Beyond Chance-Constrained Convex Mixed-Integer Optimization: A Generalized Calafiore-Campi Algorithm and the notion of SS-optimization

The scenario approach developed by Calafiore and Campi to attack chance-constrained convex programs utilizes random sampling on the uncertainty parameter to substitute the original problem with a representative continuous convex optimization with $N$ convex constraints which is a relaxation of the original. Calafiore and Campi provided an explicit estimate on the size $N$ of the sampling relaxation to yield high-likelihood feasible solutions of the chance-constrained problem. They measured the probability of the original constraints to be violated by the random optimal solution from the relaxation of size $N$. This paper has two main contributions. First, we present a generalization of the Calafiore-Campi results to both integer and mixed-integer variables. In fact, we demonstrate that their sampling estimates work naturally for variables restricted to some subset $S$ of $\mathbb R^d$. The key elements are generalizations of Helly's theorem where the convex sets are required to intersect $S \subset \mathbb R^d$. The size of samples in both algorithms will be directly determined by the $S$-Helly numbers. Motivated by the first half of the paper, for any subset $S \subset \mathbb R^d$, we introduce the notion of an $S$-optimization problem, where the variables take on values over $S$. It generalizes continuous, integer, and mixed-integer optimization. We illustrate with examples the expressive power of $S$-optimization to capture sophisticated combinatorial optimization problems with difficult modular constraints. We reinforce the evidence that $S$-optimization is "the right concept" by showing that the well-known randomized sampling algorithm of K. Clarkson for low-dimensional convex optimization problems can be extended to work with variables taking values over $S$.Comment: 16 pages, 0 figures. This paper has been revised and split into two parts. This version is the second part of the original paper. The first part of the original paper is arXiv:1508.02380 (the original article contained 24 pages, 3 figures

Deep XMM-Newton Spectroscopic and Timing Observations of the Isolated Radio Millisecond Pulsar PSR J0030+0451

We present deep XMM-Newton EPIC spectroscopic and timing X-ray observations of the nearby solitary radio millisecond pulsar, PSR J0030+0451. Its emission spectrum in the 0.1-10 keV range is found to be remarkably similar to that of the nearest and best studied millisecond pulsar, PSR J0437-4715, being well described by a predominantly thermal two-temperature model plus a faint hard tail evident above ~2 keV. The pulsed emission in the 0.3-2 keV band is characterized by two broad pulses with pulsed fraction ~60-70%, consistent with a mostly thermal origin of the X-rays only if the surface polar cap radiation is from a light-element atmosphere. Modeling of the thermal pulses permits us to place constraints on the neutron star radius of R>10.7 (95% confidence) and R>10.4 km (at 99.9% confidence) for M=1.4 M_sun.Comment: 8 pages, 7 figures; accepted for publication in The Astrophysical Journa

The value of information in biosecurity risk-benefit assessment: an application to red imported fire ants

Policy makers are confronted daily with uncertainty, especially in complex areas like biosecurity. One way to improve decision-making and reduce uncertainties is to collect more information. Information is costly – whether the value of improved decision-making justifies the cost is a fundamental question facing policy makers. This paper addresses that question by making three practical contributions for binary choices (such as whether to implement or forego a particular policy). First, it analyses the determinants of the value of information, and how that value changes with features of the problem. Second, it uses this analysis to derive simple rules of thumb which provide upper bounds on the value of additional information. Third, it provides a practical application of the value of information in deciding whether to attempt eradication of the red imported fire ant.Environmental Economics and Policy,

SOLVING FIRE DEPARTMENT STATION LOCATION PROBLEM USING MODIFIED BINARY GENETIC ALGORITHM: A CASE STUDY OF SAMSUN IN TURKEY

Fire and traffic accident are the most common problem in our daily lives. Fire department location for the purpose of easy response and recovery is a significant problem today. The best location of a fire department station determines the rate of recovery of many injured people after traffic accident, fire outbreak, and so on. In this paper, we considered the best location of fire stations. In addition, we also considered where the station is setup. Surveying problem is modeled as a mixed integer programming. It is solved by modified binary genetic algorithm, coding with GAMS. Modified binary GA is different from known GA with respect to binary decision variables. Due to this problem, initial value of the objective function was obtained from known GA. Then finally, the best result was achieved from binary GA

SOLVING FIRE DEPARTMENT STATION LOCATION PROBLEM USING MODIFIED BINARY GENETIC ALGORITHM: A CASE STUDY OF SAMSUN IN TURKEY

Fire and traffic accident are the most common problem in our daily lives. Fire department location for the purpose of easy response and recovery is a significant problem today. The best location of a fire department station determines the rate of recovery of many injured people after traffic accident, fire outbreak, and so on. In this paper, we considered the best location of fire stations. In addition, we also considered where the station is setup. Surveying problem is modeled as a mixed integer programming. It is solved by modified binary genetic algorithm, coding with GAMS. Modified binary GA is different from known GA with respect to binary decision variables. Due to this problem, initial value of the objective function was obtained from known GA. Then finally, the best result was achieved from binary GA

Generation of Particles and Seeding

One of the most important elements in laser velocimetry, yet the most neglected, is the small particle embedded in the flow field that scatters the light necessary to make velocity measurements. An attempt to remove the confusion in choosing a seeding method by assessing many of the techniques currently used is presented. Their characteristics and typical limitations imposed by various applications are outlined. The ramifications of these methods on measurement accuracy are addressed

Orbital transfer vehicle concept definition and system analysis study. Volume 1A: Executive summary. Phase 2

The objectives of the Phase 2 study were to improve the orbit transfer vehicle (OTV) concept definition by focusing on the following issues: the impact of mission requirements on OTV system design; OTV basing concepts on the Space Shuttle, separate platforms, and/or remote locations; cost reduction of an OTV program to improve its economic benefits and support its acquisition. The OTV mission scenario includes a wide range of missions the main drivers of which are manned GEO servicing, mid-inclination/polar DOD, and lunar/planetary projects. A mission model is presented which includes the type and number of missions per year and the estimated propellant requirements. To accomplish the missions, many OTV concepts were defined including ground-based OTVs launched either in the STS orbiter, the aft cargo carrier, or a heavy lift launch vehicle, and a space-based OTV. System and program trade studies were conducted using performance, cost, safety/risk, and operations/growth criteria. The study shows that mission requirements and substantial economic benefits justify a reusable, cryogenic (H2/O2) space-based OTV. Such a system would not be subjected to Earth-to-orbit launch loads and would not be constained in size or weight. Safety is enhanced by the fact that the system components are launched unfueled. Its inherent reusability and ability to be refueled in space make the space-based OTV very economical to operate