Branch Algorithm Research Articles

Close-Enough Facility Location

This paper introduces the concept of close-enough in the context of facility location. It is assumed that customers are willing to move from their homes to close-enough pickup locations. Given that the number of pickup locations is expanding every day, it is assumed that pickup locations can be placed everywhere. Conversely, the set of potential location for opening facilities is discrete as well as the set of customers. Opening facilities and pickup points entails an installation budget and a distribution cost to transport goods from facilities to customers and pickup locations. The (p,t)-Close-Enough Facility Location Problem is the problem of deciding where to locate p facilities among the finite set of candidates, where to locate t pickup points in the plane and how to allocate customers to facilities or to pickup points so that all the demand is satisfied and the total cost is minimized. In this paper, it is proved that the set of initial infinite number of pickup locations is finite in practice. Two mixed-integer linear programming models are proposed for the discrete problem. The models are enhanced with valid inequalities and a branch and price algorithm is designed for the most promising model. The findings of a comprehensive computational study reveal the performance of the different models and the branch and price algorithm and illustrate the value of pickup locations.

Resummation and Simulation of Soft Gluon Effects beyond Leading Color.

We present first results of resumming soft gluon effects in a simulation of high-energy collisions beyond the leading-color approximation. We work to all orders in QCD perturbation theory using a new parton branching algorithm. This amplitude evolution algorithm resembles a parton shower that is able to systematically include color-suppressed terms. We find that color-suppressed terms can significantly contribute to jet veto cross sections.

Improved Analysis of Highest-Degree Branching for Feedback Vertex Set

Recent empirical evaluations of exact algorithms for Feedback Vertex Set have demonstrated the efficiency of a highest-degree branching algorithm with a degree-based pruning. In this paper, we prove that this empirically fast algorithm runs in \(O(3.460^k n)\) time, where k is the solution size. This improves the previous best \(O(3.619^k n)\)-time deterministic algorithm obtained by Kociumaka and Pilipczuk (Inf Process Lett 114:556–560, 2014. https://doi.org/10.1016/j.ipl.2014.05.001).

Dynamic construction site layout planning: an application of branch and bond algorithm

PurposeThis paper develops a platform that can be used to determine how to effectively and efficiently deal with a large number of temporary facilities under a constrained site condition(s). The ultimate goal is to reduce the material handling costs between transformation phases of construction works occurring during the project's development period.Design/methodology/approachEmpirical and deductive research is first adopted to mathematical model dynamic site layout planning using the branch and bond algorithm (B&B). Second, a real-life construction project is examined to illustrate how dynamic site layout planning (using the aforementioned B&B algorithm and a computer software program called LINGO) can reduce the material handling costs. The application of the proposed methodology is then showcased against a case study that utilizes a comparative analysis between the “dynamic” and “statistic” site planning approaches.FindingsBy dividing the construction period into different phases, the developed model is shown to be capable of optimizing the material handling costs between the phases of transformation during construction works. Optimal costs are also considered using the site boundary and unit cost for moving construction materials between two facilities. The comparative analysis results illustrate that the B&B algorithm reduces material handling costs by 33%.Practical implicationsThe proposed model offers an effective planning algorithm for the site layout and location of temporary facilities. More specifically, it can make a substantial improvement in reducing the travel time and material handling cost between the temporary facilities in the construction sites.Originality/valueThe primary knowledge contribution of this study to the site layout is successfully deal with the unequal area problem of temporary site facilities and incorporates the concept of dynamics site planning into the algorithm.

Underwater Object Recognition Using Point-Features, Bayesian Estimation and Semantic Information.

This paper proposes a 3D object recognition method for non-coloured point clouds using point features. The method is intended for application scenarios such as Inspection, Maintenance and Repair (IMR) of industrial sub-sea structures composed of pipes and connecting objects (such as valves, elbows and R-Tee connectors). The recognition algorithm uses a database of partial views of the objects, stored as point clouds, which is available a priori. The recognition pipeline has 5 stages: (1) Plane segmentation, (2) Pipe detection, (3) Semantic Object-segmentation and detection, (4) Feature based Object Recognition and (5) Bayesian estimation. To apply the Bayesian estimation, an object tracking method based on a new Interdistance Joint Compatibility Branch and Bound (IJCBB) algorithm is proposed. The paper studies the recognition performance depending on: (1) the point feature descriptor used, (2) the use (or not) of Bayesian estimation and (3) the inclusion of semantic information about the objects connections. The methods are tested using an experimental dataset containing laser scans and Autonomous Underwater Vehicle (AUV) navigation data. The best results are obtained using the Clustered Viewpoint Feature Histogram (CVFH) descriptor, achieving recognition rates of , and , respectively, clearly showing the advantages of using the Bayesian estimation ( increase) and the inclusion of semantic information ( further increase).

Optimizing wind farms layouts for maximum energy production using probabilistic inference: Benchmarking reveals superior computational efficiency and scalability

Successful development of wind farms relies on the optimal siting of wind turbines to maximize the power capacity under stochastic wind conditions and wake losses caused by neighboring turbines. This paper presents a novel method to quickly generate approximate optimal layouts to support infrastructure design decisions. We model the quadratic integer formulation of the discretized layout design problem with an undirected graph that succinctly captures the spatial dependencies of the design parameters caused by wake interactions. On the undirected graph, we apply probabilistic inference using sequential tree-reweighted message passing to approximate turbine siting. We assess the effectiveness of our method by benchmarking against a state-of-the-art branch and cut algorithm under varying wind regime complexities and wind farm discretization resolutions. For low resolutions, probabilistic inference can produce optimal or nearly optimal turbine layouts that are within 3% of the power capacity of the optimal layouts achieved by state-of-the-art formulations, at a fraction of the computational cost. As the discretization resolution (and thus the problem size) increases, probabilistic inference produces optimal layouts with up to 9% more power capacity than the best state-of-the-art solutions at a much lower computational cost.

Enhanced branch-bound-remember and iterative beam search algorithms for type II assembly line balancing problem

This study presents an enhanced iterative branch, bound and remember (IBBRe) algorithm as an exact method and an enhanced iterative beam search (IBSe) approach as a heuristic method to tackle the type II assembly line balancing problem. The proposed IBBRe is enhanced by utilizing additional lower bounds, a new search strategy and a new sequence of applying the lower bounds and dominance rules. The proposed IBSe is also enhanced by utilizing additional lower bounds, more dominance rules and a new station load selection criterion. The computational study demonstrates that both the proposed methods, namely IBBRe and IBSe, outperform the current state-of-the-art method (iterative beam search), and they update the upper bounds for seven cases which have been open for over two decades. Furthermore, IBBRe outperforms IBSe by achieving the best-known solutions in 301 out of the 302 test cases and might be regarded as the new state-of-the-art methodology.

A machine learning-based branch and price algorithm for a sampled vehicle routing problem

Planning of operations, such as routing of vehicles, is often performed repetitively in rea-world settings, either by humans or algorithms solving mathematical problems. While humans build experience over multiple executions of such planning tasks and are able to recognize common patterns in different problem instances, classical optimization algorithms solve every instance independently. Machine learning (ML) can be seen as a computational counterpart to the human ability to recognize patterns based on experience. We consider variants of the classical Vehicle Routing Problem with Time Windows and Capacitated Vehicle Routing Problem, which are based on the assumption that problem instances follow specific common patterns. For this problem, we propose a ML-based branch and price framework which explicitly utilizes those patterns. In this context, the ML models are used in two ways: (a) to predict the value of binary decision variables in the optimal solution and (b) to predict branching scores for fractional variables based on full strong branching. The prediction of decision variables is then integrated in a node selection policy, while a predicted branching score is used within a variable selection policy. These ML-based approaches for node and variable selection are integrated in a reliability-based branching algorithm that assesses their quality and allows for replacing ML approaches by other (classical) better performing approaches at the level of specific variables in each specific instance. Computational results show that our algorithms outperform benchmark branching strategies. Further, we demonstrate that our approach is robust with respect to small changes in instance sizes.

Multi-agent capacitated scheduling for profit-maximizing using a decomposition-based branch and cut algorithm

ABSTRACT This paper considers a distributed production network scheduling that involves heterogeneous factories with the parallel machine. Although, each factory has its own local customers as a production agent, for better load balancing of machines in the production network, the jobs can transfer among factories. In order to make the problem more realistic, in addition to considering the ability of factories in processing of jobs, the capacity constraints of factories are also included in the scheduling. The aim of this paper is to maximize the profits of jobs such that each job is assigned to precisely one factory subject to their deadlines. To solve this problem, based on the decomposition algorithm, for the first time, an efficient decomposition-based branch and cut algorithm is designed. In this regard, first, the problem is formulated as a mixed-integer linear program (MILP), then using the Benders decomposition structure and after reformulating as an assignment subproblem and single factory scheduling subproblems, a branch and cut algorithm is proposed. Finally, the obtained results of the proposed algorithm, the original MILP, and non-cooperative local scheduling, all solved by CPLEX, are compared.

A Branch & Cut algorithm for the prize-collecting capacitated location routing problem

The Capacitated location routing problem (CLRP) is the combination of two well-studied problems in Operations Research: the capacitated facility location problem (CFLP) and the multiple depots vehicle routing problem (MDVRP). Given a set of available locations and a fleet of vehicles, the aim is to determine a set of depots to open and routes of the vehicles to satisfy the customers demands. The objective of the CLRP is to minimize the total cost, that is the cost of the opened depots, the fixed cost of the vehicles and the cost of the routes while satisfying vehicle and depot capacity constraints. In this work the prize-collecting capacitated location routing problem (PC-CLRP), a new variant of the CLRP is presented. In this case it is possible to leave some customers unvisited and if a customer is visited it gives a gain. The objective is to maximize the overall benefit. A two-index formulation for the PC-CLRP and a Branch & Cut algorithm based on this model are proposed. Valid inequalities for the CLRP are adapted for the PC-CLRP. Also new valid inequalities and optimality cuts are proposed together with their corresponding separation algorithms. A hierarchical branching strategy is also included. The initial solution was provided by an Ant Colony Algorithm. The algorithm is tested on a set of instances specially designed for the new problem. Computational results showed very promising. We also compare the performance of the algorithm with recent work for CLRP on instances from the literature.

Branch &Memorize exact algorithms for sequencing problems: Efficient embedding of memorization into search trees

Memorization, as an algorithm design technique, enables to speed up algorithms at the price of increased space usage. In this work, we focus on search tree algorithms applied to sequencing problems. In these algorithms, on lower branching levels, isomorphic sub-problems may appear exponentially many times and the use of memorization is twofold: on the one hand it avoids repetitive solutions, as they correspond to identical sub-problems; on the other hand, it allows to check for dominance conditions among permutations of the same subset of elements. The idea of memorization appeared for a long time, however, to the best of the authors’ knowledge, it was only seldom applied in the number of branching algorithms proposed in the literature. In this paper, we propose a unifying framework for implementing memorization in exact branching algorithms dedicated to sequencing problems. Our proposal leads to the paradigm of Branch &Memorize and its implementation to three classical single machine problems is validated by an extensive computational experimentation that shows that the mentioned paradigm consistently improves existing exact branching algorithms. These results emphasize the idea of more systematically embedding memorization in branching algorithms.

Neurophysiological correlates of postoperative cognitive disorders

A special place among cognitive disorders in patients with cardiovascular diseases is given to postoperative cognitive dysfunction (POCD). The study aimed at investigating the patterns of beta-2 activity associated with postoperative cognitive dysfunction (POCD) in patients after coronary artery bypass grafting (CABG). The study included 60 patients who underwent neuropsychological testing 3-5 days before surgery and on the 7-10th day of CABG. A multichannel electroencephalogram of resting state with eyes closed in 62 standard leads was recorded. Statistical processing of the results was carried out using Statistica 10 (StatSoft Inc, USA) and the developed method of data clustering with a minimax criterion, a software implementation of the binary clipping and branching algorithm was used to find optimal solutions. Patients with POCD had higher pre- and postoperative high-frequency beta-2 rhythm power (20-30 Hz) compared with patients without cognitive impairment. The regression model demonstrated that POCD was associated with high values of preoperative beta-2 activity in the right frontal cortex and with low values in the left parietal areas after CABG. The clustering of beta-2 rhythm power before and after CABG revealed that the best cognitive status corresponded to a stable affiliation of patients with the selected clusters. The specific POCD correlates were established in patients after CABG. Low cognitive status was characterized by the preoperative beta-2 power increase in the right frontal areas and postoperative decrease in the left parietal cortex. The developed method for classifying patients according to the level of pre- and postoperative beta-2 rhythm power has a good discriminant ability. Stable patient affiliation with the selected clusters was associated with a higher level of cognitive status.

The Study of Depot Position Effect on Travel Distance in Order Picking Problem

Research of travel distance on single - depot position in warehouse is tremendous. This study focuses more on the effect of two-depot position on travel distance in order picking problem (OPP) by using the concept of traveling salesman problem (TSP) and exact method – Branch and Bound (B\&B) algorithm. The total distance of one-depot position is shorter than two-depot position for single and double block warehouses and the difference is less than 5%. The total distance is also compared with approximate methods – SA and TS which show that the differences are less than 5%. The sequence of location visit for one depot and two depot is similar about two third from the total location visits. For order picking problem that has more than 25 location visits, one need to consider to apply approximate approach to get the solution faster even the difference will be higher from exact approach when the number of location visit or aisle increases.

Deterministic methods versus biologically inspired methods: optimal sizing of a PV-WT-BESS system for street lighting

This paper provides a comparison between deterministic methods and biologically inspired methods for the optimal sizing of a PV-WT-BESS system. Moreover, an appropriate sizing model is provided. As an application, we consider a public street lighting for supplying a location in the city of Tangier. On one hand, based on this application, we show that branch and cut algorithm (BCA) and branch and bound algorithm (BBA) are highly accurate and efficient than the extensively used genetic algorithm (GA) and ant colony algorithm (ACA) that are shown to fail in finding not only a satisfactory solution, but even a feasible solution for our case study. On the other hand, we show that BCA is more efficient than BBA with regard to execution time and optimality. Finally, the BCA solution is selected as a suitable basis of a detailed analysis on the performance and the economic evaluation for the optimal sizing of the proposed public lighting installation.

Robust multi-product newsvendor model with uncertain demand and substitution

This work studies a Robust Multi-product Newsvendor Model with Substitution (R-MNMS), where the demand and the substitution rates are stochastic and are subject to cardinality-constrained uncertainty sets. The goal of this work is to determine the optimal order quantities of multiple products to maximize the worst-case total profit. To achieve this, we first show that for given order quantities, computing the worst-case total profit, in general, is NP-hard. Therefore, we derive the closed-form optimal solutions for the following three special cases: (1) if there are only two products, (2) if there is no substitution among different products, and (3) if the budget of demand uncertainty is equal to the number of products. For a general R-MNMS, we formulate it as a mixed-integer linear program with an exponential number of constraints and develop a branch and cut algorithm to solve it. For large-scale problem instances, we further propose a conservative approximation of R-MNMS and prove that under some certain conditions, this conservative approximation yields an exact optimal solution to R-MNMS. The numerical study demonstrates the effectiveness of the proposed approaches and the robustness of our model.

Branch and Bound Algorithm and an Improvement for Calculating the Nearest Link of Building a Railway Network

The importance of branch and bound algorithm is the mathematical improvement to find the value of (X) that Maximize or minimize the objective function within a set of feasible solution, as it is reliable on the efficient evaluation of the bounds of regions or branches of the space of the research, whether they are upper or lower. In this paper, we discussed five cases with respect to branching decisions based on network solutions to calculate the nearest link with a short time. From the results, bound and branch algorithm can develop and change the obtaining solutions for the five cases under study.

Alternative Branching Strategies in the Branch and Bound Algorithm by Using a k-clique covering vertex set for Maximum Clique Problems.

The Maximum clique problem (MCP) is graph theory problem that demand complete subgraf with maximum cardinality (maximum clique) in arbitrary graph. Solving MCP usually use Branch and Bound (BnB) algorithm, in this paper we will show how n + 1 color classes (where n is the difference between upper and lower bound) selected to form k-clique covering vertex set which later used for branching strategy can guarenteed finnding maximum clique.

Alternative Branching Strategies in the Branch and Bound Algorithm by Using a K-Clique Covering Vertex Set for Maximum Clique Problems

The maximum clique problem (MCP) is graph theory problem that demand complete subgraph with maximum cardinality (maximum clique) in arbitrary graph. Solving MCP usually use Branch and Bound (BnB) algorithm. In this paper, we will show how n + 1 color classes (where n is the difference between upper and lower bound) selected to form k-clique covering vertex set which later used for branching strategy can guarantee finding maximum clique.

Application of hyperoperations for engineering practice

This article presents some of the main points of the study for the practical application of various hyperoperations in engineering practice. The authors examined the use of hyperoperations in mathematical formalization of analytical solutions of branching algorithms, the use of new number formats for encoding information based on large numbers. The methods of applying hyperoperations considered by the authors allow them to be effectively used on modern microprocessor-based computers with a built-in mathematical coprocessor, which is an integral part of the processor core, which allows implementing algorithms based on operations of the order higher than “addition” and “subtraction”.

Matching Cut in Graphs with Large Minimum Degree

In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be {mathsf {NP}}-complete. While Matching Cut is trivial for graphs with minimum degree at most one, it is {mathsf {NP}}-complete on graphs with minimum degree two. In this paper, we show that, for any given constant c>1, Matching Cut is {mathsf {NP}}-complete in the class of graphs with minimum degree c and this restriction of Matching Cut has no subexponential-time algorithm in the number of vertices unless the Exponential-Time Hypothesis fails. We also show that, for any given constant epsilon >0, Matching Cut remains {mathsf {NP}}-complete in the class of n-vertex (bipartite) graphs with unbounded minimum degree delta >n^{1-epsilon }. We give an exact branching algorithm to solve Matching Cut for graphs with minimum degree delta ge 3 in O^*(lambda ^n) time, where lambda is the positive root of the polynomial x^{delta +1}-x^{delta }-1. Despite the hardness results, this is a very fast exact exponential-time algorithm for Matching Cut on graphs with large minimum degree; for instance, the running time is O^*(1.0099^n) on graphs with minimum degree delta ge 469. Complementing our hardness results, we show that, for any two fixed constants 1< c <4 and c^{prime }ge 0, Matching Cut is solvable in polynomial time for graphs with large minimum degree delta ge frac{1}{c}n-c^{prime }.