Some experiments in global optimization

When applied to a problem which has more than one local optimal solution, most nonlinear programming algorithms will terminate with the first local solution found. Several methods have been suggested for extending the search to find the global optimum of such a nonlinear program. In this report we present the results of some numerical experiments designed to compare the performance of various strategies for finding the global solution.     

Between a rock and a hard place: Europe in a post-INF world

The end of the 1987 Intermediate-range Nuclear Forces (INF) Treaty has the potential to plunge Europe and NATO into deep crisis. Russia’s continued violation coupled with the Donald J. Trump administration’s desire to balance against Moscow and Beijing could force a new missile debate on Europeans. Even though Washington is trying to assuage its allies, the specter of another round of INF missile deployments to Europe is not unrealistic. Meanwhile, NATO’s European members face a dilemma. Some want NATO to resolutely push back against Russia. Others want to avoid a new deployment debate, at almost all costs. The Kremlin will use these cleavages to weaken NATO. If not carefully handled, NATO’s response to the Russian missile buildup could lead to domestic turmoil in a number of European states and render the alliance ineffective for a prolonged period. Europeans need to act now and voice their preferences in the military and diplomatic domains. A number of different military options are available, below the level of deploying new INF missiles in Europe. However, Europeans need to consider trade-offs regarding crisis and arms-race stability. At the same time, it will be up to European capitals to conceptualize a new arms-control framework for the post-INF world, one that takes into account today’s geopolitical realities and the entanglement of modern conventional and nuclear forces. Given the Trump administration’s loathing of arms control, concepts of mutual restraint may well have to wait for the next US administration. In any case, that should not stop Europeans from taking on more responsibility for their own security.     

Random disambiguation paths for traversing a mapped hazard field

We consider the problem of safely and swiftly navigating through a spatial arrangement of potential hazard detections in which each detection has associated with it a probability that the detection is indeed a true hazard. When in close proximity to a detection, we assume the ability—for a cost—to determine whether or not the hazard is real. Our approach to this problem involves a new object, the random disambiguation path (RDP), which is a curve‐valued random variable parametrized by a binary tree with particular properties. We prove an admissibility result showing that there is positive probability that the use of an RDP reduces the expected traversal length compared to the conventional shortest zero‐risk path, and we introduce a practically computable additive‐constant approximation to the optimal RDP. The theoretical considerations are complemented by simulation and example. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Log‐concave and concave distributions in reliability

Nonparametric classes of life distributions are usually based on the pattern of aging in some sense. The common parametric families of life distributions also feature monotone aging. In this paper we consider the class of log‐concave distributions and the subclass of concave distributions. The work is motivated by the fact that most of the common parametric models of life distributions (including Weibull, Gamma, log‐normal, Pareto, and Gompertz distributions) are log‐concave, while the remaining life of maintained and old units tend to have a concave distribution. The classes of concave and log‐concave distributions do not feature monotone aging. Nevertheless, these two classes are shown to have several interesting and useful properties. We examine the closure of these classes under a number of reliability operations, and provide sharp reliability bounds for nonmaintained and maintained units having life distribution belonging to these classes. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 419–433, 1999     

Screening multi-dimensional heterogeneous populations for infectious diseases under scarce testing resources,with application to COVID-19

Testing provides essential information for managing infectious disease outbreaks, such as the COVID-19 pandemic. When testing resources are scarce, an important managerial decision is who to test. This decision is compounded by the fact that potential testing subjects are heterogeneous in multiple dimensions that are important to consider, including their likelihood of being disease-positive, and how much potential harm would be averted through testing and the subsequent interventions. To increase testing coverage, pooled testing can be utilized, but this comes at a cost of increased false-negatives when the test is imperfect. Then, the decision problem is to partition the heterogeneous testing population into three mutually exclusive sets: those to be individually tested, those to be pool tested, and those not to be tested. Additionally, the subjects to be pool tested must be further partitioned into testing pools, potentially containing different numbers of subjects. The objectives include the minimization of harm (through detection and mitigation) or maximization of testing coverage. We develop data-driven optimization models and algorithms to design pooled testing strategies, and show, via a COVID-19 contact tracing case study, that the proposed testing strategies can substantially outperform the current practice used for COVID-19 contact tracing (individually testing those contacts with symptoms). Our results demonstrate the substantial benefits of optimizing the testing design, while considering the multiple dimensions of population heterogeneity and the limited testing capacity.     

New purification algorithms for linear programming

Two new algorithms are presented for solving linear programs which employ the opposite-sign property defined for a set of vectors in m space. The first algorithm begins with a strictly positive feasible solution and purifies it to a basic feasible solution having objective function value no less under maximization. If this solution is not optimal, then it is drawn back into the interior with the same objective function value, and a restart begins. The second algorithm can begin with any arbitrary feasible point. If necessary this point is purified to a basic feasible solution by dual-feasibility–seeking directions. Should dual feasibility be attained, then a duality value interval is available for estimating the unknown objective function value. If at this juncture the working basis is not primal feasible, then further purification steps are taken tending to increase the current objective function value, while simultaneously seeking another dual feasible solution. Both algorithms terminate with an optimal basic solution in a finite number of steps.     

Humanitarian response to hurricane disasters: Coordinating flood‐risk mitigation with fundraising and relief operations

To alleviate flooding, caused by hurricanes, governments build structural barriers called levees. In addition, relief providers such as the nongovernmental organizations and charities raise funds, and procure and deliver supplies (food, water, and medicines) for humanitarian relief. The strategy for managing disasters must, therefore, weigh the costs and benefits of building levees as well as procuring and delivering supplies. We use a three‐stage decision making framework to study how the investment in levee capacity can be integrated with supply procurements, fundraising, and rapid response. One of our major findings is that a large fundraising cost discourages postdisaster funding, implying relatively large investments in levee and prepositioned supplies. That notwithstanding, a large social value (of saving life) can tilt the balance in favor of postdisaster funding. If the levee capacity increases, funding for predisaster procurement is reduced without affecting postdisaster funding. For a sufficiently large increase in capacity, however, postdisaster response becomes superfluous. We also find that hurricane uncertainty motivates levees with large capacity. In contrast, levee‐failures motivate levees with small capacity.     

The road not taken: Conflict termination and guerrillaism in the American Civil War

Irrespective our views on the rationality of our opponent's continuing to conduct operations against us, unless utterly extirpated, he retains a vote on when and how conflict will end. This is because war is about power — compelling another actor to do something he would not otherwise do, or to cease doing something he would otherwise prefer to do. In planning for conflict termination we should account for the peculiarities of opponents who may decide not to quit when we have beat them fair and square. We do not desire that they cease conventional fighting, but that they cease fighting altogether.     

A note on optimal pricing for finite capacity queueing systems with multiple customer classes

This article investigates optimal static prices for a finite capacity queueing system serving customers from different classes. We first show that the original multi‐class formulation in which the price for each class is a decision variable can be reformulated as a single dimensional problem with the total load as the decision variable. Using this alternative formulation, we prove an upper bound for the optimal arrival rates for a fairly large class of queueing systems and provide sufficient conditions that ensure the existence of a unique optimal arrival rate vector. We show that these conditions hold for M/M/1/m and M/G/s/s systems and prove structural results on the relationships between the optimal arrival rates and system capacity. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008