Binary Problem Research Articles

Calculating Global Minimum Points to Binary Polynomial Optimization Problem: Optimizing the Optimal PMU Localization Problem as a Case-Study

State estimation (SE) is an algorithmic function of an energy management system (EMS). SE provides an actual-time monitoring and control of modern electrical power grids. State Estimation can be worked with sufficiency using Phasor Measurement Units optimally placed within a power grid. This paper concerns the implementation of proper algorithms embedded in optimization solvers to the optimal PMU localization problem solving globally. The optimization model is formulated as a 0 - 1 nonlinear minimization problem. The problem is transformed to a polyhedron using linearization methods and B&B tree. In this model, we use a linear cost function under polynomial constraints and binary restrictions on the design variables in a symbolic format. This mathematical model is programmed in the YALMIP environment which is fully compatible with MATLAB. The 0 - 1 Nonlinear Programming (NLP) model is suitable for getting concisely global optimal solutions. The optimal solution is given by a wrapped optimization engine including a local optimizer routine performing together with a mixed-Integer-Linear Programming routine. The solution is achieved within a zero-gap precisely encountered during the iterative process. This tolerance criterion is a necessity for a successful implementation of the B&B tree because it ensures global optimality with an acceptance relative gap. The minimization model is implemented in a YALMIP code fully compatible with MATLAB in two stages. Initially, an objective function with one term is minimized to discover a number of sensors for wide-area monitoring, control and state estimator applications. Then, an extra product is considered in the objective to suffice maximum reliability for observing the network buses. The numerical minimization models are applied to standard power networks in the direction to be solved globally.

Improved cooperative Ant Colony Optimization for the solution of binary combinatorial optimization applications

AbstractBinary combinatorial optimization plays a crucial role in various scientific and engineering fields. While deterministic approaches have traditionally been used to solve these problems, stochastic methods, particularly metaheuristics, have gained popularity in recent years for efficiently handling large problem instances. Ant Colony Optimization (ACO) is among the most successful metaheuristics and is frequently employed in non‐binary combinatorial problems due to its adaptability. Although for binary combinatorial problems ACO can suffer from issues such as rapid convergence to local minima, its eminently parallel structure means that it can be exploited to solve large and complex problems also in this field. In order to provide a versatile ACO implementation that achieves competitive results across a wide range of binary combinatorial optimization problems, we introduce a parallel multicolony strategy with an improved cooperation scheme to maintain search diversity. We evaluate our proposal (Binary Parallel Cooperative ACO, BiPCACO) using a comprehensive benchmark framework, showcasing its performance and, most importantly, its flexibility as a successful all‐purpose solver for binary combinatorial problems.

Landscape approximation of low-energy solutions to binary optimization problems

Landscape approximation of low-energy solutions to binary optimization problems

MultiClassMetabo: A Superior Classification Model Constructed Using Metabolic Markers in Multiclass Metabolomics.

Multiclass metabolomics has become a popular technique for revealing the mechanisms underlying certain physiological processes, different tumor types, or different therapeutic responses. In multiclass metabolomics, it is highly important to uncover the underlying biological information on biosamples by identifying the metabolic markers with the most associations and classifying the different sample classes. The classification problem of multiclass metabolomics is more difficult than that of the binary problem. To date, various methods exist for constructing classification models and identifying metabolic markers consisting of well-established techniques and newly emerging machine learning algorithms. However, how to construct a superior classification model using these methods remains unclear for a given multiclass metabolomic data set. Herein, MultiClassMetabo has been developed for constructing a superior classification model using metabolic markers identified in multiclass metabolomics. MultiClassMetabo can enable online services, including (a) identifying metabolic markers by marker identification methods, (b) constructing classification models by classification methods, and (c) performing a comprehensive assessment from multiple perspectives to construct a superior classification model for multiclass metabolomics. In summary, MultiClassMetabo is distinguished for its capability to construct a superior classification model using the most appropriate method through a comprehensive assessment, which makes it an important complement to other available tools in multiclass metabolomics. MultiClassMetabo can be accessed at http://idrblab.cn/multiclassmetabo/.

Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics

Chaotic maps are sources of randomness formed by a set of rules and chaotic variables. They have been incorporated into metaheuristics because they improve the balance of exploration and exploitation, and with this, they allow one to obtain better results. In the present work, chaotic maps are used to modify the behavior of the binarization rules that allow continuous metaheuristics to solve binary combinatorial optimization problems. In particular, seven different chaotic maps, three different binarization rules, and three continuous metaheuristics are used, which are the Sine Cosine Algorithm, Grey Wolf Optimizer, and Whale Optimization Algorithm. A classic combinatorial optimization problem is solved: the 0-1 Knapsack Problem. Experimental results indicate that chaotic maps have an impact on the binarization rule, leading to better results. Specifically, experiments incorporating the standard binarization rule and the complement binarization rule performed better than experiments incorporating the elitist binarization rule. The experiment with the best results was STD_TENT, which uses the standard binarization rule and the tent chaotic map.

Self-stabilizing indulgent zero-degrading binary consensus

Guerraoui proposed an indulgent solution for the binary consensus problem. Namely, he showed that an arbitrary behavior of the failure detector never violates safety requirements even if it compromises liveness. Consensus implementations are often used in a repeated manner. Dutta and Guerraoui proposed a zero-degrading solution, i.e., during system runs in which the failure detector behaves perfectly, a node failure during one consensus instance has no impact on the performance of future instances.Our study, which focuses on indulgent zero-degrading binary consensus, aims at the design of an even more robust communication abstraction. We do so through the lenses of self-stabilization—a very strong notion of fault-tolerance. In addition to node and communication failures, self-stabilizing algorithms can recover after the occurrence of arbitrary transient faults; these faults represent any violation of the assumptions according to which the system was designed to operate (as long as the algorithm code stays intact).This work proposes the first, to the best of our knowledge, self-stabilizing algorithm for indulgent zero-degrading binary consensus for time-free message-passing systems prone to detectable process failures. The proposed algorithm recovers within a finite time after the occurrence of the last arbitrary transient fault. Since the proposed solution uses an Ω failure detector, we also present the first, to the best of our knowledge, self-stabilizing asynchronous Ω failure detector, which is a variation on the one by Mostéfaoui, Mourgaya, and Raynal.

COMIC: An unsupervised change detection method for heterogeneous remote sensing images based on copula mixtures and Cycle-Consistent Adversarial Networks

In this paper, we consider the problem of change detection (CD) with two heterogeneous remote sensing (RS) images. For this problem, an unsupervised change detection method has been proposed recently based on the image translation technique of Cycle-Consistent Adversarial Networks (CycleGANs), where one image is translated from its original modality to the modality of the other image so that the difference map can be obtained by performing arithmetical subtraction. However, the difference map derived from subtraction is susceptible to image translation errors, in which case the changed area and the unchanged area are less distinguishable. To overcome the above shortcoming, we propose a new unsupervised copula mixture and CycleGAN-based CD method (COMIC), which combines the advantages of copula mixtures on statistical modeling and the advantages of CycleGANs on data mining. In COMIC, the pre-event image is first translated from its original modality to the post-event image modality. After that, by constructing a copula mixture, the joint distribution of the features from the heterogeneous images can be learnt according to quantitive analysis of the dependence structure based on the translated image and the original pre-event image, which are of the same modality and contain totally the same objects. Then, we model the CD problem as a binary hypothesis testing problem and derive its test statistics based on the constructed copula mixture. Finally, the difference map can be obtained from the test statistics and the binary change map (BCM) is generated by K-means clustering. We perform experiments on real RS datasets, which demonstrate the superiority of COMIC over the state-of-the-art methods.

Linearizing Binary Optimization Problems Using Variable Posets for Ising Machines

Linearizing Binary Optimization Problems Using Variable Posets for Ising Machines

Fixed-point Grover Adaptive Search for Quadratic Binary Optimization Problems

Fixed-point Grover Adaptive Search for Quadratic Binary Optimization Problems

Testing initial solutions in a variable neighbourhood search for binary integer programming problems

Testing initial solutions in a variable neighbourhood search for binary integer programming problems

Automated Design of Collaboration-Based Hybrid Metaheuristics.

Hybridization plays a prominent role in bolstering the performance of optimization algorithms (OAs), yet designing efficient hybrid OAs tailored to intricate optimization problems persists as a formidable task. This article introduces a novel top-down methodology for the automated design of hybrid OAs, treating algorithm design as a meta-optimization problem. A general design template for collaboration-based hybrid OAs is developed, integrating a multitude of hybridization strategies for the first time. Besides, a mathematical model is built to formulate the meta-optimization problem of algorithm design. To address the meta-optimization challenge, an improved multifactorial evolutionary algorithm is proposed to automatically design efficient hybrid metaheuristics in a multitasking environment for the given instances with diverse features. To verify the effectiveness of the proposed design methodology, it is applied to the CEC2017 benchmark functions and the binary knapsack problem. Numerical results have demonstrated the feasibility and effectiveness of the proposed methodology for both continuous and combinatorial optimization benchmarks.

Multiobjective ranking binary artificial bee colony for gene selection problems using microarray datasets

Microarray cancer gene expression datasets are high dimensional and complex for efficient computational analysis. Thus, selecting high discriminative genes from microarray data has become increasingly interesting in the field of bioinformatics. This article addresses the problem of designing a gene selection algorithm which is modeled as a multiobjective optimization problem with the sensitivity, specificity and the number of selected genes. Then, a multi-objective ranking binary artificial bee colony algorithm based on decomposition is proposed to select the optimal subset of dimensions from the original high dimensional data while retaining a subset that satisfies the defined objective. First, the Fisher-Markov selector is used to choose a fixed number of microarray data. Second, to make artificial bee colony algorithm suitable for the binary problem, a novel binary update strategy is proposed to balance the exploration and exploitation ability. Third, multi-objective ranking binary artificial bee colony algorithm is proposed by integrating tchebycheff approach into the ranking binary artificial bee colony algorithm. Finally, the multi-objective ranking binary artificial bee colony algorithm based on decomposition (MORBABC/D) method is used for feature selection, and extreme learning machine is used as the classifier with 10 fold cross-validation method. In order to show the effectiveness and efficiency of the algorithm, the proposed algorithm is tested on eight microarray dataset. Experimental studies have been carried out to investigate the ability of the proposed algorithm.

Earthquake forecast by imbalance machine learning using geophysical predictors

In the present paper we consider the earthquake forecast as a binary problem of machine learning on the imbalanced data base applied to five regions of Georgia. For the training we used geophysical data base collected in 2017-2021, namely, variations of statistical characteristics of geomagnetic field components, seismic activity, water level in deep boreholes and tides. In this version a new predictor – the weighted seismic activity for previous 5 days - – is added compared to the predictors’ list used in previous papers. Besides, the length of the used database is increased 3 times compared to the earlier results. As in the database the earthquakes of M > 3.5 are rare, the number of negative cases is large (there are many days without EQs of M > 3.5), meaning that there is a strong imbalance between positive and negative cases of the order of 1:20; we apply the specific methodology Matthews’ correlation coefficient (MCC) and F1 score to avoid the strong imbalance effect.

An improved binary particle swarm optimization algorithm for clinical cancer biomarker identification in microarray data

Background and ObjectiveThe limited number of samples and high-dimensional features in microarray data make selecting a small number of features for disease diagnosis a challenging problem. Traditional feature selection methods based on evolutionary algorithms are difficult to search for the optimal set of features in a limited time when dealing with the high-dimensional feature selection problem. New solutions are proposed to solve the above problems. MethodsIn this paper, we propose a hybrid feature selection method (C-IFBPFE) for biomarker identification in microarray data, which combines clustering and improved binary particle swarm optimization while incorporating an embedded feature elimination strategy. Firstly, an adaptive redundant feature judgment method based on correlation clustering is proposed for feature screening to reduce the search space in the subsequent stage. Secondly, we propose an improved flipping probability-based binary particle swarm optimization (IFBPSO), better applicable to the binary particle swarm optimization problem. Finally, we also design a new feature elimination (FE) strategy embedded in the binary particle swarm optimization algorithm. This strategy gradually removes poorer features during iterations to reduce the number of features and improve accuracy. ResultsWe compared C-IFBPFE with other published hybrid feature selection methods on eight public datasets and analyzed the impact of each improvement. The proposed method outperforms other current state-of-the-art feature selection methods in terms of accuracy, number of features, sensitivity, and specificity. The ablation study of this method validates the efficacy of each component, especially the proposed feature elimination strategy significantly improves the performance of the algorithm. ConclusionsThe hybrid feature selection method proposed in this paper helps address the issue of high-dimensional microarray data with few samples. It can select a small subset of features and achieve high classification accuracy on microarray datasets. Additionally, independent validation of the selected features shows that those chosen by C-IFBPFE have strong correlations with disease phenotypes and can identify important biomarkers from data related to biomedical problems.

Augmenting an electronic Ising machine to effectively solve boolean satisfiability

With the slowdown of improvement in conventional von Neumann systems, increasing attention is paid to novel paradigms such as Ising machines. They have very different approach to solving combinatorial optimization problems. Ising machines have shown great potential in solving binary optimization problems like MaxCut. In this paper, we present an analysis of these systems in boolean satisfiability (SAT) problems. We demonstrate that, in the case of 3-SAT, a basic architecture fails to produce meaningful acceleration, largely due to the relentless progress made in conventional SAT solvers. Nevertheless, careful analysis attributes part of the failure to the lack of two important components: cubic interactions and efficient randomization heuristics. To overcome these limitations, we add proper architectural support for cubic interaction on a state-of-the-art Ising machine. More importantly, we propose a novel semantic-aware annealing schedule that makes the search-space navigation much more efficient than existing annealing heuristics. Using numerical simulations, we show that such an “Augmented” Ising Machine for SAT is projected to outperform state-of-the-art software-based, GPU-based and conventional hardware SAT solvers by orders of magnitude.

A two-phase method for compaction path planning and control of the impact roller

Compaction efficiency and quality are extraordinarily significant for branch-line airport construction engineering. However, a human-determined compaction path is generally adopted during the compaction, negatively impacting compaction efficiency and quality. A two-phase approach to the compaction path is proposed to address the problem. The first phase focuses on the establishment of a model to optimize the impact roller’s complete-coverage compaction path (CCCP) to improve compaction efficiency. In this phase, the optimization problem of the CCCP is equivalent to the traveling salesman problem (TSP). Next, the optimization of the CCCP is formulated and solved as a binary integer programming problem. Finally, a method for determining the optimal traversal compaction sequence is proposed to obtain the optimal CCCP based on the secondary development of the Gurobi optimizer. In the second phase, to guarantee the compaction quality, the path navigation modulus is designed to precisely control the compaction path. Combining the compaction path planning with the path control, an integrated system is developed to provide a better service for practical earthwork compaction engineering in airport construction. The results of the simulation experiment and field experiment indicate that the CCCP determined by the proposed optimization method in the first phase can improve the compaction efficiency compared to the human-determined compaction path. In addition, the developed system can effectively generate the CCCP. Meanwhile, the developed system can provide a visual path navigation and precise path control during the compaction to ensure the compaction quality, verifying that the proposed method can offer a novel idea for compaction path control.

Individual subject evaluated difficulty of adjustable mazes generated using quantum annealing

In this study, the maze generation using quantum annealing is proposed. We reformulate a standard algorithm to generate a maze into a specific form of a quadratic unconstrained binary optimization problem suitable for the input of the quantum annealer. To generate more difficulty mazes, we introduce an additional cost function Qupdate to increase the difficulty. The difficulty of the mazes was evaluated by the time to solve the maze of 12 human subjects. To check the efficiency of our scheme to create the maze, we investigated the time-to-solution of a quantum processing unit, classical computer, and hybrid solver. The results show that Qupdate generates difficult mazes tailored to the individual. Furthermore, it show that the quantum processing unit is more efficient at generating mazes than other solvers. Finally, we also present applications how our results could be used in the future.

A Hybrid Lane Detection Model for Wild Road Conditions

This paper presents a lane detection system in unstructured, complex environments in real time. We formulated lane detection as a binary segmentation problem and proposed a novel hybrid Convolutional Neural Network (CNN) architecture by fusing encoder-decoder network with a sequence of dilated convolution network. We computed weighted average of outputs of these branches for lane detection and introduced a new loss function for binary semantic segmentation to counter the imbalance between lane and non-lane pixels. The proposed model achieved 95.19% accuracy on TuSimple dataset. To evaluate the system with respect to unstructured road scenarios, we created an Indian Lane Dataset (ILD) with 6149 labelled images from India Driving Dataset (IDD). We reported mIoU (Intersection Over Union) of 0.31 on IDD which was higher than other state-of-the art lane detection models. Finally, we undertook an ablation study to understand effectiveness of two parallel branches, i.e., encoder-decoder and dilated convolution branches and the proposed loss function.

Cutting-Edge Trajectory Optimization through Quantum Annealing

This paper introduces an innovative approach to explore the capabilities of Quantum Annealing (QA) for trajectory optimization in dynamic systems. The proposed method involves transforming trajectory optimization problems into equivalent binary optimization problems using Quadratic Unconstrained Binary Optimization (QUBO) representation. The procedure is general and adaptable, making it applicable to a wide range of optimal control problems that entail the satisfaction of dynamic, boundary, and path constraints. Specifically, the trajectory is discretized and approximated using polynomials. In contrast to the conventional approach of determining the polynomial degree (n) solely based on the number of boundary conditions, a specific factor is introduced in our method to augment the polynomial degree. As a result, the ultimate polynomial degree is calculated as a composite of two components: n = l + (m−1), where m denotes the count of boundary conditions and l signifies the number of independent variables. By leveraging inverse dynamics, the control required to follow the approximated trajectory can be determined as a linear function of independent variables l. As a result, the optimization function, which is represented by the integral of the square of the control, can be formulated as a QUBO problem and the QA is employed to find the optimal binary solutions.

Classifying Tensile Loading History of Continuous Carbon Fiber Composites Using X‐Ray Scattering and Machine Learning

The tensile loading history of continuous carbon fiber composites is classified using machine learning (ML) and crystallographic data from the polymer matrix. Composites with polyamide‐4,10 matrix and unidirectional 10° and 45°, and 0°/90° cross‐ply layups are subjected to single‐cycle uniaxial tensile loads corresponding to 25–90% of their nominal maximum strain, and mapped by X‐ray diffraction with approximately 1000 data points from each layup. The unit cell alterations are used as a feature set for optimizing three ML algorithms; linear discriminant analysis, support vector machines (SVM), and gradient‐boosted decision trees (GBDT), with the objective of predicting five discrete loading magnitudes of the respective layups. It is demonstrated that SVMs and GBDTs can be trained to achieve a classification accuracy of >90% on unseen test data, both in cases where the feature set consists of data points from individual layups only, but also when data from the three layups are aggregated. The performance of the models is also shown to be similar to a binary problem, in which the composites are categorized according to a threshold load.