Elective course planning

Efficient planning increasingly becomes an indispensable tool for management of both companies and public organizations. This is also the case for high school management in Denmark, because the growing individual freedom of the students to choose courses makes planning much more complex. Due to reforms, elective courses are today an important part of the curriculum, and elective courses are a good way to make high school education more attractive for the students. In this article, the problem of planning the elective courses is modeled using integer programming and three different solution approaches are suggested, including a Branch-and-Price framework using partial Dantzig-Wolfe decomposition. Explicit Constraint Branching is used to enhance the solution process, both on the original IP model and in the Branch-and-Price algorithm. To the best of our knowledge, no exact algorithm for the Elective Course Planning Problem has been described in the literature before. The proposed algorithms are tested on data sets from 98 of the 150 high schools in Denmark. The tests show that for the majority of the problems, the optimal solution can be obtained within the one hour time bound. Furthermore the suggested algorithms achieve better results than the currently applied meta-heuristic.     

Optimal intentional islanding to enhance the robustness of power grid networks

Intentional islanding of a power system can be an emergency response for isolating failures that might propagate and lead to major disturbances. Some of the islanding techniques suggested previously do not consider the power flow model; others are designed to minimize load shedding only within the islands. Often these techniques are computationally expensive. We aim to find approaches to partition power grids into islands to minimize the load shedding not only in the region where the failures start, but also in the topological complement of the region. We propose a new constraint programming formulation for optimal islanding in power grid networks. This technique works efficiently for small networks but becomes expensive as size increases. To address the scalability problem, we propose two grid partitioning methods based on modularity, properly modified to take into account the power flow model. They are modifications of the Fast Greedy algorithm and the Bloom algorithm, and are polynomial in running time. We tested these methods on the available IEEE test systems. The Bloom type method is faster than the Fast Greedy type, and can potentially provide results in networks with thousands of nodes. Our methods provide solutions which retain at least 40–50% of the system load. Overall, our methods efficiently balance load shedding and scalability.     

In-plane and out-of-plane constraint effects under pressurized thermal shocks

Transferability of fracture toughness data obtained on small scale specimens to a full-scale cracked structure is one of the key issues in integrity assessment of engineering structures. In order to transfer fracture toughness under different constraints, both in-plane and out-of-plane constraint effect should be considered for the specimens and structures. In this paper both in-plane and out-of-plane constraint effects of a crack in a reference reactor pressure vessel (RPV) subjected to pressurized thermal shocks (PTSs) are analyzed by two-parameter and three-parameter methods. The comparison between elastic and elastic–plastic analysis shows that the constraint effect varies with the material property. T₁₁ (the second term of William’s extension acting parallel to the crack plane) generally displays a reversed relation to the stress intensity factor (SIF) with the transient time, which indicates that the loading (SIF) plays an important role on the in-plane constraint effect. The thickness at the crack tip contributes more than the loading to the out-of-plane constraint, such that T₃₃ (the second term of William’s extension acting along the thickness) displays a similar relation to ε₃₃ (strain along the thickness direction) and a different relation to T₁₁ during the transient. The results demonstrate that both in-plane and out-of-plane constraint effect should be analyzed separately in order to describe precisely the stress distribution ahead of the crack tip.     

On constraint qualifications for second-order optimality conditions depending on a single Lagrange multiplier

We present new constraint qualifications (CQs) to ensure the validity of some well-known second-order optimality conditions. Our main interest is on second-order conditions that can be associated with numerical methods for solving constrained optimization problems. Such conditions depend on a single Lagrange multiplier, instead of the whole set of Lagrange multipliers. For each condition, we characterize the weakest CQ that guarantees its fulfillment at local minimizers, while proposing new weak conditions implying them. Relations with other CQs are discussed.     

Necessary and sufficient conditions for regularity of constraints in convex programming

This paper derives some necessary and sufficient conditions for (Lagrangian) regularity of the nondifferentiable convex programming problem. Furthermore, some weakest constraint qualifications are presented using the supporting functions and their derivatives, the outer normal cones, the single constraint function and its directional derivatives and epigraph and the projections of the outer normal cones     

基于蕴涵算子族L-λ-R0的模糊推理反向α-三I约束算法

提出了基于蕴涵算子族L-λ-R0的模糊推理的思想,这将有助于提高推理结果的可靠性.针对蕴涵算子族L-λ-R0给出了模糊推理的FMP模型及FMT模型的反向α-三I约束算法.     

Some theoretical limitations of second-order algorithms for smooth constrained optimization

In second-order algorithms, we investigate the relevance of the constant rank of the full set of active constraints in ensuring global convergence to a second-order stationary point under a constraint qualification. We show that second-order stationarity is not expected in the non-constant rank case if the growth of so-called tangent AKKT2 sequences is not controlled. Since no algorithm controls their growth, we argue that there is a theoretical limitation of algorithms in finding second-order stationary points without constant rank assumptions.     

Principles for the Design of Large Neighborhood Search

Large neighborhood search (LNS) is a combination of constraint programming (CP) and local search (LS) that has proved to be a very effective tool for solving complex optimization problems. However, the practice of applying LNS to real world problems remains an art which requires a great deal of expertise. In this paper, we show how adaptive techniques can be used to create algorithms that adjust their behavior to suit the problem instance being solved. We present three design principles towards this goal: cost-based neighborhood heuristics, growing neighborhood sizes, and the application of learning algorithms to combine portfolios of neighborhood heuristics. Our results show that the application of these principles gives strong performance on a challenging set of job shop scheduling problems. More importantly, we are able to achieve robust solving performance across problem sets and time limits. This material is based upon works supported by the Science Foundation Ireland under Grant No. 00/PI.1/C075, the Embark Initiative of the Irish Research Council of Science Engineering and Technology under Grant PD2002/21, and ILOG, S.A.     

估算一元弱酸溶液pH的近似式及约束条件

利用一元二次方程估算一元弱酸溶液的[H+]是化学分析工作者经常采用的方法。酸的离解常数Ka和浓度c的数值相对大小和其乘积cKa是获得各种近似式的关键因素。本文通过实例计算归纳出了如下结论:(1)当c Ka≥10Kw时,可忽略水的离解,则[H~+]=1/2(-K_a+(K_a~2+4_cK_a)(1/2)),并首次指出了c Ka≥10Kw判据的边界条件为c≥6×10~(-6)mol·L~(-1);(2)当Ka≥19c时,弱酸可做强酸处理,通常情况下有[H+]=c,对较强弱酸的稀溶液,该近似式有重要应用价值;(3)当满足c≥105Ka时,可忽略弱酸的离解,即认为[HA]≈c,则[H~+]=(K_w+cK_a)(1/2)。实际上,c≥6×10~(-6)mol·L~(-1)的弱酸溶液,都可用近似式获得令人满意的pH计算结果。     

关于（y,z）限制的BSDE解

本文讨论漂移系数g（S,·,·）不满足Lipschitz条件的一类例向随机微机方程（BSDE）关于（x,y）限制条件下最小g-上解的存在唯一性,为此我们讨论了这一类BSDE的比较定理．推广了[1]在g（s,·,·）关于（x,y）满足Lipschitz条件下的结果．