•Surveys literature starting from 1950s era military applications.•Covers interdiction problems dealing with asymmetric information and stochasticity.•Focuses on mathematical programming based ...analyses of interdiction problems.
This paper discusses the development of interdiction optimization models and algorithms, with an emphasis on mathematical programming techniques and future research challenges in the field. After presenting basic interdiction concepts and notation, we recount the motivation and models behind founding research in the network interdiction field. Next, we examine some of the most common means of solving interdiction problems, focusing on dualization models and extended formulations solvable by row-generation techniques. We then examine contemporary interdiction problems involving incomplete information, information asymmetry, stochasticity, and dynamic play. We conclude by discussing several emerging applications in the field of network interdiction.
The effective radiative forcing, which includes the instantaneous forcing plus adjustments from the atmosphere and surface, has emerged as the key metric of evaluating human and natural influence on ...the climate. We evaluate effective radiative forcing and adjustments in 17 contemporary climate models that are participating in the Coupled Model Intercomparison Project (CMIP6) and have contributed to the Radiative Forcing Model Intercomparison Project (RFMIP). Present-day (2014) global-mean anthropogenic forcing relative to pre-industrial (1850) levels from climate models stands at 2.00 (±0.23) W/sq. m, comprised of 1.81 (±0.09) W/sq. m from CO2, 1.08 (± 0.21) W/sq. m from other well-mixed greenhouse gases, −1.01 (± 0.23) W/sq. m from aerosols and −0.09 (±0.13) W/sq. m from land use change. Quoted uncertainties are 1 standard deviation across model best estimates, and 90 % confidence in the reported forcings, due to internal variability, is typically within 0.1 W/sq. m. The majority of the remaining 0.21 W/sq. m is likely to be from ozone. In most cases, the largest contributors to the spread in effective radiative forcing (ERF) is from the instantaneous radiative forcing (IRF) and from cloud responses, particularly aerosol–cloud interactions to aerosol forcing. As determined in previous studies, cancellation of tropospheric and surface adjustments means that the stratospherically adjusted radiative forcing is approximately equal to ERF for greenhouse gas forcing but not for aerosols, and consequentially, not for the anthropogenic total. The spread of aerosol forcing ranges from −0.63 to −1.37 W/sq. m, exhibiting a less negative mean and narrower range compared to 10 CMIP5 models. The spread in 4×CO2 forcing has also narrowed in CMIP6 compared to 13 CMIP5 models. Aerosol forcing is uncorrelated with climate sensitivity. Therefore, there is no evidence to suggest that the increasing spread in climate sensitivity in CMIP6 models, particularly related to high-sensitivity models, is a consequence of a stronger negative present-day aerosol forcing and little evidence that modelling groups are systematically tuning climate sensitivity or aerosol forcing to recreate observed historical warming.
We examine bilevel mixed-integer programs whose constraints and objective functions depend on both upper- and lower-level variables. The class of problems we consider allows for nonlinear terms to ...appear in both the constraints and the objective functions, requires all upper-level variables to be integer, and allows a subset of the lower-level variables to be integer. This class of bilevel problems is difficult to solve because the upper-level feasible region is defined in part by optimality conditions governing the lower-level variables, which are difficult to characterize because of the nonconvexity of the follower problem. We propose an exact finite algorithm for these problems based on an optimal-value-function reformulation. We demonstrate how this algorithm can be tailored to accommodate either optimistic or pessimistic assumptions on the follower behavior. Computational experiments demonstrate that our approach outperforms a state-of-the-art algorithm for solving bilevel mixed-integer linear programs.
We consider a special class of two-stage stochastic integer programming problems with binary variables appearing in both stages. The class of problems we consider constrains the second-stage ...variables to belong to the intersection of sets corresponding to first-stage binary variables that equal one. Our approach seeks to uncover strong dual formulations to the second-stage problems by transforming them into dynamic programming (DP) problems parameterized by first-stage variables. We demonstrate how these DPs can be formed by use of binary decision diagrams, which then yield traditional Benders inequalities that can be strengthened based on observations regarding the structure of the underlying DPs. We demonstrate the efficacy of our approach on a set of stochastic traveling salesman problems.
•This research focuses on a variant of shortest-path interdiction problems.•The interdictor may not have perfect information on data.•A bounding-and-partitioning approach can solve expected-value ...interdiction problems.•Computation time depends mostly on the number of uncertain arcs.
We study a shortest-path interdiction problem in which the interdictor acts first to lengthen a subset of arcs, and an evader acts second to select a shortest path across the network. In this problem, the cost for an evader’s arc consists of a base cost if the arc is not interdicted, plus an additional cost that is incurred if the arc is interdicted. The interdictor is not aware of the base costs when the interdiction action is taken, but does know that the base cost values are uniformly distributed within given (arc-specific) intervals. The evader, on the other hand, observes the exact value of the base costs, plus the additional costs due to interdiction actions. The interdictor’s problem is thus to maximize the expected minimum cost attainable by the evader. We provide a partitioning algorithm for computing an exact optimal solution to this problem, leveraging bounds gleaned from Jensen’s inequality as proposed in an earlier study on a maximum-flow interdiction problem. We also provide several algorithmic strategies for accelerating the convergence of the algorithm and demonstrate their effectiveness on randomly generated instances.
While previous studies have suggested a substantial role of ozone‐depleting substances (ODSs) in historical climate change, their relative contribution to historical anthropogenic warming has not ...been quantified before. Analyzing all‐but‐one‐forcing, 20‐member ensembles of historical simulations with a state‐of‐the‐art Earth System Model, we find that over the 1955–2005 period ODSs are responsible for 30% of global warming, 37% of Arctic warming, and 33% of summertime Arctic sea ice loss. Effective Radiative Forcing (ERF) calculations reveal that the global warming response to ODSs per unit of ERF is about 20% larger than for CO2, which may be due to stronger feedbacks and the difference in temporal evolution with ODSs having leveled off and CO2 still increasing in 2005. While the response to both peaks in the Arctic, the ODS ERF opposes Arctic amplification more than the CO2 ERF. Our findings highlight the importance of the Montreal Protocol for mitigating future climate change.
Plain Language Summary
Ozone‐depleting substances (ODSs) are chemicals developed in the 1920s and 1930s for use in spray cans, refrigerators and plastic foams. Their commercial use increased rapidly in the 1950s and 1960s, but their phase out is underway since the signing of the Montreal Protocol in the 1987, following the identification of their devastating impact on the stratospheric ozone layer. It is well known that ODSs are powerful greenhouse gases, with the second largest warming effect between 1955 and 2005. However, their relative contribution to past global warming has not been quantified previously using comprehensive climate models. Here we show that ODSs were responsible for roughly a third of late 20th Century global warming, Arctic warming and Arctic sea ice decline. In addition, we find that the impact of ODSs on global temperatures is about 20% larger than expected based on the impacts they have on the radiative balance. The impacts of ODSs peak in the Arctic, while their radiative forcing peaks in the tropics, and thus opposes Arctic warming amplification. These findings enhance our understanding of drivers of past climate change, and highlight the importance of the Montreal Protocol for future climate change mitigation.
Key Points
Between 1955 and 2005, global warming from ozone‐depleting substances (ODSs) was more than half of that due to CO2, and about one third of total anthropogenic warming
ODSs have been about 20% more effective than CO2 at causing global warming per unit radiative forcing
ODS warming peaks in the Arctic and is 66% of that due to CO2, while their Effective Radiative Forcing (ERF) opposes Arctic amplification more than the CO2 ERF
This paper examines a class of three-stage sequential defender-attacker-defender problems. In these problems the defender first selects a subset of assets to protect, the attacker next damages a ...subset of unprotected assets in the “interdiction” stage, after which the defender optimizes a “recourse” problem over the surviving assets. These problems are notoriously difficult to optimize, and almost always require the recourse problem to be a convex optimization problem. Our contribution is a new approach to solving defender-attacker-defender problems. We require all variables in the first two stages to be binary-valued, but allow the recourse problem to take any form. The proposed framework focuses on solving the interdiction problem by restricting the defender to select a recourse decision from a sample of feasible vectors. The algorithm then iteratively refines the sample to force finite convergence to an optimal solution. We demonstrate that our algorithm not only solves interdiction problems involving NP-hard recourse problems within reasonable computational limits, but it also solves shortest path fortification and interdiction problems more efficiently than state-of-the-art algorithms tailored for that problem, finding optimal solutions to real-road networks having up to 300,000 nodes and over 1,000,000 arcs.
Activity since 1995 at Soufrière Hills Volcano (SHV), Montserrat has alternated between andesite lava extrusion and quiescence, which are well correlated with seismicity and ground deformation ...cycles. Large variations in SO2 flux do not correlate with these alternations, but high and low HCl/SO2 characterize lava dome extrusion and quiescent periods respectively. Since lava extrusion ceased (February 2010) steady SO2 emissions have continued at an average rate of 374 tonnes/day (± 140 t/d), and incandescent fumaroles (temperatures up to 610oC) on the dome have not changed position or cooled. Occasional short bursts (over several hours) of higher (∼ 10x) SO2 flux have been accompanied by swarms of volcano‐tectonic earthquakes. Strain data from these bursts indicate activation of the magma system to depths up to 10 km. SO2 emissions since 1995 greatly exceed the amounts that could be derived from 1.1 km3 of erupted andesite, and indicating extensive partitioning of sulfur into a vapour phase, as well as efficient decoupling and outgassing of sulfur‐rich gases from the magma. These observations are consistent with a vertically extensive, crustal magmatic mush beneath SHV. Three states of the magmatic system are postulated to control degassing. During dormant periods (103 to 104 years) magmatic vapour and melts separate as layers from the mush and decouple from each other. In periods of unrest (years) without eruption, melt and fluid layers become unstable, ascend and can amalgamate. Major destabilization of the mush system leads to eruption, characterized by magma mixing and release of volatiles with different ages, compositions and sources.
Key Points:
SO2 fluxes from the Soufriere Hills volcano are decoupled from magma
SO2 gas is sourced at depth and emerges in pulses associated with seismicity
Magma systemssegregate fluids and melt then destablize to erupt
We address the problem of maximizing the lifetime of a wireless sensor network with energy-constrained sensors and a mobile sink. The sink travels among discrete locations to gather information from ...all the sensors. Data can be relayed among sensors and then to the sink location, as long as the sensors and the sink are within a certain threshold distance of each other. However, sending information along a data link consumes energy at both the sender and the receiver nodes. A vital problem that arises is to prescribe sink stop durations and data flow patterns that maximally prolong the life of the network, defined as the amount of time until any node exhausts its energy. We describe linear programming and column generation approaches for this problem, and also for a version in which data can be delayed in its transmission to the sink. Our column generation approach exploits special structures of the linear programming formulations so that all subproblems are shortest path problems with non-negative costs. Computational results demonstrate the efficiency of the proposed algorithms.
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