Branching Strategy Research Articles

Vascularization of the gastrointestinal tract of the bottlenose dolphin (Tursiops truncatus, Montagu 1821).

Odontocetes primarily rely on fish, cephalopods, and crustaceans as their main source of nutrition. In the digestive system, their polygastric complex exhibits similarities to that of their closest terrestrial relatives such as cows, sheep, and giraffes, while the entero-colic tract shares similarities with terrestrial carnivores. The morphology, caliber, and structure of the odontocete intestine are relatively constant, and, since there is no caecum, a distinction between the small and large intestine and their respective subdivisions is difficult. To address this issue, we used the intestinal vascularization pattern, specifically the course and branching of the celiac artery (CA) and the cranial and caudal mesenteric arteries (CrMA and CdMA). A series of pictures and dissections of 10 bottlenose dolphins (Tursiops truncatus) were analyzed. Additionally, we performed a cast by injecting colored polyurethane foam in both arteries and veins to measure the caliber of the arteries and clarify their monopodial or dichotomous branching. Our results showed the presence of multiple duodenal arteries (DAs) detaching from the CA. The CrMA gave origin to multiple jejunal arteries, an ileocolic artery (ICA), and, in six cases, a CdMA. In four specimens, the CdMA directly originated from the abdominal aorta. The ICA gave rise to the mesenteric ileal branches (MIB) and mesenteric anti-ileal branches and the right colic arteries (RCA) and the middle colic arteries. From the CdMA originated the left colic and cranial rectal arteries (LCA and CrRA). The measurements revealed a mixed monopodial and dichotomous branching scheme. The analysis of the arteries and their branching gave us an instrument, based on comparative anatomy, to distinguish between the different intestinal compartments. We used the midpoint of anastomoses between MIB and RCA to indicate the border between the small and the large intestine, and the midpoint of anastomoses between LCA and CrRA, to tell the colon from the rectum. This pattern suggested an elongation of the duodenum and a shortening of the colic tract that is still present in this species. These findings might be related to the crucial need to possess a long duodenal tract to digest prey ingested whole without chewing. A short aboral part is also functional to avoid gas-producing colic fermentation. The rare origin of the CdMA on the CrMA might instead be a consequence of the cranial thrust of the abdominopelvic organs related to the loss of the pelvic girdle that occurred during the evolution of cetaceans.

An algorithm for stochastic convex-concave fractional programs with applications to production efficiency and equitable resource allocation

We propose an algorithm to solve convex and concave fractional programs and their stochastic counterparts in a common framework. Our approach is based on a novel reformulation that involves differences of square terms in the constraints, and subsequent employment of piecewise-linear approximations of the concave terms. Using the branch-and-bound (B&B) framework, our algorithm adaptively refines the piecewise-linear approximations and iteratively solves convex approximation problems. The convergence analysis provides a bound on the optimality gap as a function of approximation errors. Based on this bound, we prove that the proposed B&B algorithm terminates in a finite number of iterations and the worst-case bound to obtain an ϵ-optimal solution reciprocally depends on the square root of ϵ. Numerical experiments on Cobb–Douglas production efficiency and equitable resource allocation problems support that the algorithm efficiently finds a highly accurate solution while significantly outperforming the benchmark algorithms for all the small size problem instances solved. A modified branching strategy that takes the advantage of non-linearity in convex functions further improves the performance. Results are also discussed when solving a dual reformulation and using a cutting surface algorithm to solve distributionally robust counterpart of the Cobb–Douglas example models.

Electric vehicle-based express service network design with recharging management: A branch-and-price approach

With soaring fuel prices and the imperative to reduce global carbon emissions, electric vehicles (EVs) possess unparalleled advantages in terms of sustainability. Consequently, numerous express service providers have commenced the implementation of EV-based express service networks. However, designing an effective service network for EV fleets necessitates considering recharging operations during the route planning process. In this study, we explore a problem involving the design of an EV-based express service network under the constraint of limited recharging resources, while taking into account power management for each EV throughout the entire operational cycle. To address this challenge, we present a mixed-integer optimization model incorporating a Dantzig–Wolfe reformulation. Additionally, we develop resource extension functions that enable an efficient dynamic labeling algorithm, incorporating dominance rules, to solve complex subproblems. We propose a branch-and-price framework that integrates an aggregated branching strategy and a heuristic upper-bound technique, enabling the attainment of exact solutions for instances involving large fleet sizes. Computational experiments conducted on realistic instances, involving up to 20 terminals and over 2000 EVs, substantiate the efficiency of our approach.

Superior TRAIL gene expression and cancer cell apoptosis mediated by highly branched-linear poly(β-amino ester)s

Extensive efforts have been dedicated to enhancing the expression of tumor necrosis factor-related apoptosis-inducing ligand (TRAIL) in cancer cells for the development of effective cancer treatments. However, highly safe and efficient delivery of TRAIL gene remains a significant challenge, especially using cationic polymers. Here, a series of highly branched-linear poly(β-amino ester)s (H-LPAEs) are developed through a unique oligomer branching strategy. H-LPAEs exhibit a more uniform distribution of linear segments and branching units, leading to excellent DNA condensation and favorable physicochemical properties of H-LPAE/DNA polyplexes. In SW1353 and BMSC cells, the optimized H-LPAEs, H-LPAEB4−S5−TMPTA, achieves superior gene transfection efficiency of 58.0% and 33.4%, which were 2.5-fold and 2.0-fold higher than that of the leading commercial gene transfection reagent, Lipofectamine 3000. Excitingly, H-LPAEB4−S5−TMPTA mediated 56.7% and 28.1% cell apoptosis in HepG2 cells and HeLa cells highlighting its potential application in cancer gene therapy. In addition, locally administered H-LPAEB4−S5−TMPTA delivered TRAIL DNA to HepG2 xenograft tumors and inhibited tumor growth in vivo. This study not only proposes a novel strategy for synthesizing poly(β-amino ester)s with a unique branched-linear topology but also identifies a promising candidate for highly efficient TRAIL gene transfection.

Global optimization for cardinality-constrained minimum sum-of-squares clustering via semidefinite programming

AbstractThe minimum sum-of-squares clustering (MSSC), or k-means type clustering, has been recently extended to exploit prior knowledge on the cardinality of each cluster. Such knowledge is used to increase performance as well as solution quality. In this paper, we propose a global optimization approach based on the branch-and-cut technique to solve the cardinality-constrained MSSC. For the lower bound routine, we use the semidefinite programming (SDP) relaxation recently proposed by Rujeerapaiboon et al. (SIAM J Optim 29(2):1211–1239, 2019). However, this relaxation can be used in a branch-and-cut method only for small-size instances. Therefore, we derive a new SDP relaxation that scales better with the instance size and the number of clusters. In both cases, we strengthen the bound by adding polyhedral cuts. Benefiting from a tailored branching strategy which enforces pairwise constraints, we reduce the complexity of the problems arising in the children nodes. For the upper bound, instead, we present a local search procedure that exploits the solution of the SDP relaxation solved at each node. Computational results show that the proposed algorithm globally solves, for the first time, real-world instances of size 10 times larger than those solved by state-of-the-art exact methods.

A branch-and-regret algorithm for the same-day delivery problem

We study a dynamic vehicle routing problem where stochastic customers request urgent deliveries characterized by restricted time windows. The aim is to use a fleet of vehicles to maximize the number of served requests and minimize the traveled distance. The problem is known in the literature as the same-day delivery problem, and it is of high importance because it models a number of real-world applications, including the delivery of online purchases. We solve the same-day delivery problem by proposing a novel branch-and-regret algorithm in which sampled scenarios are used to anticipate future events and an adaptive large neighborhood search is iteratively invoked to optimize routing plans. The branch-and-regret is equipped with four innovation elements: a new way to model the subproblem, a new policy to generate scenarios, new consensus functions, and a new branching scheme Extensive computational experiments on a large variety of instances prove the outstanding performance of the branch-and-regret, also in comparison with recent literature, in terms of served requests, traveled distance, and computational effort.

Efficient and stable proton conduction achieved by accommodation of the membrane-wide cross-linking and branching strategies

Fabrication of high-temperature proton exchange membranes (HTPEMs) with high and durable proton conductivity, and sufficient mechanical/oxidative stability is of great significance but challenging. Herein, a flexible branched polymer (broPBI), a cross-linkable water-soluble proton conductor (PBSA), and a multi-functional cross-linker with high content of imidazole rings (BrABPBI) were designed to fabricate HTPEMs with good comprehensive performances. The branching structure of broPBI provided large free volume, high content of terminal groups, and interconnected main-chains, which are conducive to efficient proton conduction and improved mechanical property. BrABPBI covalently crosslinked broPBI and PBSA to form membrane-wide cross-linking structure, improving the mechanical strength and oxidative resistance while avoiding leaching of PBSA. The secondary amines in broPBI and PBSA became tertiary amines after cross-linking, which have higher basicity and thus higher doping capacity of PBSA. However, overusing of cross-linking or branching can deteriorate membrane performances. To achieve comprehensive good performance, the two strategies were appropriately accommodated in broPBI-BrABPBI-PBSA membranes. At 180 °C, the proton conductivity of broPBI-BrABPBI(20%)-PBSA(50%) composite membrane reached 0.140, 0.0701, and 0.0310 S cm−1 at 100% RH, 50% RH, and 0% RH, respectively. The membrane has excellent mechanical properties, proton conductivity, and oxidative stability, with low leaching of PBSA, demonstrating promising application prospects.

Research on Cloud Task Scheduling Algorithm with Conflict Constraints Based on Branch-and-Price

The low-energy task scheduling of cloud computing systems is a key issue in the field of cloud computing. Nevertheless, existing works on task scheduling lack consideration of the conflict relationship between tasks and focus on heuristic and other approximate algorithms. Thus, solving the problem of minimizing energy consumption with antiaffinity constraints between tasks and designing an efficient exact algorithm for task scheduling is a major challenge. This paper abstracts the problem into a multidimensional bin packing model with conflict constraints. The model is decomposed by the Lagrange relaxation principle and Dantzig–Wolfe decomposition principle. Moreover, we propose an accurate algorithm based on branch-and-price. The algorithm benefits from a new initial solution generation scheme based on maximum cliques and dominant resource proportion, and a multipattern branching strategy. The efficiency of the proposed branch-and-price algorithm is verified by a number of numerical experiments.

Upgrading edges in the Graphical TSP

In this paper we present a generalization of the Graphical Traveling Salesman Problem (GTSP). Given a communication graph in which not all direct connections are necessarily possible, the Graphical Traveling Salesman Problem consists of finding the shortest tour that visits each node at least once. In this work, we assume the availability of a budget that allows to upgrade, i.e. reduce their traversal cost, some of the current connections and we propose the problem of designing the minimum cost tour using this budget. We propose and study a formulation for the problem, verifying that the polyhedron associated with the set of feasible solutions of a relaxed version of the problem is a full-dimensional polytope. We present families of valid inequalities that reinforce the model and pre-processing techniques to reduce the number of variables of the formulation. To solve the problem, we propose a branch-and-cut algorithm that uses the introduced valid inequalities, as well as a heuristic to obtain good upper bounds and a tailor-made branching strategy. Comprehensive computational experiments on a new set of benchmark instances are presented to assess the performance of this exact method.

R-SALSA: A branch, bound, and remember algorithm for the workload smoothing problem on simple assembly lines

We consider a simple assembly line balancing problem with given cycle time and number of stations. A quadratic objective function based on a so-called smoothness index SX levels the workloads of the stations. For this problem, called SALBP-SX, only a few solution procedures have been proposed in literature so far. In this paper, we extend and improve the branch-and-bound procedure SALSA (Simple Assembly Line Smoothing Algorithm) of Walter et al. (2021) to a bidirectional branch, bound, and remember algorithm called R-SALSA (R for remember). Like SALSA, it is based on a dynamic programming scheme which pre-determines potential workloads of the stations and provides a construction plan for possible station loads. This scheme is extended by the new concept of supporters and preventers which significantly enhances branching, bounding, and logical tests. Furthermore, a tailored heuristic that searches for improved initial solutions, a bidirectional branching scheme and additional dominance rules are integrated. In extensive computational experiments, we find out that our new procedure clearly outperforms all former exact solution procedures on benchmark data sets with up to 1000 tasks.

Improving energy aware nanosatellite task scheduling by a branch-cut-and-price algorithm

CubeSats are small satellite platforms that have become increasingly popular for space research due to their small size, modular design, and affordability. However, their limited power and communication capabilities present significant challenges for the development and operation of these satellites. One of the main challenges is to effectively manage the limited power resources available on CubeSats for supporting the various tasks and payloads of the satellite. Addressing these challenges requires careful task scheduling that considers the power requirements and importance of different tasks and the trade-offs between power consumption and other factors such as data rate, volume, and accuracy. Decision-making in task scheduling for CubeSats often involves solving large mixed-integer programming (MIP) problems, which can be computationally intensive and time-consuming. To address this challenge, we propose a branch-cut-and-price algorithm for CubeSats that improves upon previous approaches in the literature. We apply dual stabilization to column generation and propose new valid inequalities; resort to an effectively implemented dynamic programming (DP) algorithm to generate multiple columns in parallel; and rely on a new branching strategy based on pseudocosts to reduce the number of nodes and improve the overall performance of the method. Our results demonstrate the effectiveness of these enhancements for solving a complex task scheduling problem in the context of CubeSats compared to the state-of-the-art approach, and further highlight its potential to improve the efficiency and accuracy of mission planning and operations for these small satellite platforms.

Combining local branching and descent method for solving the multiple‐choice knapsack problem with setups

AbstractIn this paper, the multiple‐choice knapsack problem with setups is tackled with an iterative method, where both local branching and descent method cooperate. First, an iterative procedure is designed for solving a series of mixed integer programming problems combined with a special reduced subproblem; that is, a combined model built by injecting some valid cardinality constraints. Second, the local branching‐based learning strategy is embedded into an iterative search to mimic the variable neighborhood descent method, such that the local branching strategy drives the search process for enhancing the quality of the solutions. Third, the proposed method is experimentally analyzed on benchmark instances extracted from the literature, where its provided (lower) bounds are compared to those reached by methods published in the literature and the Cplex solver. Finally, its performance is evaluated by providing a statistical analysis.

A lightweight semi-centralized strategy for the massive parallelization of branching algorithms

Several NP-hard problems are solved exactly using exponential-time branching strategies, whether it be branch-and-bound algorithms, or bounded search trees in fixed-parameter algorithms. The number of tractable instances that can be handled by sequential algorithms is usually small, whereas massive parallelization has been shown to significantly increase the space of instances that can be solved exactly. However, previous centralized approaches require too much communication to be efficient, whereas decentralized approaches are more efficient but have difficulty keeping track of the global state of the exploration.In this work, we propose to revisit the centralized paradigm while avoiding previous bottlenecks. In our strategy, the center has lightweight responsibilities, requires only a few bits for every communication, but is still able to keep track of the progress of every worker. In particular, the center never holds any task but is able to guarantee that a process with no work always receives the highest priority task globally.Our strategy was implemented in a generic C++ library called GemPBA, which allows a programmer to convert a sequential branching algorithm into a parallel version by changing only a few lines of code. An experimental case study on the vertex cover problem demonstrates that some of the toughest instances from the DIMACS challenge graphs that would take months to solve sequentially can be handled within two hours with our approach.

Auto-Optimizing Connection Planning Method for Chain-Type Modular Self-Reconfiguration Robots

Chain-type modular robots are capable of self-reconfiguration (SR), where the connection relationship between modules is changed according to the environment and tasks. This article focuses on the connection planning of SR based on multiple in-degree single out-degree (MISO) modules. The goal is to calculate the optimal connection planning solution: the sequence with the fewest detachment and attachment actions. To this end, we propose an auto-optimizing connection planning method that contains a polynomial-time algorithm to calculate near-optimal solutions and an exponential-time algorithm to further optimize the solutions automatically when some CPUs are idle. The method combines rapidity and optimality in the face of an NP-complete problem by using configuration pointers, strings that uniquely specify the robot's configuration. Our polynomial-time algorithm, in-degree matching (IM) uses the interchangeability of connection points to reduce reconfiguration steps. Our exponential-time algorithm, tree-based branch and bound (TBB) further optimizes the solutions to the optimum by a new branching strategy and stage cost. In the experiments, we verify the feasibility of the auto-optimizing method combining IM and TBB, and demonstrate the superiority of IM over Greedy-CM in the SR of MISO modules and the near-optimality of IM compared to the optimal solutions of TBB.

Two extended formulations for the virtual network function placement and routing problem

AbstractGiven a bi‐directed graph modeling a telecommunication network, and a set of origin‐destination pairs representing traffic requests (commodities) along with their associated Service Function Chains (SFCs), the Virtual Network Function Placement and Routing Problem (VNFPRP) aims to find, for each commodity, one latency‐constrained routing path that visits the required Virtual Network Functions in a specific order. The function installation costs together with the node activation costs have to be minimized. In this paper, we present two extended Mixed Integer Programming (MIP) formulations to model the VNFPRP. For each formulation we define the master problem, the pricing problem, the associated Lagrangian bound and a specific branching scheme, in order to derive an efficient Branch‐and‐Price algorithm. We also provide several families of valid inequalities to strengthen the LP‐relaxation bounds. Computational results are reported comparing the performance of the two Branch‐and‐Price algorithms with a compact MIP formulation and its Branch‐and‐Benders‐cut implementation on a set of SNDlib instances representing telecommunication networks.

Multi-period single-allocation hub location-routing: Models and heuristic solutions

This work investigates the use of time-dependent decisions in the context of hub-location routing. Instead of setting up the entire system at once, a planning horizon partitioned into several periods is considered during which the system is to be phased-in. In addition to installing the hubs, decisions are also to be made concerning the hub-level network, namely, the hub edges to use. The origin-destination flows are assumed to be time-dependent as well as the costs underlying the problem which include, set up costs for hubs and hub edges and variable operational costs at the hubs. A mathematical model is developed for the problem that can be solved up to proven optimality with a general-purpose solver for small instances of the problem. For larger instances, a four-phase matheuristic that combines principles of relax-and-fix, variable neighborhood descent and local branching schemes is proposed. In addition, two variants of the matheuristic have been developed. The above model and methodology are tested using data generated by extending existing hub location instances to our problem. The obtained results are detailed and analyzed in depth. The major conclusion is that by capturing time in the decision-making process, one may find solutions that better hedge against parameter changes throughout time. Furthermore, the overall procedure presented in this work is quite general in the sense that it can be easily adapted to other multi-period decision making problems and different objective functions.

Electric bus scheduling with the self-adaptive charging strategy based on a course selection idea

This paper investigates the electric bus scheduling problem, aiming to design collaborative service and charging schedules. A self-adaptive charging strategy is introduced, allowing electric buses to be recharged partially and flexibly. Then, a mixed-integer programme model is built for the problem, based on a course selection idea that considers continuous time. Two models for scenarios considering prior greedy and full charging strategies are also established for comparison. Next, a greed-based branch-and-price algorithm is developed for model solving, which incorporates a greedy attachment heuristic for the initialisation and a customised branching scheme based on the course flow. The results of a case study in Beijing show the efficiency of the proposed algorithm and the superiority of the self-adaptive charging strategy. Compared with the two prior charging strategies, the average energy replenishment of electric buses is reduced by 22.47% and 35.99%, and the system cost is reduced by 5.47% and 5.60%.

CasSABER for Programmable In Situ Visualization of Low and Nonrepetitive Gene Loci.

Site-specific imaging of target genes using CRISPR probes is essential for understanding the molecular mechanisms of gene function and engineering tools to modulate its downstream pathways. Herein, we develop CRISPR/Cas9-mediated signal amplification by exchange reaction (CasSABER) for programmable in situ imaging of low and nonrepetitive regions of the target gene in the cell nucleus. The presynthesized primer-exchange reaction (PER) probe is able to hybridize multiple fluorophore-bearing imager strands to specifically light up dCas9/sgRNA target-bound gene loci, enabling in situ imaging of fixed cellular gene loci with high specificity and signal-to-noise ratio. In combination with a multiround branching strategy, we successfully detected nonrepetitive gene regions using a single sgRNA. As an intensity-codable and orthogonal probe system, CasSABER enables the adjustable amplification of local signals in fixed cells, resulting in the simultaneous visualization of multicopy and single-copy gene loci with similar fluorescence intensity. Owing to avoiding the complexity of controlling in situ mutistep enzymatic reactions, CasSABER shows good reliability, sensitivity, and ease of implementation, providing a rapid and cost-effective molecular toolkit for studying multigene interaction in fundamental research and gene diagnosis.

Spatial Branching for Conic Non-Convexities in Optimal Electricity-Gas Flow

This paper proposes a novel geometry-based spatial branching strategy for conic non-convex equations in integrated electricity-gas systems. The proposed strategy is embedded in a spatial branch-and-bound algorithm to solve optimal electricity-gas flow problems for their exact solutions. Numerical results on multiple test cases verify the effectiveness and superiority of the proposed method.

On the Use of Gray Codes for Solving 0-1 Combinatorial Problems of Optimization in Environmental and Economic Systems

Introduction. The application of binary-reflected (mirror, reflexive) Gray codes for solving combinatorial problems with pseudo-Boolean functions (polynomials from Boolean variables) is considered. A recursive Ehrlich algorithm is given for generating a sequence of lines n-bit Gray codes, in which each subsequent line differs from the previous one by only one digit (bit). As an example of the effectiveness of the use of these codes, the solution of two combinatorial problems with Boolean variables with a complete enumeration of solutions is considered, and it is shown how these codes can be used to efficiently calculate the values of the objective function and constraints. The results of an experimental study are presented, which show that Gray codes can be practically applied in branching schemes, for example, in the branch and bound method, when the number of variables in the branching nodes of the decision algorithm does not exceed 35. Purpose. The purpose of the article is to show the developers of algorithms and programs how to apply Gray codes in various branching schemes of the decision algorithm, for example, in the branch and bound method, when the number of binary (Boolean) variables at the nodes of the tree is small (less than 35). The technique. The research methodology is based on a computational experiment for solving the 0-1 knapsack problem with the proposed algorithm of exhaustive search the solution with partial and full recalculation of the values of objective function and constraint of the problem. During the experiment, the accuracy of solving the problem by a “greedy” heuristic algorithm with time complexity O(n2) was also checked. Results. As a result of the experiment, it was found that the algorithm with a partial recalculation of the objective function and restrictions can be used for practical calculations in branching schemes, when the number of variables in the nodes of the branching tree does not exceed 35. The algorithm with partial recalculation is faster than the algorithm with full recalculation on average by 7 times. The heuristic "greedy" algorithm can be applied in practice to solve the 0-1 problem of a knapsack of large dimension (more than 10,000 items), when need to obtain an approximate value of the objective function at the limited computing resources. Scientific novelty and practical significance. The novelty of the work lies in the proposed approach to solving combinatorial optimization problems with pseudo-Boolean functions using Gray codes. The efficiency of the proposed algorithm with a partial recalculation of the values of the objective function and constraints is shown, and its can be applied in practice in various branching schemes of the decision algorithm. Keywords: Gray codes, combinatorial optimization problems, problem solving time.