A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs

Bilevel optimization problems are very challenging optimization models arising in many important practical contexts, including pricing mechanisms in the energy sector, airline and telecommunication industry, transportation networks, critical infrastructure defense, and machine learning. In this paper, we consider bilevel programs with continuous and discrete variables at both levels, with linear objectives and constraints (continuous upper level variables, if any, must not appear in the lower level problem). We propose a general-purpose branch-and-cut exact solution method based on several new classes of valid inequalities, which also exploits a very effective bilevel-specific preprocessing procedure. An extensive computational study is presented to evaluate the performance of various solution methods on a common testbed of more than 800 instances from the literature and 60 randomly generated instances. Our new algorithm consistently outperforms (often by a large margin) alternative state-of-the-art methods from the literature, including methods exploiting problem-specific information for special instance classes. In particular, it solves to optimality more than 300 previously unsolved instances from the literature. To foster research on this challenging topic, our solver is made publicly available online

Melt in the Greenland EastGRIP ice core reveals Holocene warm events

We present a record of melt events obtained from the East Greenland Ice Core Project (EastGRIP) ice core in central northeastern Greenland, covering the largest part of the Holocene. The data were acquired visually using an optical dark-field line scanner. We detect and describe melt layers and lenses, seen as bubble-free layers and lenses, throughout the ice above the bubble–clathrate transition. This transition is located at 1150 m depth in the EastGRIP ice core, corresponding to an age of 9720 years b2k. We define the brittle zone in the EastGRIP ice core as that from 650 to 950 m depth, where we count on average more than three core breaks per meter. We analyze melt layer thicknesses, correct for ice thinning, and account for missing layers due to core breaks. Our record of melt events shows a large, distinct peak around 1014 years b2k (986 CE) and a broad peak around 7000 years b2k, corresponding to the Holocene Climatic Optimum. In total, we can identify approximately 831 mm of melt (corrected for thinning) over the past 10 000 years. We find that the melt event from 986 CE is most likely a large rain event similar to that from 2012 CE, and that these two events are unprecedented throughout the Holocene. We also compare the most recent 2500 years to a tree ring composite and find an overlap between melt events and tree ring anomalies indicating warm summers. Considering the ice dynamics of the EastGRIP site resulting from the flow of the Northeast Greenland Ice Stream (NEGIS), we find that summer temperatures must have been at least 3 ± 0.6 ∘C warmer during the Early Holocene compared to today

Ice-core data used for the construction of the Greenland Ice-Core Chronology 2005 and 2021 (GICC05 and GICC21)

We here describe, document, and make available a wide range of data sets used for annual-layer identification in ice cores from DYE-3, GRIP, NGRIP, NEEM, and EGRIP. The data stem from detailed measurements performed both on the main deep cores and shallow cores over more than 40 years using many different setups developed by research groups in several countries and comprise both discrete measurements from cut ice samples and continuous-flow analysis data. The data series were used for counting annual layers 60 000 years back in time during the construction of the Greenland Ice-Core Chronology 2005 (GICC05) and/or the revised GICC21, which currently only reaches 3800 years back. Now that the underlying data are made available (listed in Table 1) we also release the individual annual-layer positions of the GICC05 timescale which are based on these data sets. We hope that the release of the data sets will stimulate further studies of the past climate taking advantage of these highly resolved data series covering a large part of the interior of the Greenland ice sheet

A first chronology for the East Greenland Ice-core Project (EGRIP) over the Holocene and last glacial termination

This paper provides the first chronology for the deep ice core from the East Greenland Ice-core Project (EGRIP) over the Holocene and the late last glacial period. We rely mainly on volcanic events and common peak patterns recorded by dielectric profiling (DEP) and electrical conductivity measurement (ECM) for the synchronization between the EGRIP, North Greenland Eemian Ice Drilling (NEEM) and North Greenland Ice Core Project (NGRIP) ice cores in Greenland. We transfer the annual-layer-counted Greenland Ice Core Chronology 2005 (GICC05) from the NGRIP core to the EGRIP ice core by means of 381 match points, typically spaced less than 50 years apart. The NEEM ice core has previously been dated in a similar way and is only included to support the match-point identification. We name our EGRIP timescale GICC05-EGRIP-1. Over the uppermost 1383.84 m, we establish a depth–age relationship dating back to 14 967 years b2k (years before the year 2000 CE). Tephra horizons provide an independent validation of our match points. In addition, we compare the ratio of the annual layer thickness between ice cores in between the match points to assess our results in view of the different ice-flow patterns and accumulation regimes of the different periods and geographical regions. For the next years, this initial timescale will be the basis for climatic reconstructions from EGRIP high-resolution proxy data sets, e.g. stable water isotopes, chemical impurity or dust records

Interdiction Games and Monotonicity, with Application to Knapsack Problems

Two-person interdiction games represent an important modeling concept for applications in marketing, defending critical infrastructure, stopping nuclear weapons projects, or preventing drug smuggling. We present an exact branch-and-cut algorithm for interdiction games under the assumption that feasible solutions of the follower problem satisfy a certain monotonicity property. Prominent examples from the literature that fall into this category are knapsack interdiction, matching interdiction, and packing interdiction problems. We also show how practically relevant interdiction variants of facility location and prize-collecting problems can be modeled in our setting. Our branch-and-cut algorithm uses a solution scheme akin to Benders decomposition based on a family of so-called interdiction cuts. We present modified and lifted versions of these cuts along with exact and heuristic procedures for the separation of interdiction cuts and heuristic separation procedures for the other versions. In addition, we derive further valid inequalities and present a new heuristic procedure. We computationally evaluate the proposed algorithm on a benchmark of 360 knapsack interdiction instances from literature, including 27 instances for which the optimal solution was not known. Our approach is able to solve each of them to optimality within about one minute of computing time on a standard PC (in most cases, within just seconds), and it is up to some orders of magnitude faster than any previous approach from the literature. To further assess the effectiveness of our branch-and-cut algorithm, an additional computational study is performed on 144 randomly generated instances based on 0/1 multidimensional knapsack problems

A dual-ascent-based branch-and-bound framework for the prize-collecting Steiner tree and related problems

We present a branch-and-bound (B&B) framework for the asymmetric prize-collecting Steiner tree problem (APCSTP). Several well-known network design problems can be transformed to the APCSTP, including the Steiner tree problem (STP), prize-collecting Steiner tree problem (PCSTP), maximum-weight connected subgraph problem (MWCS), and node-weighted Steiner tree problem (NWSTP). The main component of our framework is a new dual ascent algorithm for the rooted APCSTP, which generalizes Wong’s dual ascent algorithm for the Steiner arborescence problem. The lower bounds and dual information obtained from the algorithm are exploited within powerful bound-based reduction tests and for guiding primal heuristics. The framework is complemented by additional alternative-based reduction tests. Extensive computational results on benchmark instances for the PCSTP, MWCS, and NWSTP indicate the framework’s effectiveness, as most instances from literature are solved to optimality within seconds, including most of the (previously unsolved) largest instances from the recent DIMACS Challenge on Steiner trees. Moreover, results on new asymmetric instances for the APCSTP are reported. Since the addressed network design problems are frequently used for modeling various real-world applications (e.g., in bioinformatics), the implementation of the presented B&B framework has been made publicly available

Synchronizing ice-core and U ∕ Th timescales in the Last Glacial Maximum using Hulu Cave ¹⁴C and new ¹⁰Be measurements from Greenland and Antarctica

Between 15 and 27 kyr b2k (thousands of years before 2000 CE) during the last glacial, Greenland experienced a prolonged cold stadial phase, interrupted by two short-lived warm interstadials. Greenland ice-core calcium data show two periods, preceding the interstadials, of anomalously high atmospheric dust loading, the origin of which is not well understood. At approximately the same time as the Greenland dust peaks, the Chinese Hulu Cave speleothems exhibit a climatic signal suggested to be a response to Heinrich Event 2, a period of enhanced ice-rafted debris deposition in the North Atlantic. In the climatic signal of Antarctic ice cores, moreover, a relative warming occurs between 23 and 24.5 kyr b2k that is generally interpreted as a counterpart to a cool climate phase in the Northern Hemisphere. Proposed centennial-scale offsets between the polar ice-core timescales and the speleothem timescale hamper the precise reconstruction of the global sequence of these climatic events. Here, we examine two new 10Be datasets from Greenland and Antarctic ice cores to test the agreement between different timescales, by taking advantage of the globally synchronous cosmogenic radionuclide production rates. Evidence of an event similar to the Maunder Solar Minimum is found in the new 10Be datasets, supported by lower-resolution radionuclide data from Greenland and 14C in the Hulu Cave speleothem, representing a good synchronization candidate at around 22 kyr b2k. By matching the respective 10Be data, we determine the offset between the Greenland ice-core chronology, GICC05, and the Antarctic chronology for the West Antarctic Ice Sheet Divide ice core (WDC), WD2014, to be 125 ± 40 years. Furthermore, via radionuclide wiggle-matching, we determine the offset between the Hulu speleothem and ice-core timescales to be 375 years for GICC05 (75–625 years at 68 % confidence) and 225 years for WD2014 (−25–425 years at 68 % confidence). The rather wide uncertainties are intrinsic to the wiggle-matching algorithm and the limitations set by data resolution. The undercounting of annual layers in GICC05 inferred from the offset is hypothesized to have been caused by a combination of underdetected annual layers, especially during periods with low winter precipitation, and misinterpreted unusual patterns in the annual signal during the extremely cold period often referred to as Heinrich Stadial 1.</p

Intersection cuts for Bilevel optimization

The exact solution of bilevel optimization problems is a very challenging task that received more and more attention in recent years, as witnessed by the flourishing recent literature on this topic. In this paper we present ideas and algorithms to solve to proven optimality generic Mixed-Integer Bilevel Linear Programs (MIBLP’s) where all constraints are linear, and some/all variables are required to take integer values. In doing so, we look for a general-purpose approach applicable to any MIBLP (under mild conditions), rather than ad-hoc methods for specific cases. Our approach concentrates on minimal additions required to convert an effective branch-and-cut MILP exact code into a valid MIBLP solver, thus inheriting the wide arsenal of MILP tools (cuts, branching rules, heuristics) available in modern solvers