Binary Problem Research Articles

Branch and price for submodular bin packing

The Submodular Bin Packing (SMBP) problem asks for packing unsplittable items into a minimal number of bins for which the capacity utilization function is submodular. SMBP is equivalent to chance-constrained and robust bin packing problems under various conditions. SMBP is a hard binary nonlinear programming optimization problem. In this paper, we propose a branch-and-price algorithm to solve this problem. The resulting price subproblems are submodular knapsack problems, and we propose a tailored exact branch-and-cut algorithm based on a piece-wise linear relaxation to solve them. To speed up column generation, we develop a hybrid pricing strategy to replace the exact pricing algorithm with a fast pricing heuristic. We test our algorithms on instances generated as suggested in the literature. The computational results show the efficiency of our branch-and-price algorithm and the proposed pricing techniques.

Integrated mathematical optimisation approach for the tower crane hook routing problem to satisfy material demand requests on-site

Optimising decisions around the location and operation of tower cranes can improve the workflow in construction projects. Traditionally, the location and allocation problems involved in tower crane operations in the literature have been solved separately from the assignment of material supply points to demand points and the scheduling of the crane’s activity sequence across supply and demand points on a construction site. To address the gap, this paper proposes a binary integer programming problem, where location of the tower crane, allocation of supply points to material-demanding regions, and routing of hook of the crane based on activity sequencing of the hook across supply and material-demanding regions on site are optimised. The novelty in this work is in the way the crane’s activity scheduling is modelled via mathematical programming, based on routing the hook movement to meet material demand, through minimising tower crane operating costs. A realistic case study is solved to assess the validity of the model. The model is contrasted with results obtained from other solving algorithms commonly adopted in the literature, along with a solution proposed by an experienced practitioner. Results indicate that all instances can be solved when compared to other meta-heuristics that fail to achieve an optimum solution. Compared to the solution proposed by the practitioner, the results of the proposed model achieve a 46% improvement in objective function value. Planners should optimise decisions related to the location of the crane, the crane’s hook movement to meet service requests, and supply points’ locations and assignment to material-demanding regions simultaneously for effective crane operations.

Optimizing over the efficient set of the binary bi-objective knapsack problem

This paper deals with the problem of optimizing a linear function over the efficient set of a 0-1 bi-objective knapsack problem. Such a function represents the main criterion of the problem posed. The resolution process is based essentially on dynamic programming. The proposed method provides a subset of efficient solutions including one which optimizes the main criterion without having to enumerate all the efficient solutions of the problem. Numerical experiments are reported, different instances with large sizes of the associated efficient sets are considered to show the efficiency of our algorithm compared with an approach proposed in the literature.

Fault-Tolerant Cooperative Signal Detection for Petahertz Short-Range Communication With Continuous Waveform Wideband Detectors

Motivated by unique scattering properties at petahertz frequencies, we present a novel statistical model of fault-tolerant cooperative signal detection for short-range optical petahertz wireless communications, where a single-scattering assumption holds valid. We characterize the received non-line-of-sight (NLOS) signal by a fault-tolerant continuous waveform wideband detector with a non-zero failure probability. To better reflect the physical properties of the petahertz communication, both signal-independent and signal-dependent noise sources are considered in characterizing the received signal. The distribution of the received signal is quantified with each scattered path following the Málaga distribution. We leverage the location flexibility of randomly distributed collaborative users, considering each user experiences an independent channel condition. Utilizing the Neyman-Pearson criterion, we develop the binary hypothesis testing problem and subsequently derive the likelihood ratio for the test statistics. Moreover, to quantify the performance, a framework is developed for the average area under the receiver operating characteristic (ROC) curve for both single user and cooperative scenarios. An optimal decision fusion with a majority rule for fault-tolerant signal detection is applied to exploit the maximum spectrum opportunity. It is found that with the optimal voting rule and for a given target error rate, the network requires fewer collaborative secondary users than the total number of users available in an optical network. However, in the limiting case, it is shown that, as the cost function approaches its minimum or maximum value within its allowable range, the optimal number of collaborative users becomes independent of the failure probabilities. With the realistic assumption of fault-tolerant users, it is found that the false alarm probability increases faster than the detection probability.

Dendritic Cell Algorithm with Grouping Genetic Algorithm for Input Signal Generation

The artificial immune system, an excellent prototype for developing Machine Learning, is inspired by the function of the powerful natural immune system. As one of the prevalent classifiers, the Dendritic Cell Algorithm (DCA) has been widely used to solve binary problems in the real world. The classification of DCA depends on a data pre-processing procedure to generate input signals, where feature selection and signal categorization are the main work. However, the results of these studies also show that the signal generation of DCA is relatively weak, and all of them utilized a filter strategy to remove unimportant attributes. Ignoring filtered features and applying expertise may not produce an optimal classification result. To overcome these limitations, this study models feature selection and signal categorization into feature grouping problems. This study hybridizes Grouping Genetic Algorithm (GGA) with DCA to propose a novel DCA version, GGA-DCA, for accomplishing feature selection and signal categorization in a search process. The GGA-DCA aims to search for the optimal feature grouping scheme without expertise automatically. In this study, the data coding and operators of GGA are redefined for grouping tasks. The experimental results show that the proposed algorithm has significant advantages over the compared DCA expansion algorithms in terms of signal generation.

Robust Dynamic TEP With an Security Criterion: A Computationally Efficient Model

This paper presents a hybrid column-and-constraint-generation augmented-Lagrangian algorithm to efficiently solve the robust security-constrained dynamic transmission expansion planning (TEP) problem. The column-and-constraint generation algorithm separates the TEP problem into a master problem and a set of subproblems decomposable by time period. Additionally, the computationally expensive master problem is decomposed into three computationally efficient sub-master problems: an upper-master quadratic problem, a middle-master quadratic unconstrained binary problem, and a lower-master quadratic unconstrained problem. A set of auxiliary variables are used to relax as real ones the binary variables corresponding to the status of candidate transmission lines enabling the master problem decomposition. The solutions of the three sub-master problems are coordinated using a three-block alternating direction method of multipliers algorithm to enforce binary variables to be binary. An initialization strategy based on load shedding is used to enhance the performance of the proposed algorithm. Simulation results on the IEEE 118-bus test system show the efficient performance of the proposed algorithm for solving security-constrained dynamic TEP problems.

A new Classifier Chain method of BERT Models For Multi-label Classification of Arabic Abusive Language on Social Media

Moving beyond classical single-label classification tasks proves to be crucial nowadays since the majority of real-life problems are inherently multi-label. Various tasks require involving, for one single instance as an input, several classes simultaneously or none of them. Particularly, detecting abusive texts in Arabic social networks intuitively carries several manifestations with regard to the targets’ referred characteristics like gender, race, sexual orientation, etc. Existing multi-label algorithms either invest considerable complexity to handle labels’ correlation or explicitly ignore this information to deal with each label as an independent binary problem. To remedy the abovementioned problems, this paper proposes a new multi-label classification solution based on deep neural networks. The main idea is to exploit the correlation between all the dataset's labels to break it into ordered subsets. Then, follow that order to implement a chain of BERT classifiers. Each classifier is therefore trained on a corresponding subset and passes its output via feature space to the following one. For a new instance, we gather all the classifiers’ results and pick the best one for each class. Experiments showed that our approach significantly outperformed the single classifier's method using BERT as well as other neural network architectures on our Arabic abusive language dataset. 91%,76%, and 82% were achieved respectively for precision, recall, and F1-score. Moreover, we further investigated the performance of our approach on Kaggle multi-label research paper dataset and achieved very promising results.

Development of a Prototype Sensory Device as a Substitute for Single Sided Deaf People in Developing Nations

Hearing loss is the inability to hear sounds ranging from 20 decibels or more in one or both ears. It can affect one or both ears and leads to difficulty in hearing speech or sounds in general. Single-sided deafness or unilateral hearing loss is a very widespread disability. However, most people only see hearing loss as being a binary problem assuming that you either have perfect hearing in both ears or are completely deaf in both ears, and dismiss the other types of hearing loss. Sensory substitution involves remapping the information gathered by one sensory receptor to another. Sensory receptors regardless of the signals they receive or capture, all encode the gathered information as electrochemical signals. This biological property of sensory receptors, coupled with the human brain’s neuroplasticity allows sensory receptors to be substituted, giving rise to new methods of sensory perception. This study aims to develop a sensory device known as a localizer. The localizer detects sound using numerous sound sensors, and feeds the input to the microcontrollers which then use the input to control the eccentric mass motor by implementing various motor drivers. The results gotten from this prototype device shows great improvement in the ability of a single-sided deaf person to localize sound.

Communication-Affinity Aware Colocation and Merging of Containers

Microservice architecture relies on message passing between services. Inter-service communication introduces an overhead to the applications’ overall performance. This overhead depends on the runtime placement of the services bundled in containers and it can be reduced by intelligently deploying the containers by considering the communication affinities between services. Researchers have attempted to colocate microservices and merge containers based on affinities. However, container merging has not been considered up to now. This study shows that the problem of service placement in a microservice application considering communication affinities, constrained by computational resources, can be mapped to an instance of the Binary Knapsack Problem. We propose a container colocation and merging mechanism based on a heuristic solution to the Binary Knapsack Problem. The proposed approach reduced the communication overhead of a benchmark application by 58.5% and as a result, execution time was reduced by approximately 13.4% as well.

Continuous Metaheuristics for Binary Optimization Problems: An Updated Systematic Literature Review

For years, extensive research has been in the binarization of continuous metaheuristics for solving binary-domain combinatorial problems. This paper is a continuation of a previous review and seeks to draw a comprehensive picture of the various ways to binarize this type of metaheuristics; the study uses a standard systematic review consisting of the analysis of 512 publications from 2017 to January 2022 (5 years). The work will provide a theoretical foundation for novice researchers tackling combinatorial optimization using metaheuristic algorithms and for expert researchers analyzing the binarization mechanism’s impact on the metaheuristic algorithms’ performance. Structuring this information allows for improving the results of metaheuristics and broadening the spectrum of binary problems to be solved. We can conclude from this study that there is no single general technique capable of efficient binarization; instead, there are multiple forms with different performances.

Accuracy recovery: A decomposition procedure for the synthesis of partially-specified Boolean functions

Logic Synthesis From Partial Specifications (LSFPS) is the problem of finding the hardware implementation of a Boolean function from a partial knowledge of its care set. The elements missing from the specifications are named don’t knows. The exact solution of LSFPS is the minimum size circuit of the corresponding problem in which the don’t knows set is void. Hence, in addition to the traditional objective of size minimization, the goal is to maximize the test accuracy, i.e., the accuracy of the circuit when evaluated over a subset of the don’t knows. This problem is relevant because efficient solutions can lead to hardware friendly machine learning models, not relying on black-box approaches. Indeed, LSFPS maps directly to the problem of the automatic generation of optimized topologies for Binarized Neural Networks. Furthermore, combining the exact solution with modern logic synthesis techniques would unlock unprecedented optimization capabilities. Previous works proved the effectiveness of approximate logic synthesis (ALS) for designing circuits with high test accuracy. Nonetheless, these methods sacrifice accuracy on the specifications, which banishes them from the legitimate candidates for LSFPS. In this paper, we propose accuracy recovery, a procedure to map an approximate version of the circuit to a new one that satisfies the exact functionality of the specifications. The proposed approach relies on an extension of a disjoint support decomposition algorithm. Relative experiments on the IWLS2020 benchmarks show that, on average, the addition of the designed decomposition to a synthesis flow reduces by 17.38% the number of gates and by 12.02% the depth. The usage of accuracy recovery, based on such a decomposition, yields a 95.73% accuracy in the binary MNIST problem, beating the state-of-the-art in ALS of 92.76%.

Nonlinear Integer Programming for Solving Preventive Maintenance Scheduling Problem for Cogeneration Plants with Production

Preventive maintenance (PM) is a maintenance program with activities created at a determined interval or according to certain principles, designed to reduce the likelihood of failure or deterioration of item performance. This aims to improve overall reliability and system availability. In this research, a preventive maintenance schedule (PMS) was designed for electricity and desalination of water in power plants, subject to meeting relevant constraints. The proposed methodology is used to generate a PMS for the boilers, turbines, and distillers. A nonlinear integer programming (NLIP) model was employed to address this problem. The results of the proposed method were compared with the PMS for a power station in Kuwait. The results were better in terms of the volume of production and in terms of the gap between the available production and demand in order to continue providing consumers with electricity and water without a shortage in the event of a breakdown in equipment. It produces an improvement of 12.12% and 16.58% respectively, for water and electricity. Furthermore, the sensitivity and robustness of the proposed method were analysed by increasing the maintenance duration for some equipment, increasing the demand, and adding various additional conditions. In addition, a comparison of additional conditions with a binary problem method in terms of computer time for the search for an optimal solution was carried out, where the model provided an optimal solution in a reasonable time. Among the most important benefits that the user can obtain for this technique are extending the life of the equipment, increasing efficiency, and reducing expenses.

A review of 10 × 10 and 20 × 20 grid-type wind turbine placement problems solving by metaheuristics.

Wind energy is the most important renewable energy source produced by wind turbines. The optimal placement of wind turbines is a challenging binary optimization problem. Maximizing production capacity and minimizing the number of turbines (accordingly minimizing the installation cost) are the main objectives. Metaheuristic algorithms can solve binary optimization problems with optimal or near-optimal solutions. In the literature, the wind turbine placement problem (WTPP) is solved by metaheuristic algorithms from 1994 to 2020. In this work, a literature review of solving 10 × 10 and 20 × 20 grid-type WTPPs with metaheuristic algorithms is conducted. Forty-six different papers were deeply discussed and presented all the experimental results to shed light on future studies for presenting more robust metaheuristics for solving WTPPs. The key results of this review are precaution against false comparisons; presenting the current experimental results; determining the comparison parameters; and demonstrating the benchmark problem clearly. Future directions were clearly spotlighted for practitioners and researchers and new research topics for potential studies are also presented.

RGB-D salient object ranking based on depth stack and truth stack for complex indoor scenes

RGB-D salient object detection has achieved a great development in recent years due to its extensive applications. Previous studies mainly focus on simple scene images with one single object. These models usually become overwhelmed by complex scenes with multiple objects. Moreover, these methods model salient object detection as a binary segmentation problem. However, psychology studies show that humans shift their visual attention from one object to another and rank salient objects, especially in complex indoor scenes. Following the psychological studies, we propose to rank salient objects in RGB-D images of complex indoor scenes. Due to the lack of such data, we first construct a RGB-D salient object ranking dataset containing complex indoor scenes with multiple objects. The saliency ranking of different objects is defined based on the order that an observer notices these objects. The final salient object ranking result is an average across the saliency rankings of 13 observers. This RGB-D salient object ranking dataset is also analyzed with current mainstream RGB-D salient object detection dataset for comparison. Since location information provided by depth images can help to determine the saliency ranking of objects, we further propose an end-to-end network exploiting depth stack and ground truth stack to predict the order of salient objects in complex scenes. The quantitative and qualitative comparisons demonstrate the effectiveness of the proposed method.

Robust binary linear programming under implementation uncertainty

This article studies binary linear programming problems in the presence of uncertainties that may prevent implementing the computed solution. This type of uncertainty, called implementation uncertainty, is modelled affecting the decision variables rather than model parameters. The binary nature of the decision variables invalidates using existing robust models for implementation uncertainty. The robust solutions obtained are optimal for a worst-case min–max objective. Structural properties allow the reformulation of the problem as a binary linear program. Constraint relaxation and cardinality-constrained parameters control the degree of solution conservatism. An optimization problem permits the selection of solutions from the obtained set of robust solutions. Results from a case study in the context of the knapsack problem suggest the methodology yields solutions that perform well in terms of objective value and feasibility. Furthermore, the selection approach can identify robust solutions with desirable implementation characteristics.

A reinforcement learning based computational intelligence approach for binary optimization problems: The case of the set-union knapsack problem

As today’s one of the hottest topics, machine learning brings about opportunities in various research areas. Moreover, computational intelligence and metaheuristics open up new strategies, which are shown to be efficient in solving optimization problems. However, studies bringing such remarkable approaches together are still lacking. In this context, the present paper introduces a Q-learning reinforcement learning strategy for binary optimization problems. The developed algorithm works as a reinforcement and recommendation system that evaluates the used algorithms, assigns rewards, promotes or demotes them. Thus, it invokes more promising optimizers more frequently. The proposed Q-learning algorithm uses Particle Swarm Optimization (PSO), Genetic Algorithm and a hybrid of these algorithms, namely, genetic-based PSO (gbPSO) as optimizers. Therefore, it is aimed to avoid local optima by using various optimizers and gathering additional statistical data. Secondarily, all optimizers are further enhanced by adopting an initial solution generation technique and triggered random immigrants mechanism to preserve swarm diversity. In addition to these procedures, a mutation procedure that decreases the diversity is adopted. Thus, more intensified search is encouraged towards the end of search. Moreover, while PSO requires for transfer functions in order to perform in binary spaces, the adopted and further improved gbPSO does not necessarily need such auxiliary procedures. Finally, the performances of all used algorithms are analysed on a recently caught on binary problem, namely, the set-union knapsack problem, which has a wide range of real-life applications. As demonstrated by the comprehensive experimental study and appropriate statistical tests, promising improvements are achieved.

Class-specific extreme learning machine based on overall distribution for addressing binary imbalance problem

Class imbalance problem occurs when the training dataset contains significantly fewer samples of one class in contrast to another class. Conventional extreme learning machine (ELM) gives the same importance to all the samples leading to the results, which favor the majority class. To solve this intrinsic deficiency, modifications of ELM have been developed such as weighted ELM (WELM) and WELM based on the overall distribution (ODW-ELM). Recently class-specific ELM (CS-ELM) was designed for class imbalance learning. It has been shown in this work that the derivation of the output weights, \(\varvec{\beta }\), is more efficient compared to class-specific cost regulation ELM (CCRELM) for handling the class imbalance problem. Motivated by CCRELM, X. Luo et al. have proposed the classifier ODW-ELM, which is also not efficient for imbalance learning. In this work, a novel class-specific ELM based on overall distribution (OD-CSELM) and the kernelized version of OD-CSELM (OD-CSKELM) is proposed to address the binary class imbalance problem more effectively. OD-CSELM and OD-CSKELM are motivated by CS-ELM. In addition, the computational complexity of OD-CSELM and OD-CSKELM is significantly lower than WELM and kernelized WELM, respectively. The proposed work is evaluated by using the benchmark real-world imbalanced datasets. The experimental results demonstrate that the proposed work gives good generalization performance in contrast to the rest of the classifiers for class imbalance learning.

Balancing stability and efficiency in team formation as a generalized roommate problem

AbstractThe assignment of personnel to teams is a fundamental managerial function typically involving several objectives and a variety of idiosyncratic practical constraints. Despite the prevalence of this task in practice, the process is seldom approached as an optimization problem over the reported preferences of all agents. This is due in part to the underlying computational complexity that occurs when intra‐team interpersonal interactions are taken into consideration, and also due to game‐theoretic considerations, when those taking part in the process are self‐interested agents. Variants of this fundamental decision problem arise in a number of settings, including, for example, human resources and project management, military platooning, ride sharing, data clustering, and in assigning students to group projects. In this article, we study an analytical approach to “team formation” focused on the interplay between two of the most common objectives considered in the related literature: economic efficiency (i.e., the maximization of social welfare) and game‐theoretic stability (e.g., finding a core solution when one exists). With a weighted objective across these two goals, the problem is modeled as a bi‐level binary optimization problem, and transformed into a single‐level, exponentially sized binary integer program. We then devise a branch‐cut‐and‐price algorithm and demonstrate its efficacy through an extensive set of simulations, with favorable comparisons to other algorithms from the literature.

Capturing Symmetries of Quantum Optimization Algorithms Using Graph Neural Networks

Quantum optimization algorithms are some of the most promising algorithms expected to show a quantum advantage. When solving quadratic unconstrained binary optimization problems, quantum optimization algorithms usually provide an approximate solution. The solution quality, however, is not guaranteed to be good enough to warrant selecting it over the classical optimizer solution, as it depends on the problem instance. Here, we present an algorithm based on a graph neural network that can choose between a quantum optimizer and classical optimizer using performance prediction. In addition, we present an approach that predicts the optimal parameters of a variational quantum optimizer. We tested our approach with a specific quantum optimizer, the quantum approximate optimization algorithm, applied to the Max-Cut problem, which is an example of a quadratic unconstrained binary optimization problem. We observed qualitatively and quantitatively that graph neural networks are suited for a performance prediction of up to nine-vertex Max-Cut instances with a quantum approximate optimization algorithm with a depth of up to three. For the performance prediction task, the average difference between the actual quantum algorithm performance and the predicted performance is below 19.7% and, for the parameter prediction task, the solution using the predicted parameters is within 2.7% of the optimal parameter solution. Our method therefore has the capacity to find problems that are best suited for quantum solvers. The proposed method and the corresponding algorithm can be used for hybrid quantum algorithm selection.

A multi-class classification model with parametrized target outputs for randomized-based feedforward neural networks

Randomized-based Feedforward Neural Networks approach regression and classification (binary and multi-class) problems by minimizing the same optimization problem. Specifically, the model parameters are determined through the ridge regression estimator of the patterns projected in the hidden layer space (randomly generated in its neural network version) for models without direct links and the patterns projected in the hidden layer space along with the original input data for models with direct links. The targets are encoded for the multi-class classification problem according to the 1-of-J encoding (J the number of classes), which implies that the model parameters are estimated to project all the patterns belonging to its corresponding class to one and the remaining to zero. This approach has several drawbacks, which motivated us to propose an alternative optimization model for the framework. In the proposed optimization model, model parameters are estimated for each class so that their patterns are projected to a reference point (also optimized during the process), whereas the remaining patterns (not belonging to that class) are projected as far away as possible from the reference point. The final problem is finally presented as a generalized eigenvalue problem. Four models are then presented: the neural network version of the algorithm and its corresponding kernel version for the neural networks models with and without direct links. In addition, the optimization model has also been implemented in randomization-based multi-layer or deep neural networks. The empirical results obtained by the proposed models were compared to those reported by state-of-the-art models in the correct classification rate and a separability index (which measures the degree of separability in projection terms per class of the patterns belonging to the class of the others). The proposed methods show very competitive performance in the separability index and prediction accuracy compared to the neural networks version of the comparison methods (with and without direct links). Remarkably, the model provides significantly superior performance in deep models with direct links compared to its deep model counterpart.