Branching Strategy Research Articles

Jupiter-style Jet Stability

Abstract Studies of Jupiter’s zonal jets, facilitated by the two Voyager flybys, the Galileo entry probe, the Cassini flyby, and the Juno orbiter have led to two fundamental insights into inviscid shear stability that have implications for a wide range of large-scale fluid systems involving alternating shear instability. The first insight is that the analog of the Mach number for vorticity (Rossby and drift) waves, “Ma,” ensures shear stability via the criterion “Ma”−1 < 1, which includes both Kelvin–Arnol’d branches of stability, and is edged with a shock. A surprise is the well-studied first branch (KA-I), which includes as special cases the textbook shear stability theorems of Rayleigh, Kuo, Charney–Stern, and Fjørtoft, merely corresponds to “Ma”−1 < 0. The second insight is that Jupiter’s tropospheric jets achieve stability via a second branch (KA-II) strategy, a 3/4 layer, undulating control surface supplied by the dynamic topography of the planet’s deep jets, which maintains “Ma”−1 ≲ 1 via stretching vorticity. The deep jets are similarly stabilized by the spherical shape of the planet itself. Although Jupiter-style zonal jet stabilization is precluded by the torus geometry used in hot-plasma fusion reactors, it is directly applicable to the tube with ends geometry used in cool-plasma applications, including antimatter storage at high-energy colliders. In general, the lessons learned from analyzing Jupiter’s jets eliminate much of the guesswork from predicting and controlling inviscid shear instability.

Bacterial nanocellulose from agro-industrial wastes: low-cost and enhanced production by Komagataeibacter saccharivorans MD1

Bacterial nanocellulose (BNC) has been drawing enormous attention because of its versatile properties. Herein, we shed light on the BNC production by a novel bacterial isolate (MD1) utilizing various agro-industrial wastes. Using 16S rRNA nucleotide sequences, the isolate was identified as Komagataeibacter saccharivorans MD1. For the first time, BNC synthesis by K. saccharivorans MD1 was investigated utilizing wastes of palm date, fig, and sugarcane molasses along with glucose on the Hestrin-Schramm (HS) medium as a control. After incubation for 168 h, the highest BNC yield was perceived on the molasses medium recording 3.9 g/L with an initial concentration of (v/v) 10%. The physicochemical characteristics of the BNC sheets were inspected adopting field-emission scanning electron microscope (FESEM), atomic force microscopy (AFM), X-ray diffraction (XRD), and Fourier transform infrared (FTIR) analysis. The FESEM characterization revealed no impact of the wastes on either fiber diameter or the branching scheme, whereas the AFM depicted a BNC film with minimal roughness was generated using date wastes. Furthermore, a high crystallinity index was estimated by XRD up to 94% for the date wastes-derived BNC, while the FTIR analyses exhibited very similar profiles for all BNC films. Additionally, mechanical characteristics and water holding capacity of the produced BNCs were studied. Our findings substantiated that expensive substrates could be exchanged by agro-industrial wastes for BNC production conserving its remarkable physical and microstructural properties.

Necessary optimality conditions of control of stochastic compound dynamic system in case of full in-formation about state vector.

Stochastic Compound Dynamic Systems (CDS) are complex technical systems that are created through the use of precision mechanics in combination with modern telecommunications and computer technologies. Incertitude in these CDS shows up under the influence of external and internal stochastic perturbations. The constituent elements of CDS are combined into a single system because these elements perform a single complex mission. The information exchange is wireless, there is no mechanical connection between the elements of the CDS. The paper considers groups of unmanned aerial vehicles (UAVs), which are equipped with sensors or multisensors that are able to perform a mobile sensor network. The trajectories of individual elements of the mobile sensor network are trajectories formed under the influence of stochastic perturbations. This fact means that the nature of the mobile sensor network can be classified as a stochastic compound dynamic system and for the mathematical description and optimization of the movement of this system is adequate to use models and methods for optimizing stochastic CDS. The model of CDS motion is considered to be a branching trajectory or, as they say, a branched trajectory. A stochastic mathematical model of the motion of a mobile sensor network, which performs the combined mission of surveying an emergency zone, can be classified as a model of the motion of a stochastic compound dynamic system. This approach is an adequate for mathematical model creation to the mobile sensor network physical condition, for its operation in the zone of natural disaster by natural or anthropogenic origin. This paper is devoted to solving a theoretical problem related to the formulation and proof of the necessary conditions for stochastic CDS moving optimal control along a branched trajectory with an arbitrary branching scheme.

فعالية استراتيجيات التفکير المتشعب في تنمية التفکير الاحتمالي لدى تلاميذ المرحلة الإعدادية *

هدف البحث الحالي إلى تحديد فعالية استراتيجيات التفکير المتشعب في تنمية التفکير الاحتمالي لدى تلميذات المرحلة الإعدادية، تکونت عينة البحث من (64)تلميذة من تلميذات الصف الثاني الإعدادي ،موزعين على مجموعتين: تجريبية (32)تلميذة، وضابطة(32)تلميذة، بمدرستين من مدارس إدارة منية النصر التعليمية، وتم تحقيق التکافؤ بينهما من حيث بعض المتغيرات الدخيلة، وأعدت الباحثة اختبارا لقياس التفکير الاحتمالي بالإضافة إلى دليل العلم في ضوء استراتيجيات التفکير المتشعب وکراسة الأنشطة في محتوى الرياضيات، وذلک خلال الفصل الدراسي الأول لعام 2018/2019 م. وتم التوصل إلى النتائج الآتية: يوجد فرق دال إحصائيا عند مستوى دلالة (0.01) بين متوسطي درجات تلميذات المجموعتين التجريبية والضابطة في الاختبار البعدي للتفکير الاحتمالي لصالح تلميذات المجموعة التجريبية. يوجد فرق دال إحصائيا عند مستوى دلالة (0.001) بين متوسطي درجات تلميذات المجموعة التجريبية في التطبيقين البعدي/ القبلي لاختبار التفکير الاحتمالي لصالح التطبيق البعدي. الکلمات المفتاحية: استراتيجيات التفکير المتشعب- التفکير الاحتمالي. The objective of this research is to determine the effectiveness of the neural branching strategies in the development the probabilistic thinking pupils in the preparatory stage,The sample consisted of (64) prep- school students, divided into two groups: experimental group(32) students, and control group( 32) students in two schools of Menia Al-Nasr Educational Administration, and their equivalence was achieved in terms of some variables, The researcher prepared a test to measure probabilistic thinking and guide teacher by the neural branching strategies &work sheets during the first semester of 2018/2019. The results: There is a statistically significant فرق difference ذو عند at مستو ى (the level (0.01) بين between متوسطيthe درجات degrees mean تلميذات the two groups التجريبية experimental و الضابطة and the control في in the post- التطبيقapplication البعدي لاختبار to test القدرة of ability على probabilistic thinking for المجموعة the التجريبية experimental . group students . There is a statistically significant فرق difference ذو عند at مستو ى (the level (0.001) بين between متوسطيthe درجات degrees mean تلميذات the التجريبية experimental groups و الضابطة in the post- التطبيقapplication and pre- application البعدي لاختبار to test القدرة of probabilistic thinking for theالتجريبية post application keywords :The Neural Branching Strategies– Probabilistic Thinking

Streamlining variational inference for constraint satisfaction problems**This article is an updated version of: Grover A, Achim T and Ermon S 2018 Streamlining variational inference for constraint satisfaction problems Advances in Neural Information Processing Systems vol 31, ed S Bengio et al (Red Hook, NY: Curran Associates, Inc) pp 10556–66.

Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and are used to inform branching decisions during search; however, marginal estimates obtained via survey propagation are approximate and can be self-contradictory. We introduce a more general branching strategy based on streamlining constraints, which sidestep hard assignments to variables. We show that streamlined solvers consistently outperform decimation-based solvers on random k-SAT instances for several problem sizes, shrinking the gap between empirical performance and theoretical limits of satisfiability by on average for .

Evaluation of longitudinal time-lapsed in vivo micro-CT for monitoring fracture healing in mouse femur defect models

Longitudinal in vivo micro-computed tomography (micro-CT) is of interest to non-invasively capture the healing process of individual animals in preclinical fracture healing studies. However, it is not known whether longitudinal imaging itself has an impact on callus formation and remodeling. In this study, a scan group received weekly micro-CT measurements (week 0–6), whereas controls were only scanned post-operatively and at week 5 and 6. Registration of consecutive scans using a branching scheme (bridged vs. unbridged defect) combined with a two-threshold approach enabled assessment of localized bone turnover and mineralization kinetics relevant for monitoring callus remodeling. Weekly micro-CT application did not significantly change any of the assessed callus parameters in the defect and periosteal volumes. This was supported by histomorphometry showing only small amounts of cartilage residuals in both groups, indicating progression towards the end of the healing period. Also, immunohistochemical staining of Sclerostin, previously associated with mediating adverse radiation effects on bone, did not reveal differences between groups. The established longitudinal in vivo micro-CT-based approach allows monitoring of healing phases in mouse femur defect models without significant effects of anesthesia, handling and radiation on callus properties. Therefore, this study supports application of longitudinal in vivo micro-CT for healing-phase-specific monitoring of fracture repair in mice.

Multivalued decision diagrams for prize-collecting job sequencing with one common and multiple secondary resources

Multivalued decision diagrams (MDD) are a powerful tool for approaching combinatorial optimization problems. Relatively compact relaxed and restricted MDDs are applied to obtain dual bounds and heuristic solutions and provide opportunities for new branching schemes. We consider a prize-collecting sequencing problem in which a subset of given jobs has to be found that is schedulable and yields maximum total prize. The primary aim of this work is to study different methods for creating relaxed MDDs for this problem. To this end, we adopt and extend the two main MDD compilation approaches found in the literature: top down construction and incremental refinement. In a series of computational experiments these methods are compared. The results indicate that for our problem the incremental refinement method produces MDDs with stronger bounds. Moreover, heuristic solutions are derived by compiling restricted MDDs and by applying a general variable neighborhood search (GVNS). Here we observe that the top down construction of restricted MDDs is able to yield better solutions as the GVNS on small to medium-sized instances.

Comparative Analysis of Capacitated Arc Routing Formulations for Designing a New Branch-Cut-and-Price Algorithm

The current best exact algorithms for the Capacitated Arc Routing Problem are based on the combination of cut and column generation. This work presents a deep theoretical investigation of the formulations behind those algorithms, classifying them and pointing out similarities and differences, advantages and disadvantages. In particular, we discuss which families of cuts and branching strategies are suitable for each alternative and their pricing complexities. That analysis is used to justify key decisions on constructing a new branch-cut-and-price algorithm that combines several features picked from the capacitated arc routing literature with some features adapted from the most successful recent algorithms for node routing. The computational experiments show that the resulting algorithm is indeed effective and can solve almost all open instances from the classical benchmark sets.

An improved branch-cut-and-price algorithm for the two-echelon capacitated vehicle routing problem

In the paper, we propose a branch-cut-and-price algorithm for the two-echelon capacitated vehicle routing problem in which delivery of products from a depot to customers is performed using intermediate depots called satellites. Our algorithm incorporates significant improvements recently proposed in the literature for the standard capacitated vehicle routing problem such as bucket graph based labeling algorithm for the pricing problem, automatic stabilization, limited memory rank-1 cuts, and strong branching. In addition, we make some specific problem contributions. First, we introduce a new route based formulation for the problem which does not use variables to determine product flows in satellites. Second, we introduce a new branching strategy which significantly decreases the size of the branch-and-bound tree. Third, we introduce a new family of satellite supply inequalities, and we empirically show that it improves the quality of the dual bound at the root node of the branch-and-bound tree. Finally, extensive numerical experiments reveal that our algorithm can solve to optimality all literature instances with up to 200 customers and 10 satellites for the first time and thus double the size of instances which could be solved to optimality.

CDNA Display of Disulfide-Containing Peptide Library and In Vitro Evolution.

Directed in vitro evolution (IVE) is now a widely applied technology to obtain molecules that have designed new features of one's demands. We describe here experimental procedures for a cDNA display IVE to select peptide aptamers from a scaffold-based random peptide library. A three-finger (3-F) peptide library is exemplified, which has been shown its pluripotency to various target molecules. Peptide scaffolds including 3-F are refined through evolution, and they are mostly stabilized by disulfide bridges. To utilize such disulfide-containing protein library in IVE, we optimized the translation and folding conditions. Co-translational folding assisted by protein disulfide isomerase was found to have better efficiency than posttranslational refolding in the IVE. Linker is also a key element to make a tight genotype-phenotype linkage. Here, we introduced a whole procedure of IVE to use a newly designed puromycin linker, which was synthesized by a novel branching strategy. The improved linker enabled rapid and highly efficient ligation of mRNA and synthesis of protein fusions.

Production Scheduling Optimization Algorithm for the Steel-Making Continuous Casting Processes

This paper investigates steel-making continuous casting (SCC) scheduling problem. SCC is a high temperature and large-scale logistics machining process with batch production at the last stage that was identified as the key process of modern iron and steel enterprises. This paper presents a mathematical model for scheduling SCC process. The model is developed as a Mixed Zero- One Linear programming (MZOLP) based on actual production situations of SCC. The objective is to schedule a set of charges (jobs) to minimize the earliness and tardiness penalty costs as well as the charge waiting time cost. The solution methodology is developed based on a branch-and-bound algorithm. A heuristic method is presented at the beginning of the search in order to compute an initial upper bound. A lower bound and an upper bound are developed and a method for reducing branches is established based on the batch production in the continuous casting (CC) stage. Moreover, branching schemes are proposed. The branch- and- bound algorithm incorporating the initial upper bound, the lower and upper bound, the method for reducing branches, and branching schemes is tested on a set of instances. The analysis shows the efficiency of the proposed features for the algorithm.

Bi-objective Branch-and-Cut Algorithms Based on LP Relaxation and Bound Sets

Most real-world optimization problems are multi-objective by nature, with conflicting and incomparable objectives. Solving a multi-objective optimization problem requires a method that can generate all rational compromises between the objectives. This paper proposes two distinct bound set-based branch-and-cut algorithms for general bi-objective combinatorial optimization problems based on implicit and explicit lower-bound sets. The algorithm based on explicit lower-bound sets computes, for each branching node, a lower-bound set and compares it with an upper-bound set. The other fathoms branching nodes by generating a single point on the lower-bound set for each local nadir point. We outline several approaches for fathoming branching nodes, and we propose an updating scheme for the lower-bound sets that prevents us from solving the bi-objective linear programming relaxation of each branching node. To strengthen the lower-bound sets, we propose a bi-objective cutting-plane algorithm that adjusts the weights of the objective functions such that different parts of the feasible set are strengthened by cutting planes. In addition, we suggest an extension of the branching strategy “Pareto branching.” We prove the effectiveness of the algorithms through extensive computational results.

Pickup and delivery problem with incompatibility constraints

The purpose of this paper is to present a new version of the One-to-One Pickup and Delivery Problem in which a single vehicle must comply with requests for transportation from specific collect points to specific delivery points. The problem we consider, besides looking for a minimum cost route, adds extra constraints that forbid some requests to be in the vehicle at the same time.We first begin to formally define the problem and show how it is related to the classic graph coloring problem. Then, we introduce a comparative analysis of the computational performance of three integer programming formulations. Some polyhedral results of the most promising formulation are presented in order to strengthen the LP relaxation for increasing the computational efficacy of the model. We implement separation algorithms, a primal heuristic for finding feasible solutions and a branching strategy. All these elements were considered to the development of a Branch and Cut algorithm which is tested on a comprehensive test bed of instances. The algorithm proves to be capable of overcoming state-of-the-art mixed-integer solvers, both in number of solved instances and computational time.

A Branch-and-Price Algorithm for the Integrated Berth Allocation and Quay Crane Assignment Problem

This paper integrates, from a tactical perspective, berth allocation and quay-crane assignment, two important, closely related decisions in container terminal operations in a single model. To obtain optimal solutions, a branch-and-price algorithm is sought in this paper under the framework of Dantzig–Wolfe decomposition. The algorithm decomposes the original problem to a master problem that links all vessels competing for the shared resources of berths and quay cranes and multiple per-vessel pricing subproblems that can be solved efficiently in polynomial time. Specifically, in the stage of generating promising initial feasible columns, three heuristics are adopted; during the column-updating stage, the subgradient-based Lagrangian relaxation is introduced to tackle the possibly encountered degeneracy phenomenon; the branching strategy is implemented in the pricing subproblem rather than in the master problem as reported in the literature with the benefit of avoiding incurring new dual prices, simplifying the branching process; and both breadth- and depth-first searching policies are tested to select the next node to explore. With real-life data, extensive numerical experiments are conducted to select the best choice for each stage with the strengths and drawbacks of each choice provided. And then the superiority of the branch-and-price algorithm configured with the selected combination of strategies is verified by comparing it with both CPLEX, a general-purpose solver, and a set-partitioning model, a dedicated algorithm reported in the literature. In addition, the decomposition by vessels adopted in this paper is also verified numerically by comparing it with the decomposition by berths reported in the literature, and the performance of the algorithm for other problem settings has also been tested. In conclusion, the numerical experiments show that our method outperforms the commercial solver and state-of-the-art solution methods reported in the literature in terms of both solution quality and computational time.

Optimization Bounds from the Branching Dual

We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with the minimum bandwidth problem. The method strengthens a known bound for a given problem by formulating a dual problem whose feasible solutions are partial branching trees. It solves the dual problem with a “worst-bound” local search heuristic that explores neighboring partial trees. After proving some optimality properties of the heuristic, we show that it substantially improves known combinatorial bounds for the minimum bandwidth problem with a modest amount of computation. It also obtains significantly tighter bounds than depth-first and breadth-first branching, demonstrating that the dual perspective can lead to better branching strategies when the object is to find valid bounds.

A route decomposition approach for the single commodity Split Pickup and Split Delivery Vehicle Routing Problem

We address a single commodity Pickup and Delivery Vehicle Routing Problem from the literature. A network of customer nodes is given with both travel times and costs. A fleet of vehicles of limited capacity is exploited to satisfy node demands, and a set of routes must be found such that the vehicle capacities are never exceeded, each route does not exceed time resource, and cost is minimized. The demands of both pickup and delivery nodes can be split, and each node can be visited more than once. We provide new theoretical insights. We propose a new formulation where routes are decomposed into sequences of simpler substructures called clusters, mitigating the combinatorial explosion of feasible solutions. We introduce valid inequalities, and design a branch-and-price algorithm, exploiting ad hoc pricing routines and branching strategies, and embedding a rounding heuristic to speed up pruning. An extensive experimental analysis shows our method to offer simultaneously more modelling flexibility and more computational effectiveness than previous attempts from the literature. Our investigation opens also interesting insights into the use of route decomposition strategies.

Composite version of B&B algorithm: experimental verification of the efficiency

The aim of this paper is to verify the efficiency for a composite version of branch and bound algorithm combining B&B branching strategy and bounds computing with the pruning rules used in dynamic programming for selecting of direction of movement by a search tree. As criteria of efficiency we used random access memory (RAM) and time gains of finding integer programming problem solution by a composite version of branch and bound algorithm in comparison with its traditional implementation. The number of variables in the problems and restrictions did not exceed 25 and 15, respectively. Experimental verification have shown that for solving time used as a criterion of the efficiency, the advantages of composite version are beyond doubt compared to the used RAM value as criterion often taking the side of the classical B&B algorithm.

A new branch-and-bound algorithm for the Maximum Weighted Clique Problem

We study the Maximum Weighted Clique Problem (MWCP), a generalization of the Maximum Clique Problem in which weights are associated with the vertices of a graph. The MWCP calls for determining a complete subgraph of maximum weight. We design a new combinatorial branch-and-bound algorithm for the MWCP, which relies on an effective bounding procedure. The size of the implicit enumeration tree is largely reduced via a tailored branching scheme, specifically conceived for the MWCP. The new bounding function extends the classical MWCP bounds from the literature to achieve a good trade off between pruning potential and computing effort. We perform extensive tests on random graphs, graphs from the literature and real-world graphs, and we computationally show that our new exact algorithm is competitive with the state-of-the-art algorithms for the MWCP in all these classes of instances.

Dual control technique for mitigating water-hammer phenomenon in pressurized steel-piping systems

This paper examined a dual technique -based branching strategy to sustain the conventional technique skills in terms of limitation of wave oscillation period spreading. This technique consists in splitting the single plastic short-penstock used in the conventional one into dual plastic sub-short penstocks placed upstream each of the connections of the original steel piping system to other hydraulic parts. Numerical computations used the method of characteristics for the discretization of unconventional water-hammer model based on the Vitkovsky and the Kelvin-Voigt formulations. The robustness of the transient solver was evaluated by comparing the obtained numerical results with pertinent experimental results. Moreover, the efficiency of the dual technique was explored for a series of operating condition tests including up- and- down surge- initiated water hammer events. Additionally, two plastic material types were utilized for sub- short-penstock pipe-walls, including (HDPE) or (LDPE) plastic materials. Results demonstrated that dual technique is a useful tool to soften both first hydraulic-head peak and crest. Moreover, examination of wave oscillation periods confirmed that the dual technique could markedly improve the efficiency of the conventional one, providing acceptable trade-off between hydraulic-head peaks or crests attenuation, and wave oscillation period spreading limitation. Furthermore, results demonstrated that the amortization of pressure head -rise and -drop was sensitive to the plastic sub- short-penstocks dimensions.

Investigation on Redesigning Strategies for Water-Hammer Control in Pressurized-Piping Systems

This paper explored and compared the effectiveness of the inline and the branching redesign strategies used to control water-hammer surges initiated into existing steel piping systems. The piping system is handled, at its transient sensitive regions, by replacing an inline, or adding a branching, short-section made of high- or low-density polyethylene (HDPE or LDPE) pipe-wall materials. The Ramos model was used to describe the transient flow, along with the method of characteristics implemented for numerical computations. The comparison of the numerical solution with experimental data available from the literature and alternative numerical solution evidenced that the proposed model could reproduce satisfactorily the magnitude and the phase shift of pressure head evolution. Further, the robustness of the proposed protection procedures was tested with regard to water-hammer up- and down-surge mechanisms, taken separately. Results demonstrated that both utilized techniques provided a useful tool to soften both water-hammer up- and down-surges. Additionally, the amortization of pressure-head-rise and -drop was sensitive to the short-section material and size. Moreover, the branching strategy illustrated several enhancements to the inline one in terms of period spread-out limitation, while providing acceptable pressure-head damping.