Approximating nondominated sets in continuous multiobjective optimization problems

Many important problems in Operations Research and Statistics require the computation of nondominated (or Pareto or efficient) sets. This task may be currently undertaken efficiently for discrete sets of alternatives or for continuous sets under special and fairly tight structural conditions. Under more general continuous settings, parametric characterisations of the nondominated set, for example through convex combinations of the objective functions or ε‐constrained problems, or discretizations‐based approaches, pose several problems. In this paper, the lack of a general approach to approximate the nondominated set in continuous multiobjective problems is addressed. Our simulation‐based procedure only requires to sample from the set of alternatives and check whether an alternative dominates another. Stopping rules, efficient sampling schemes, and procedures to check for dominance are proposed. A continuous approximation to the nondominated set is obtained by fitting a surface through the points of a discrete approximation, using a local (robust) regression method. Other actions like clustering and projecting points onto the frontier are required in nonconvex feasible regions and nonconnected Pareto sets. In a sense, our method may be seen as an evolutionary algorithm with a variable population size. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

A generalization of the weighted set covering problem

We study a generalization of the weighted set covering problem where every element needs to be covered multiple times. When no set contains more than two elements, we can solve the problem in polynomial time by solving a corresponding weighted perfect b‐matching problem. In general, we may use a polynomial‐time greedy heuristic similar to the one for the classical weighted set covering problem studied by D.S. Johnson [Approximation algorithms for combinatorial problems, J Comput Syst Sci 9 (1974), 256–278], L. Lovasz [On the ratio of optimal integral and fractional covers, Discrete Math 13 (1975), 383–390], and V. Chvatal [A greedy heuristic for the set‐covering problem, Math Oper Res 4(3) (1979), 233–235] to get an approximate solution for the problem. We find a worst‐case bound for the heuristic similar to that for the classical problem. In addition, we introduce a general type of probability distribution for the population of the problem instances and prove that the greedy heuristic is asymptotically optimal for instances drawn from such a distribution. We also conduct computational studies to compare solutions resulting from running the heuristic and from running the commercial integer programming solver CPLEX on problem instances drawn from a more specific type of distribution. The results clearly exemplify benefits of using the greedy heuristic when problem instances are large. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Optimal power control in a wireless network using a model with stochastic link coefficients

This paper addresses optimal power allocation in a wireless communication network under uncertainty. The paper introduces a framework for optimal transmit power allocation in a wireless network where both the useful and interference coefficients are random. The new approach to power control is based on a stochastic programming formulation with probabilistic SIR constraints. This allows to state the power allocation problem as a convex optimization problem assuming normally or log‐normally distributed communication link coefficients. Numerical examples illustrate the performance of the optimal stochastic power allocation. A distributed algorithm for the decentralized solution of the stochastic power allocation problem is discussed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

编队协同反导决策方案优选

为了充分地调度好编队全部的抗导资源,实现抗导弹群的成功概率最大,在利用随机服务系统理论对编队协同反导决策方案各指标值进行计算的基础上,将"模糊优选理论"与"协同学原理"有机地结合起来,求解了在反舰导弹到达强度与舰空导弹的单发杀伤概率在不同值的情况下,编队协同反导决策方案的隶属度,为编队指挥员进行反导决策方案的优选提供了科学依据。     

随机共振技术在微弱舰船轴频电场信号检测中的应用

针对在强背景噪声中检测微弱舰船轴频电场信号的问题,提出了基于随机共振技术的检测方法.首先,介绍了随机共振利用噪声增强信号能量从而提高信噪比的基本原理,并在此基础上给出了利用随机共振检测微弱周期信号的模型.然后,将低信噪比的船模轴频电场测量数据输入到检测模型并对输出信号作功率谱分析,结果表明:随机共振技术能十分有效地从复杂背景噪声中检测出微弱舰船轴频电场信号,在微弱信号处理领域相比传统方法具有很大的优势.最后,结合检测实例,初步分析了系统参数对随机共振系统输出信号频谱分布的影响,为随机共振技术的进一步工程应用打下了良好的基础.     

Modeling the operation of multireservoir systems using decomposition and stochastic dynamic programming

Stochastic dynamic programming models are attractive for multireservoir control problems because they allow non‐linear features to be incorporated and changes in hydrological conditions to be modeled as Markov processes. However, with the exception of the simplest cases, these models are computationally intractable because of the high dimension of the state and action spaces involved. This paper proposes a new method of determining an operating policy for a multireservoir control problem that uses stochastic dynamic programming, but is practical for systems with many reservoirs. Decomposition is first used to reduce the problem to a number of independent subproblems. Each subproblem is formulated as a low‐dimensional stochastic dynamic program and solved to determine the operating policy for one of the reservoirs in the system. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

基于随机加权法的BAYES精度评定

从工程应用的角度出发 ,在极小现场子样条件下 ,讨论了如何利用验前信息与现场子样来对导弹的命中精度进行评定 ,将随机加权法与BAYES方法结合起来 ,提出了基于随机加权法的BAYES精度评定方法 ,并通过算例证实了方法的正确性     

Selecting T for a periodic review inventory model with staggered deliveries

Consider a single‐item, periodic review, infinite‐horizon, undiscounted, inventory model with stochastic demands, proportional holding and shortage costs, and full backlogging. Orders can arrive in every period, and the cost of receiving them is negligible (as in a JIT setting). Every T periods, one audits the current stock level and decides on deliveries for the next T periods, thus incurring a fixed audit cost and—when one schedules deliveries—a fixed order cost. The problem is to find a review period T and an ordering policy that satisfy the average cost criterion. The current article extends an earlier treatment of this problem, which assumed that the fixed order cost is automatically incurred once every T periods. We characterize an optimal ordering policy when T is fixed, prove that an optimal review period T** exists, and develop a global search algorithm for its computation. We also study the behavior of four approximations to T** based on the assumption that the fixed order cost is incurred during every cycle. Analytic results from a companion article (where μ/σ is large) and extensive computational experiments with normal and gamma demand test problems suggest these approximations and associated heuristic policies perform well when μ/σ ≥ 2. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 329–352, 2000     

On lifetimes in random environments

For a component operating in random environment, whose hazard rate is assumed to be the realization of a suitable increasing stochastic process, conditions are found such that its lifetime is increasing in likelihood ratio (ILR). For the lifetimes of two components of the same kind some comparisons based on partial stochastic orders are presented. Some applications to the case of repairable components are finally provided. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 365–375, 1998     

采用SHLPN分析特种车载总线网络可靠性

针对特种车载总线网络可靠性难以评估的问题,提出采用随机高级Petri网(Stochastic High-level Petri Net,SHLPN)分析特种车载总线网络可靠性。深入分析特种车载总线网络故障模式的基础上,将其等效为冗余总线控制器模块、远程终端模块和冗余链路模块的串联,分别建立各个模块的SHLPN模型,得到了各个模块的稳态可用度计算式,进而综合得到特种车载总线网络的稳态可用度计算式。最后,实例分析验证了所提方法的有效性。