Branch Algorithm Research Articles

Dynamic gaussian deep belief network design and stock market application

Stock price forecasting has been an important topic for investors, researchers, and analysts. In this paper, a prediction model of Dynamic Gaussian Deep Belief Network (DGDBN) is proposed. Generally, the network structure of traditional Deep Belief Network (DBN) determines the performance of its time series prediction. Most previous research uses artificial experience to adjust the network structure, it is difficult to ensure performance and time efficiency by constantly trying. In addition, the accuracy of the traditional DBN stacked by binary Restricted Boltzmann Machines(RBM) needs to be improved when solving the time series problem. The DGDBN designed in this paper contains two points: The first point is to add Gaussian noise to the RBM. The second point is to realize the increase or decrease branch algorithm of hidden layer structure according to the connection weights and average percentage error (MAPE). Finally, the forecast for the stocks of United Technologies Corporation and Unisys Corp, DGDBN is compared with DBN and LSTM. The root means square error (RMSE) increases by 15% and 65%. The interesting thing we found is that the number of neurons in the last layer of the DGDBN network has a greater effect than other layers.

Designing an integrated blockchain-enabled supply chain network under uncertainty

With the development of communication infrastructure, the design of supply chains has changed significantly. Blockchain technology, as one of the most cutting-edge technologies, can promote transparency among members of the supply chain network. To the best of our knowledge, this is the first study that tries to develop a novel bi-objective optimization model to integrate the transparency resulting from the use of blockchain for designing a three-level supply chain network. The first objective function is to minimize total cost while the second objective function seeks to maximize transparency based on the application of blockchain technology. Moreover, it is worth noting that it is the first attempt to investigate the role of a blockchain model under stochastic conditions. The bi-objectiveness and stochastic nature of the proposed model are then treated using Fuzzy Goal Programming (FGP) and Chance-Constrained programming (CCP) approaches, respectively. To tackle the problem, an improved Branch and Efficiency (B&E) algorithm is developed by incorporating transparency along with cost and service. The impacts of blockchain exclusively through transparency (Case 1) or through transparency, cost, and benefits (Case 2) in Supply Chain Design (SCD) are compared. The results demonstrated that the first case has less computational complexity and better scalability, while the second case has more transparency, less congestion, and more security. As one of the main implications, supply chain managers who are focused on cost minimization as well as transparency maximization are advised to take into account the trade-off between featuring costs and benefits of blockchain technology.

Recognition of single upper limb motor imagery tasks from EEG using multi-branch fusion convolutional neural network.

Motor imagery-based brain-computer interfaces (MI-BCI) have important application values in the field of neurorehabilitation and robot control. At present, MI-BCI mostly use bilateral upper limb motor tasks, but there are relatively few studies on single upper limb MI tasks. In this work, we conducted studies on the recognition of motor imagery EEG signals of the right upper limb and proposed a multi-branch fusion convolutional neural network (MF-CNN) for learning the features of the raw EEG signals as well as the two-dimensional time-frequency maps at the same time. The dataset used in this study contained three types of motor imagery tasks: extending the arm, rotating the wrist, and grasping the object, 25 subjects were included. In the binary classification experiment between the grasping object and the arm-extending tasks, MF-CNN achieved an average classification accuracy of 78.52% and kappa value of 0.57. When all three tasks were used for classification, the accuracy and kappa value were 57.06% and 0.36, respectively. The comparison results showed that the classification performance of MF-CNN is higher than that of single CNN branch algorithms in both binary-class and three-class classification. In conclusion, MF-CNN makes full use of the time-domain and frequency-domain features of EEG, can improve the decoding accuracy of single limb motor imagery tasks, and it contributes to the application of MI-BCI in motor function rehabilitation training after stroke.

Parton shower generator based on the Gribov-Levin-Ryskin equation

We develop a novel Monte Carlo parton branching algorithm based on the Gribov-Levin-Ryskin (GLR) equation. The formulations of both forward evolution and backward evolution for the GLR equation are presented. The results from the Monte Carlo implementation of the GLR equation are in full agreement with its numerical solutions. Our work thus paves the way for developing an event generator that embodies the saturation effect.

Patient appointment scheduling at hemodialysis centers: An exact branch and price approach

Scheduling patient appointments at a hemodialysis center presents a unique setting. Unlike other appointment scheduling problems in healthcare systems, patients are scheduled for a series of dialysis treatment appointments instead of a single appointment. In this study, we formulate this multiple-appointment system as a set-partitioning problem that allows partial schedules to be feasible. We employ a Branch and Price (BP) algorithm to solve the problem, however, the pricing sub-problem proves to be exceedingly challenging for state-of-the-art dynamic programming algorithms. Therefore, we propose a novel decomposition of the sub-problem and design an efficient embedded Column Generation (CG) algorithm to find the optimal solution. We further design a greedy heuristic that enhances the computational efficiency of the BP algorithm. Our proposed BP algorithms efficiently solve challenging instances that are simulated based on the data from a collaborating hemodialysis center. Specifically, the Enhanced CG-embedded BP algorithm accelerates the CPU time on average by 78% compared to the Base BP algorithm (32% and 59% compared to the Enhanced and the CG-embedded BP algorithms, respectively). We also compare the optimal results with the current scheduling policy at the center. Our proposed Enhanced CG-embedded BP algorithm improves the percentage of leftover appointments by 98% on average and the hours of deviations per patient by 46% on average, compared to the current policy.

The successful branching algorithm comparison in probabilistic safety assessment

In this paper, the technical requirements of quantitative analysis in the PSA standards sought to carry out corresponding research. Different models are used to analyze and compare the commonly used successful branching algorithms, and the compliance of each algorithm with the PSA standards is listed. Algorithm analysis and testing show that the ability to propagate success branch logic is the key to ensuring reasonable results. On the other hand, before carrying out quantitative analysis, we should identify whether there are high probability events (>0.1), non-monotonic system, mutual exclusion logic structure, etc, in the model. Then select the appropriate algorithm, and the analysis results of cutest, importance measure and uncertainty can be reasonable expounded. This paper conducts further research on the technical requirements related to quantitative analysis in the PSA standard, and gives the compliance status of the commonly used successful branch algorithms with the PSA standard. After research, the algorithms that are not recommended include the Ignore Event Tree Success algorithm and the “success probability” processing method. The former is provided in some PSA software, but because it does not consider the logic of successful branching, it will produce erroneous cut sets, which is also a practice that the PSA standard clearly does not support. Even if the numerical results are very different from other algorithms in some cases, they should not be used. Although the latter is considered to be usable in the current PSA standard, manual processing will bring a great workload, and it is not feasible in actual engineering.

A sampling-based matheuristic for the continuous-time stochastic inventory routing problem with time-windows

This article considers a continuous-time variant of the stochastic inventory routing problem. In most of the articles present in the literature related to inventory routing, customers reveal their demands at the end of each period, which is when the inventory level is calculated. In the variant of the problem at hand, the demand that each customer experiences on each period, results in a continuous decrease of the inventory for the customer during the period. This characteristic strongly affects the quantities that can be delivered to each customer and, if the deliveries are not sufficient or arrive too late, they can cause some stock-out situations within the periods. In the inventory routing problem, the vendor manages all the replenishment decisions of the vendees and, therefore, creates delivery plans for a planning horizon, aiming to reduce the routing, consistency, inventory and lost-sales costs. We formulate the problem as a two-stage mathematical program. Customers experience a continuous stochastic demand within each period and present information about inventory level and capacity at each period, as well as the time windows in which deliveries can take place. To solve this problem, we develop a matheuristic solution approach based on an adaptive large neighborhood search algorithm. In addition, we evaluate the impact of applying recourse actions to deal with expected lost sales during the planning horizon. We compare the performance of the algorithm with adapted variants of the multiple scenario approach and the branch and regret algorithms from the literature. Samples based on the stochastic demands are considered in the algorithms, to find robust solutions that can minimize the objective function. We evaluate the solutions by means of a sample average estimator procedure, and we compare the efficiency of the algorithms as well as the impact of different levels of stochasticity.

Improving the Parameters of the Regenerative Braking Mode of the Thyristor Rectifier-inverter Converter by Addition the Diode-transistor Discharge Branch and New Operation Algorithm

Thyristor rectifier-inverter converters are widely used. The power factor of the standard converter of locomotives does not exceed 65% in this mode, which does not meet the requirements of the national standard for electric locomotives with collector traction motors. This fact is due to the need to turn on the thyristor in advance, in the wrong half-period, from the point of view of energy transfer to the electrical network. Such turning-on of the converter leads to a large amount of reactive energy transmitted to the electrical network by an electric locomotive. The purpose of this work is to compare the modes of the standard and new rectifier-inverter converters. The new rectifier-inverter converter in the recovery mode works with switching of the diode–thyristor branch and with a new algorithm of operation. Both the mathematical model of converters and physical models are investigated.

MLD-MPC Approach for Three-Tank Hybrid Benchmark Problem

The present paper aims at validating a Model Predictive Control (MPC), based on the Mixed Logical Dynamical (MLD) model, for Hybrid Dynamic Systems (HDSs) that explicitly involve continuous dynamics and discrete events. The proposed benchmark system is a three-tank process, which is a typical case study of HDSs. The MLD-MPC controller is applied to the level control of the considered tank system. The study is initially focused on the MLD approach that allows consideration of the interacting continuous dynamics with discrete events and includes the operating constraints. This feature of MLD modeling is very advantageous when an MPC controller synthesis for the HDSs is designed. Once the MLD model of the system is well-posed, then the MPC law synthesis can be developed based on the Mixed Integer Programming (MIP) optimization problem. For solving this MIP problem, a Branch and Bound (B&B) algorithm is proposed to determine the optimal control inputs. Then, a comparative study is carried out to illustrate the effectiveness of the proposed hybrid controller for the HDSs compared to the standard MPC approach. Performances results show that the MLD-MPC approach outperforms the standard MPC one that doesn’t consider the hybrid aspect of the system. The paper also shows a behavioral test of the MLD-MPC controller against disturbances deemed as liquid leaks from the system. The results are very satisfactory and show that the tracking error is minimal less than 0.1% in nominal conditions and less than 0.6% in the presence of disturbances. Such results confirm the success of the MLD-MPC approach for the control of the HDSs.

Solving the Traveling Salesman Problem with release dates via branch and cut

In this paper we study the Traveling Salesman Problem with release dates (TSP-rd) and completion time minimization. The TSP-rd considers a single vehicle and a set of customers that must be served exactly once with goods that arrive to the depot over time, during the planning horizon. The time at which each requested good arrives is called release date and it is known in advance. The vehicle can perform multiple routes, however, it cannot depart to serve a customer before the associated release date. Thus, the release date of the customers in each route must not be greater than the starting time of the route. The objective is to determine a set of routes for the vehicle, starting and ending at the depot, where the completion time needed to serve all customers is minimized. We propose a new Integer Linear Programming model and develop a branch and cut algorithm with tailored enhancements to improve its performance. The algorithm proved to be able to significantly reduce the computation times when compared to a compact formulation tackled using a commercial mathematical programming solver, obtaining 24 new optimal solutions on benchmark instances with up to 30 customers within one hour. We further extend the benchmark to instances with up to 50 customers where the algorithm proved to be efficient. Building upon these results, the proposed model is adapted to new TSP-rd variants (Capacitated and Prize-Collecting TSP), with different objectives: completion time minimization and traveling distance minimization. To the best of our knowledge, our work is the first in-depth study to report extensive results for the TSP-rd through a branch and cut, establishing a baseline and providing insights for future approaches. Overall, the approach proved to be very effective and gives a flexible framework for several variants, opening the discussion about formulations, algorithms and new benchmark instances.

Solving discrete linear fractional bilevel programs with multiple objectives at the upper level

<p style='text-indent:20px;'>This paper proposes an exact method to solve an integer linear fractional bilevel problem with multiple objectives at the upper level, designated by <inline-formula><tex-math id="M1">\begin{document}$ IFMOBP $\end{document}</tex-math></inline-formula>. The proposed algorithm generates a set of efficient solutions using a branch and cut algorithm based on a continuous upper level linear fractional problem. Then, the integer optimal solution obtained is tested for optimality of the lower level problem. First, the integer optimal solution of the bilevel problem is sought with a single objective function at each level. After that, an efficient cut is added and new integer solutions are determined. The efficient set is updated each time a candidate bilevel feasible solution non dominated is got and the process ends when there are no unexplored parts of the original domain. The proposed method is based on a dantzig cut to find the next best integer solution of the first objective function of the upper level, an efficient cut to get the set of efficient solutions for the main problem, and the classical branch and bound technique for integer decision variables. After the presentation of the algorithm, a numerical example and computational experiments are provided.</p>

Algorithmic identification of atypical diabetes in electronic health record (EHR) systems.

Understanding atypical forms of diabetes (AD) may advance precision medicine, but methods to identify such patients are needed. We propose an electronic health record (EHR)-based algorithmic approach to identify patients who may have AD, specifically those with insulin-sufficient, non-metabolic diabetes, in order to improve feasibility of identifying these patients through detailed chart review. Patients with likely T2D were selected using a validated machine-learning (ML) algorithm applied to EHR data. "Typical" T2D cases were removed by excluding individuals with obesity, evidence of dyslipidemia, antibody-positive diabetes, or cystic fibrosis. To filter out likely type 1 diabetes (T1D) cases, we applied six additional "branch algorithms," relying on various clinical characteristics, which resulted in six overlapping cohorts. Diabetes type was classified by manual chart review as atypical, not atypical, or indeterminate due to missing information. Of 114,975 biobank participants, the algorithms collectively identified 119 (0.1%) potential AD cases, of which 16 (0.014%) were confirmed after expert review. The branch algorithm that excluded T1D based on outpatient insulin use had the highest percentage yield of AD (13 of 27; 48.2% yield). Together, the 16 AD cases had significantly lower BMI and higher HDL than either unselected T1D or T2D cases identified by ML algorithms (P<0.05). Compared to the ML T1D group, the AD group had a significantly higher T2D polygenic score (P<0.01) and lower hemoglobin A1c (P<0.01). Our EHR-based algorithms followed by manual chart review identified collectively 16 individuals with AD, representing 0.22% of biobank enrollees with T2D. With a maximum yield of 48% cases after manual chart review, our algorithms have the potential to drastically improve efficiency of AD identification. Recognizing patients with AD may inform on the heterogeneity of T2D and facilitate enrollment in studies like the Rare and Atypical Diabetes Network (RADIANT).

Idle-parked vehicles assisted collaborative resource allocation in VEC based on Stackelberg game

With the advent of autonomous vehicles, how to meet the computing demands of vehicles with computing-intensive and latency-sensitive tasks becomes a challenge. Vehicular Edge Computing (VEC) is an advanced computing paradigm that improves the Quality of Service (QoS) of vehicles by offloading tasks to VEC servers. However, the computing resources of the VEC server are limited and thus cannot meet the offloading needs of the vehicle. This paper proposes to use idle-parked vehicles to assist the VEC server to offload computing tasks, which increases the resource capacity and expands the communication range. Firstly, we propose an idle-parked vehicle-assisted VEC model, which incentivizes idle-parked vehicles to assist VEC server computing tasks by obtaining rewards from VEC servers. Secondly, this paper proposes a more flexible dynamic offloading scheme based on comprehensive consideration of the selection strategy and pricing strategy. Then, based on the Stackelberg game, the interaction between the VEC server and the idle-parked vehicle is analyzed, and utilize backward induction to prove that there is a unique Nash equilibrium in this game. Finally, an improved joint selection decision and pricing decision algorithm based on the Branch and Bound (JSPBB) algorithm is proposed, which achieves the optimal pricing under the condition of maximizing the utility of idle-parked vehicles and each VEC server under this pricing optimal offloading strategy to maximize system utility. The simulation results can show that the proposed algorithm can solve the problem effectively and has good performance so that the system can obtain higher benefits.

A new branch and efficiency algorithm for an optimal design of the supply chain network in view of resilience, inequity and traffic congestion

A new branch and efficiency algorithm for an optimal design of the supply chain network in view of resilience, inequity and traffic congestion

A branch and efficiency algorithm to design a sustainable two-echelon supply chain network considering traffic congestion and uncertainty.

This work aims to design a sustainable two-echelon supply chain not only based on the widely used cost perspective, but also based on the efficient use and preservation of limited resources. For this purpose, a branch and efficiency (B&E) algorithm is developed, which includes an optimization model and an evaluation model. The proposed tri-objective optimization model simultaneously minimizes the total cost of the supply chain, maximizes the sustainability score, and minimizes inequity among customers. The solutions obtained from the optimization model are then evaluated by extended data envelopment analysis (EDEA) models based on common criteria (i.e., cost and service) and traffic congestion criterion. To take into account real-world conditions, parameters related to labor and demand are assumed under uncertainty. Since the presented models consist of more than one objective function, fuzzy goal programming (FGP) method is utilized to tread the multi-objectiveness. The obtained results from tackling a case study problem demonstrate that considering sustainability issues can positively affect both the economic and social aspects of the problem. Furthermore, the developed B&E algorithm is able to reduce costs in each iteration; this is what supply chain managers are interested in. On the other hand, this algorithm can provide more services to applicants compared to one of the competing algorithms.

Branch and Price Algorithm for Multi-Trip Vehicle Routing with a Variable Number of Wagons and Time Windows

Motivated by the transportation needs of modern-day retailers, we consider a variant of the vehicle routing problem with time windows in which each truck has a variable capacity. In our model, each vehicle can bring one or more wagons. The clients are visited within specified time windows, and the vehicles can also make multiple trips. We give a mathematical programming formulation for the problem, and a branch and price algorithm is developed to solve the model. In each iteration of branch and price, column generation is used. Different subproblems are created based on the different capacities to find the best column. We use CPLEX to solve the problem computationally and extend Solomon’s instances to evaluate our approach. To our knowledge, ours is the first such study in this field.

Efficient parallel branch-and-bound approaches for exact graph edit distance problem

Graph Edit Distance (GED) is a well-known measure used in the graph matching to measure the similarity/dissimilarity between two graphs by computing the minimum cost of edit operations needed to transform one graph into another. This process, Which appears to be simple, is known NP-hard and time consuming since the search space is increasing exponentially. One way to optimally solve this problem is by using Branch and Bound (B&B) algorithms, Which reduce the computation time required to explore the whole search space by performing an implicit enumeration of the search space instead of an exhaustive one based on a pruning technique. nevertheless, They remain inefficient when dealing with large problem instances due to the impractical running time needed to explore the whole search space. To overcome this issue, We propose in this paper three parallel B&B approaches based on shared memory to exploit the multi-core CPU processors: First, a work-stealing approach where several instances of the B&B algorithm explore a single search tree concurrently achieving speedups up to 24× faster than the sequential version. Second, a tree-based approach where multiple parts of the search tree are explored simultaneously by independent B&B instances achieving speedups up to 28×. Finally, Due to the irregular nature of the GED problem, two load-balancing strategies are proposed to ensure a fair workload between parallel processes achieving impressive speedups up to 300×. all experiments have been carried out on well-known datasets

Batching and scheduling in a continuous-discrete hybrid flowshop: Lagrangian relaxation-based heuristic algorithms

ABSTRACT We study a two-stage hybrid flow shop problem arising from a fine chemicals production facility, where the first stage is a continuous chemical reaction process and the second stage is a discrete filling-packaging process. The objective is to minimise the total weighted completion time through batching of the jobs and scheduling of the batches at first stage and scheduling of the jobs at second stage. We formulate the problem as a mixed integer programming model and develop a Lagrangian relaxation-based framework for solving it, where the original problem is decomposed into family-level subproblems, and each subproblem is transformed into a set-partitioning problem. The subproblems are solved to optimality via branch and price algorithm. We also propose two heuristic algorithms for reducing computational efforts without much loss of solution quality. Finally, we conduct computational experiments with both randomly generated and real data sets to test the performance of the three proposed algorithms and demonstrate that the algorithms perform efficiently.

A New Heuristic Algorithm for Multi Vehicle Routing Problem with AND/OR-Type Precedence Constraints and Hard Time Windows

In this paper the classic known Multi Vehicle Routing Problem (VRP) is studied where classically several vehicles are set in a central depot, depending on the allocation strategy, each vehicle starts traveling to visit a set of nodes one after another to provide a service of gathering or delivering commodities with the aim of minimizing total traveling distances and costs. In the current paper, this classic problem is extended by new approach of AND/OR precedence constraints (PC) which have not been considered so far in the related literature. Traditionally, PC have been considered in VRPs as the 'AND' type, where the immediate successor of a node cannot be visited until its predecessor nodes have reached their end of services. However by additional OR-type precedence constraints, there are some interconnected nodes through the concept of OR, therein no mandatory need to visit all predecessors of a successor node is acquired before it can be met, and only finishing a part of them can let to that particular node to get visited. This fact is widely observed in pickup and routing and distribution real cases where requisites for some specific products can be fulfilled via various potential suppliers. Implementation of this type of PC graph in VRP is considered as the first introduction and application in the category of this problem. So, initially, the problem is mathematically formulated, then, due to problem’s NP-hard complexity and allocation-routing characteristics, a decomposition-based technique is utilized to solve the problem. The procedure is based on recently enhanced Benders’ decomposition approach named as Branch and Search Algorithm, partitioning the original main problem into allocation and routing parts. Unlike the previous version of Benders algorithm, logic based, this newly promoted method acts in a way that at the allocation level, it generates partition of nodes with feasible solutions in lower routing level. The routing part itself has been enhanced by heuristics to cover AND/OR PC graphs. Furthermore, the efficiency of the proposed solution procedure is tested and verified by running on several generated problems in different sizes and in the larger scale it is implemented on the real case of a distribution company in Iran.

The perfect matching cut problem revisited

In a graph, a perfect matching cut is an edge cut that is a perfect matching. perfect matching cut (pmc) is the problem of deciding whether a given graph has a perfect matching cut, and is known to be NP-complete. We revisit the problem and show that pmc remains NP-complete when restricted to bipartite graphs of maximum degree 3 and arbitrarily large girth. Complementing this hardness result, we give two graph classes in which pmc is polynomial-time solvable. The first one includes claw-free graphs and graphs without an induced path on five vertices, the second one properly contains all chordal graphs. Assuming the Exponential Time Hypothesis, we show there is no O⁎(2o(n))-time algorithm for pmc even when restricted to n-vertex bipartite graphs, and also show that pmc can be solved in O⁎(1.2721n) time by means of an exact branching algorithm.