need to be evaluated in the branch‐and‐bound enumeration tree. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 341–355, 1999     

基于改进Markov模型软件测试策略

针对已有软件测试Markov模型与工程实践不符的情况，通过引入软件需求覆盖率改进Markov模型。在改进的Markov模型基础上，本文以软件测试过程中测试总代价最小为控制目标，采用交叉熵方法修正测试剖面，由优化测试剖面生成测试用例序列。仿真结果表明这种方法能够有效地降低软件测试总代价，是一种有效的软件测试方法。     

The discrete max-min problem

The historic max-min problem is examined as a discrete process rather than in its more usual continuous mode. Since the practical application of the max-min model usually involves discrete objects such as ballistic missiles, the discrete formulation of the problem seems quite appropriate. This paper uses an illegal modification to the dynamic programming process to obtain an upper bound to the max-min value. Then a second but legal application of dynamic programming to the minimization part of the problem for a fixed maximizing vector will give a lower bound to the max-min value. Concepts of optimal stopping rules may be applied to indicate when sufficiently near optimal solutions have been obtained.     

A specially structured nonlinear integer resource allocation problem

We present an algorithm for solving a specially structured nonlinear integer resource allocation problem. This problem was motivated by a capacity planning study done at a large Health Maintenance Organization in Texas. Specifically, we focus on a class of nonlinear resource allocation problems that involve the minimization of a convex function over one general convex constraint, a set of block diagonal convex constraints, and bounds on the integer variables. The continuous variable problem is also considered. The continuous problem is solved by taking advantage of the structure of the Karush‐Kuhn‐Tucker (KKT) conditions. This method for solving the continuous problem is then incorporated in a branch and bound algorithm to solve the integer problem. Various reoptimization results, multiplier bounding results, and heuristics are used to improve the efficiency of the algorithms. We show how the algorithms can be extended to obtain a globally optimal solution to the nonconvex version of the problem. We further show that the methods can be applied to problems in production planning and financial optimization. Extensive computational testing of the algorithms is reported for a variety of applications on continuous problems with up to 1,000,000 variables and integer problems with up to 1000 variables. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 770–792, 2003.     

A note on the optimality of index priority rules for search and sequencing problems

We show that the linear objective function of a search problem can be generalized to a power function and/or a logarithmic function and still be minimized by an index priority rule. We prove our result by solving the differential equation resulting from the required invariance condition, therefore, we also prove that any other generalization of this linear objective function will not lead to an index priority rule. We also demonstrate the full equivalence between two related search problems in the sense that a solution to either one can be used to solve the other one and vice versa. Finally, we show that the linear function is the only function leading to an index priority rule for the single‐machine makespan minimization problem with deteriorating jobs and an additive job deterioration function. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Stochastic regret minimization for revenue management problems with nonstationary demands

We study an admission control model in revenue management with nonstationary and correlated demands over a finite discrete time horizon. The arrival probabilities are updated by current available information, that is, past customer arrivals and some other exogenous information. We develop a regret‐based framework, which measures the difference in revenue between a clairvoyant optimal policy that has access to all realizations of randomness a priori and a given feasible policy which does not have access to this future information. This regret minimization framework better spells out the trade‐offs of each accept/reject decision. We proceed using the lens of approximation algorithms to devise a conceptually simple regret‐parity policy. We show the proposed policy achieves 2‐approximation of the optimal policy in terms of total regret for a two‐class problem, and then extend our results to a multiclass problem with a fairness constraint. Our goal in this article is to make progress toward understanding the marriage between stochastic regret minimization and approximation algorithms in the realm of revenue management and dynamic resource allocation. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 433–448, 2016     

Analysis of algorithms for two‐stage flowshops with multi‐processor task flexibility

In this article we introduce a 2‐machine flowshop with processing flexibility. Two processing modes are available for each task: namely, processing by the designated processor, and processing simultaneously by both processors. The objective studied is makespan minimization. This production environment is encountered in repetitive manufacturing shops equipped with processors that have the flexibility to execute orders either individually or in coordination. In the latter case, the product designer exploits processing synergies between two processors so as to execute a particular task much faster than a dedicated processor. This type of flowshop environment is also encountered in labor‐intensive assembly lines where products moving downstream can be processed either in the designated assembly stations or by pulling together the work teams of adjacent stations. This scheduling problem requires determining the mode of operation of each task, and the subsequent scheduling that preserves the flowshop constraints. We show that the problem is ordinary NP‐complete and obtain an optimal solution using a dynamic programming algorithm with considerable computational requirements for medium and large problems. Then, we present a number of dynamic programming relaxations and analyze their worst‐case error performance. Finally, we present a polynomial time heuristic with worst‐case error performance comparable to that of the dynamic programming relaxations. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Minimizing sums and products of linear fractional functions over a polytope

In this paper, we develop efficient deterministic algorithms for globally minimizing the sum and the product of several linear fractional functions over a polytope. We will show that an elaborate implementation of an outer approximation algorithm applied to the master problem generated by a parametric transformation of the objective function serves as an efficient method for calculating global minima of these nonconvex minimization problems if the number of linear fractional terms in the objective function is less than four or five. It will be shown that the Charnes–Cooper transformation plays an essential role in solving these problems. Also a simple bounding technique using linear multiplicative programming techniques has remarkable effects on structured problems. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 583–596, 1999     

Models for multi-item continuous review inventory policies subject to constraints

Models are formulated for determining continuous review (Q, r) policies for a multiitem inventory subject to constraints. The objective function is the minimization of total time-weighted shortages. The constraints apply to inventory investment and reorder workload. The formulations are thus independent of the normal ordering, holding, and shortage costs. Two models are presented, each representing a convex programming problem. Lagrangian techniques are employed with the first, simplified model in which only the reorder points are optimized. In the second model both the reorder points and the reorder quantities are optimized utilizing penalty function methods. An example problem is solved for each model. The final section deals with the implementation of these models in very large inventory systems.     

二次型极小化问题带误差的迭代算法

证明了二次型极小化问题带误差的迭代算法的有效性,所得结果推广了关于二次型极小化问题迭代的收敛性。     

VNS和SA相结合的指挥控制资源部署

针对指挥控制资源部署问题,引入任务复杂度来定义决策实体的工作负载,并建立以最小化决策实体工作负载的均方根为目标的优化模型。针对传统的层次聚类法容易陷入局部最优,提出了一种变邻域搜索(Variable Neighborhood Search,VNS)和模拟退火(Simulated Annealing,SA)相结合的具有全局性的求解方法,使用VNS进行全局寻优,使用SA对VNS中的邻域进行局部寻优。最后通过一个联合作战案例的平台调度方案,验证了所提方法的优越性。