Branch-and-bound Research Articles

Rigorous performance assessment of the algorithms for resolving motor unit action potential superpositions

It is necessary to decompose the intra-muscular EMG signal to extract motor unit action potential (MUAP) waveforms and firing times. Some algorithms were proposed in the literature to resolve superimposed MUAPs, including Peel-Off (PO), branch and bound (BB), genetic algorithm (GA), and particle swarm optimization (PSO). This study aimed to compare these algorithms in terms of overall accuracy and running time. Two sets of two-to-five MUAP templates (set1: a wide range of energies, and set2: a high degree of similarity) were used. Such templates were time-shifted, and white Gaussian noise was added. A total of 1000 superpositions were simulated for each template and were resolved using PO (also, POI: interpolated PO), BB, GA, and PSO algorithms. The generalized estimating equation was used to identify which method significantly outperformed, while the overall rank product was used for overall ranking. The rankings were PSO, BB, GA, PO, and POI in the first, and BB, PSO, GA, PO, POI in the second set. The overall ranking was BB, PSO, GA, PO, and POI in the entire dataset. Although the BB algorithm is generally fast, there are cases where the BB algorithm is too slow and it is thus not suitable for real-time applications.

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.

Globally Optimal Camera Orientation Estimation from Line Correspondences by BnB algorithm

This letter is concerned with the problem of estimating camera orientation from a set of 2D/3D line correspondences, which is a major part of the Perspective-n-Line (PnL) problem. There are some cases that usually occur in real applications for PnL: the input line correspondences are corrupted by mismatches (a.k.a. outlier correspondences). The RANdom SAmple Consensus (RANSAC) algorithm is the de facto standard for solving outlier-contaminated PnL problems. However, RANSAC is a non-deterministic algorithm, which means that it produces a reasonable result only with a certain probability. Therefore, a PnL algorithm that could obtain a certifiably optimal solution from outlier-contaminated data is a matter of priority for some safety-critical applications. In this letter, we take a big step towards this goal by investigating globally optimal camera orientation estimation algorithms. Firstly, we decouple the rotation and translation estimation of a PnL problem by considering the geometrical property of the PnL problem. The Branch-and-Bound (BnB) algorithm is applied and it globally searches the entire rotation space to obtain the optimal camera orientation. To investigate the performance of our method, we tested the proposed algorithm on both synthetic and real data, and the results show that our algorithms can obtain the optimal camera orientation and are more robust than several state-of-the-art PnL methods.

Enabling Sustainable Underwater IoT Networks With Energy Harvesting: A Decentralized Reinforcement Learning Approach

In this article, we study an energy sustainable Internet-of-Underwater Things (IoUT) network with tidal energy harvesting. Specifically, an analytical model is first developed to analyze the performance of the IoUT network, characterizing the stochastic nature of energy harvesting and traffic demands of IoUT nodes, and the salient features of acoustic communication channels. It is found that the spatial uncertainty resulting from underwater acoustic communication may cause a severe fairness issue. As such, an optimization problem is formulated to maximize the network throughput under fairness constraints, by tuning the random access parameters of each node. Given the global network information, including the number of nodes, energy harvesting rates, communication distances, etc., the optimization problem can be efficiently solved with the Branch and Bound (BnB) method. Considering a realistic network where the network information may not be available at the IoUT nodes, we further propose a multiagent reinforcement learning approach for each node to autonomously adapt the random access parameter based on the interactions with the dynamic network environment. The numerical results show that the proposed learning algorithm greatly improves the throughput performance compared with the existing solutions, and approaches the derived theoretical bound.

Using Heuristic and Branch and Bound Methods to Solve a Multi-Criteria Machine Scheduling Problem

In this paper, we investigate some methods to solve one of the multi-criteria machine scheduling problems. The discussed problem is the total completion time and the total earliness jobs To solve this problem, some heuristic methods are proposed which provided good results. The Branch and Bound (BAB) method is applied with new suggested upper and lower bounds to solve the discussed problem, which produced exact results for in a reasonable time.

Efficient Similarity Point Set Registration by Transformation Decomposition.

Point set registration is one of the basic problems in computer vision. When the overlap ratio between point sets is small or the relative transformation is large, local methods cannot guarantee the accuracy. However, the time complexity of the branch and bound (BnB) optimization used in most existing global methods is exponential in the dimensionality of parameter space. Therefore, seven-Degrees of Freedom (7-DoF) similarity transformation is a big challenge for BnB. In this paper, a novel rotation and scale invariant feature is introduced to decouple the optimization of translation, rotation, and scale in similarity point set registration, so that BnB optimization can be done in two lower dimensional spaces. With the transformation decomposition, the translation is first estimated and then the rotation is optimized by maximizing a robust objective function defined on consensus set. Finally, the scale is estimated according to the potential correspondences in the obtained consensus set. Experiments on synthetic data and clinical data show that our method is approximately two orders of magnitude faster than the state-of-the-art global method and more accurate than a typical local method. When the outlier ratio with respect to the inliers is up to 1.0, our method still achieves accurate registration.

Relay Selection, Scheduling, and Power Control in Wireless-Powered Cooperative Communication Networks

Relay nodes are used to improve the throughput, delay and reliability performance of energy harvesting networks by assisting both energy and information transfer between sources and access point. Previous studies on radio frequency energy harvesting networks are limited to single-source-single/multiple-relay networks. In this paper, a novel joint relay selection, scheduling and power control problem for multiple-source-multiple-relay network is formulated with the objective of minimizing the total duration of wireless power and information transfer. The formulated problem is non-convex mixed-integer non-linear programming problem, and proven to be NP-hard. We first formulate a sub-problem on scheduling and power control for a given relay selection. We propose an efficient optimal algorithm based on a bi-level optimization over power transfer time allocation. Then, for optimal relay selection, we present optimal exponential-time Branch-and-Bound (BB) based algorithm where the nodes are pruned with problem specific lower and upper bounds. We also provide two BB-based heuristic approaches limiting the number of branches generated from a BB-node, and a relay criterion based lower complexity heuristic algorithm. The proposed algorithms are demonstrated to outperform conventional harvest-then-cooperate approaches with up to 87% lower schedule length for various network settings with at least 7.88 times higher algorithm runtime.

Operational Optimization of Integrated Energy System Based on Coordinated Complementary of Cold, Heat and Electricity Loads

Integrated Energy Systems (Integrated Energy System, IES) to pluripotent and complementary energy ladder as the core, will greatly improve the system’s energy efficiency, to achieve a variety of complementary energy flow optimization. By establishing a cold-heat-electricity integrated energy system, taking the lowest total operating cost of the system as the objective function, considering the equipment model constraints and power balance constraints, the day-to-day load simulation is used to optimize the economic operation of the integrated energy system; at the same time, the system operates in winter and summer. The operating conditions vary greatly, and the quarterly adjustment operation mode is adopted, and the branch and bound (BaB) algorithm is used to solve the optimization model. The simulation results show that the energy supply of the system is balanced, the “source-charge-storage” complementarity is strong, the system operates flexibly, cost-effectively, and at the same time, the system emits less polluting gas, which is beneficial to environmental protection.

Real-time pricing for smart grid with multi-energy microgrids and uncertain loads: a bilevel programming method

As distributed energy (DE) and storage devices being integrated into microgrids (MGs), demand side management (DSM) is getting more and more complicated. The real-time pricing (RTP) mechanism based on demand response (DR) is an ideal method for DSM, which can achieve supply–demand balance and maximize social welfare in the future. This paper proposes a hierarchical market framework to address RTP between the power supplier and multi-microgrids (MMGs). Firstly, an expectation bilevel model is proposed to adjust the energy scheduling of MMGs, including uncertain loads, multi-energy-supply and storage devices,etc. In the proposed bilevel model, the upper level aims to maximize the profit of the power supplier, while the lower level is formulated to maximize the expectation of total welfares for MMGs. Then, the lower level is transformed into a deterministic optimization problem by mathematical techniques. To solve the model, a hybrid algorithm-called distributed PSO-BBA, is put forward by combining the particle swarm optimization (PSO) and the branch and bound algorithm (BBA). In this algorithm, the PSO and BBA are employed to address the subproblems of upper and lower levels, respectively. Finally, simulations on several situations show that the proposed distributed RTP method is applicable and effective under uncertainties, and can reduce the computational complexity as well. The results show that the hierarchical energy dispatch framework is not only more reasonable but also can increase the profits of power suppliers and the welfare of MGs effectively.

Value-Based Hierarchical Information Collection for AUV-Enabled Internet of Underwater Things

The Internet of Underwater Things (IoUT) shows great potential in realizing the smart ocean. Underwater acoustic sensor networks (UWASNs) are the main existing form of IoUT but face with reliable data transmission problems. To tackle this issue, this article considers using the autonomous underwater vehicle (AUV) as a mobile collector to construct a reliable hierarchical information collection system while the Value of Information (VoI) is used as a main metric to measure the Quality of Information (QoI). We first establish a realistic model for characterizing the behaviors of AUV and sensor nodes as well as the challenging environments. Then, to construct a hierarchical architecture, we design a sink node (SN) selection scheme by jointly considering VoI conservation and energy load balancing. After that, we focus on AUV path planning with the objective of maximizing the VoI of the total network. We formulate the problem as a combinatorial optimization problem and provide an integer linear programming (ILP) model for this problem. An optimal algorithm based on the branch-and-bound (BB) method is proposed for seeking for the optimal solution, in which the lower bound and upper bound calculation strategies are specifically designed. Two near-optimal heuristic algorithms based on the concepts of the ant colony algorithm (ACA) and the genetic algorithm (GA) are also provided for further reducing the computation complexity. Finally, simulations validate the effectiveness of the proposed algorithms.

Tool for Simulating Branch and Bound Computations

AbstractThe paper describes a simulator of parallel Branch and Bound (BnB) method. Several subdomain trees for benchmark functions are analyzed, a characteristic Gaussian-like distribution is discovered. An algorithm of artificial tree generation is formulated according to this criterion. The process of simulator modeling is described, several computational experiments are conducted. Their results show a hyperbolic decrease trend for modeled time as the number of computational units grows, which is concluded to be similar to real systems.

A Learning Based Branch and Bound for Maximum Common Subgraph Related Problems

The performance of a branch-and-bound (BnB) algorithm for maximum common subgraph (MCS) problem and its related problems, like maximum common connected subgraph (MCCS) and induced Subgraph Isomorphism (SI), crucially depends on the branching heuristic. We propose a branching heuristic inspired from reinforcement learning with a goal of reaching a tree leaf as early as possible to greatly reduce the search tree size. Experimental results show that the proposed heuristic consistently and significantly improves the current best BnB algorithm for the MCS, MCCS and SI problems. An analysis is carried out to give insight on why and how reinforcement learning is useful in the new branching heuristic.

Risk-Aware Edge Computation Offloading Using Bayesian Stackelberg Game

Mobile Edge Computing (MEC) is delivering a rich portfolio of computation services to enable ultra-low latency and location-awareness for emerging mobile applications. However, the vulnerability of this new paradigm to potential security and privacy issues prevents mobile users from fully embracing its advantage. While various defensive strategies have been proposed to secure the connection between the end devices and edge servers, an equally important issue, the server-side risk is still under-investigated for most edge computing systems. To handle these server-side risks, a Risk-aware Computation Offloading (RCO) policy is proposed to distribute computation tasks safely among geographically distributed edge sites under server-side attacks. RCO takes into account the strategic behaviors of the potential attackers in the edge system and finds an appropriate balance between risk management and service delay reduction. The Bayesian Stackelberg game is employed to formulate the RCO problem, which describes an appropriate relation between the edge system (as a defender) and the attacker. In particular, the Bayesian Stackelberg game captures the uncertainty of attacker’s behavior and enables RCO to work even when the edge system does not know precisely the attacker that it is playing against. To facilitate the derivation of Stackelberg equilibria, two pruning rules, Heuristic Pruning (HP) and Branch-and-Bound (BaB), are proposed. HP prunes by analyzing the user demand distribution and attacker types, and BaB prunes by obtaining the tight upper/lower bound of edge system utility with the assist of disjunctive programming and Bender’s cut.

Point Set Registration for 3D Range Scans Using Fuzzy Cluster-Based Metric and Efficient Global Optimization.

This study presents a new point set registration method to align 3D range scans. In our method, fuzzy clusters are utilized to represent a scan, and the registration of two given scans is realized by minimizing a fuzzy weighted sum of the distances between their fuzzy cluster centers. This fuzzy cluster-based metric has a broad basin of convergence and is robust to noise. Moreover, this metric provides analytic gradients, allowing standard gradient-based algorithms to be applied for optimization. Based on this metric, the outlier issues are addressed. In addition, for the first time in rigid point set registration, a registration quality assessment in the absence of ground truth is provided. Furthermore, given specified rotation and translation spaces, we derive the upper and lower bounds of the fuzzy cluster-based metric and develop a branch-and-bound (BnB)-based optimization scheme, which can globally minimize the metric regardless of the initialization. This optimization scheme is performed in an efficient coarse-to-fine fashion: First, fuzzy clustering is applied to describe each of the two given scans by a small number of fuzzy clusters. Then, a global search, which integrates BnB and gradient-based algorithms, is implemented to achieve a coarse alignment for the two scans. During the global search, the registration quality assessment offers a beneficial stop criterion to detect whether a good result is obtained. Afterwards, a relatively large number of points of the two scans are directly taken as the fuzzy cluster centers, and then, the coarse solution is refined to be an exact alignment using the gradient-based local convergence. Compared to existing counterparts, this optimization scheme makes a large improvement in terms of robustness and efficiency by virtue of the fuzzy cluster-based metric and the registration quality assessment. In the experiments, the registration results of several 3D range scan pairs demonstrate the accuracy and effectiveness of the proposed method, as well as its superiority to state-of-the-art registration approaches.

Joint Beamforming Design and Receive Antenna Selection for Large-Scale MIMO Wiretap Channels

This paper investigates joint secure beamforming design and receive antenna selection problem for large-scale multiple-input-multiple-output (MIMO) wiretap channels. A Branch-And-Bound (BAB) based algorithm is utilized to search the optimal receive antenna subset under both perfect and imperfect channel state information (CSI) scenarios. First, for the perfect CSI scenario, we formulate the secrecy rate optimization problem, and an equivalent monotonically decreasing objective function is established to make the problem suitable for efficient BAB search. In each search, we propose using the weighted mean squared error minimization (WMMSE) method to tackle the optimization problem. Then, we generalize the framework to the imperfect CSI case, and the robust problem is designed to maximize the worst-case secrecy rate, the problem is challenging to solve due to the channel uncertainties. A cutting-set method is devised to solve this non-convex problem by updating the worst-case secrecy rate and channel uncertainties alternately. To reduce the design complexity, we also present an antenna selection based on the alternating optimization (AO) method. The validity of the proposed antenna selection algorithms is evaluated through numerical simulations.

Genetic Algorithm and Particle Swarm Optimization Techniques for Solving Multi-Objectives on Single Machine Scheduling Problem

In this paper, two of the local search algorithms are used (genetic algorithm and particle swarm optimization), in scheduling number of products (n jobs) on a single machine to minimize a multi-objective function which is denoted as (total completion time, total tardiness, total earliness and the total late work). A branch and bound (BAB) method is used for comparing the results for (n) jobs starting from (5-18). The results show that the two algorithms have found the optimal and near optimal solutions in an appropriate times.

Solving the Lexicographic Multi-Objective Mixed-Integer Linear Programming Problem using branch-and-bound and grossone methodology

In the previous work (see [1]) the authors have shown how to solve a Lexicographic Multi-Objective Linear Programming (LMOLP) problem using the Grossone methodology described in [2]. That algorithm, called GrossSimplex, was a generalization of the well-known simplex algorithm, able to deal numerically with infinitesimal/infinite quantities.The aim of this work is to provide an algorithm able to solve a similar problem, with the addition of the constraint that some of the decision variables have to be integer. We have called this problem LMOMILP (Lexicographic Multi-Objective Mixed-Integer Linear Programming).This new problem is solved by introducing the GrossBB algorithm, which is a generalization of the Branch-and-Bound (BB) algorithm. The new method is able to deal with lower-bound and upper-bound estimates which involve infinite and infinitesimal numbers (namely, Grossone-based numbers). After providing theoretical conditions for its correctness, it is shown how the new method can be coupled with the GrossSimplex algorithm described in [1], to solve the original LMOMILP problem. To illustrate how the proposed algorithm finds the optimal solution, a series of LMOMILP benchmarks having a known solution is introduced. In particular, it is shown that the GrossBB combined with the GrossSimplex is able solve the proposed LMOMILP test problems with up to 200 objectives.

Globally Optimal Vertical Direction Estimation in Atlanta World.

In man-made environments, most of the objects and structures are organized in the form of orthogonal and parallel planes. These planes can be approximated by an Atlanta world assumption, in which the normals of planes can be represented by Atlanta frames. The Atlanta world assumption has one vertical frame and multiple horizontal frames. Conventionally, given a set of inputs such as surface normals, the Atlanta frame estimation problem can be solved by a branch-and-bound (BnB) algorithm. However, the runtime of the BnB algorithm will increase greatly when the dimensionality (i.e., the number of horizontal frames) increases. In this paper, we estimate only the vertical direction, instead of all Atlanta frames at once. Accordingly, we propose a vertical direction estimation method by considering the relationship between the vertical frame and horizontal frames. Concretely, our approach employs a BnB algorithm to search the vertical direction, thereby guaranteeing global optimality without requiring prior knowledge of the number of Atlanta frames. In order to guarantee convergence, four novel bounds are investigated, by mapping a 3D hemisphere to a 2D region. We verify the feasibility of the proposed method using various challenging synthetic and real-world data.

Multi-Objective Optimization of Green Small Cell Allocation for IoT Applications in Smart City

Small cells (SCs) have proven their marvelous capability, especially dealing with high density of user equipment (UE) in the configuration of Internet of Things (IoT). It is widely accepted that the SCs concept is one of the prospective solutions for 5G networks, specifically targeting IoT, to attain the high demand in the future smart city. SC deployment has attracted the attention of multiple research efforts, due to its importance and potential towards enhancing future networking for IoT. However, there is still a lack of works providing SC allocation with comprehensive optimization modeling, which provides essential infrastructural platform to SC functionalities and services (e.g. offloading). The analysis of the number and positions of SCs, towards the simultaneous optimization of both energy efficiency and data rates, is a highly required research direction. SC allocation facilitates the sustainability and reliability, to support exponentially increasing number of users, as well as yielding feasibility of achieving high traffic demand and low latency performance, in addition to longer sustainability based on enhanced energy efficiency. In this paper, a smart small cell allocation scheme is proposed for IoT in smart city. Integer programming multi-objective optimization problem is formulated, and a new algorithm, based on the fusion of Branch-and-Bound (BnB) and Non-Dominated Sorting Genetic Algorithm II (NSGA-II), is developed. Energy efficiency optimization and data rate maximization are formulated, as mutual objectives to fulfill the key demands of IoT in smart city, based on the estimation of users' behaviors. Simulations are conducted, whose results show that the proposed Smart-SC allocation outperforms the different considered benchmarks, resulting in higher offered data rates, while achieving better energy efficiency.