Binary Optimization 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.

Integration of Simulated Quantum Annealing in Parallel Tempering and Population Annealing for Heterogeneous-Profile QUBO Exploration

Simulated Quantum Annealing (SQA) is a heuristic algorithm which can solve Quadratic Unconstrained Binary Optimization (QUBO) problems by emulating the exploration of the solution space done by a quantum annealer. It mimics the quantum superposition and tunnelling effects through a set of correlated replicas of the spins system representing the problem to be solved and performing Monte Carlo steps. However, the effectiveness of SQA over a classical algorithm strictly depends on the cost/energy profile of the target problem. In fact, quantum annealing only performs well in exploring functions with high and narrow peaks, while classical annealing is better in overcoming flat and wide energy-profile barriers. Unfortunately, real-world problems have a heterogeneous solution space and the probability of success of each solver depends on the size of the energy profile region compatible with its exploration mechanism. Therefore, significant advantages could be obtained by exploiting hybrid solvers, which combine SQA and classical algorithms. This work proposes four new quantum-classical algorithms: Simulated Quantum Parallel Tempering (SQPT), Simulated Quantum Population Annealing (SQPA), Simulated Quantum Parallel Tempering - Population Annealing v1 (SQPTPA1) and Simulated Quantum Parallel Tempering - Population Annealing v2 (SQPTPA2). They are obtained by combining SQA, Parallel Tempering (PT), and Population Annealing (PA). Their results are compared with those provided by SQA, considering benchmark QUBO problems, characterized by different profiles. Even though this work is preliminary, the obtained results are encouraging and prove hybrid solvers’ potential in solving a generic optimization problem.

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.

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.

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.

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.

Binary Aquila Optimizer for 0–1 knapsack problems

The optimization process entails determining the best values for various system characteristics in order to finish the system design at the lowest possible cost. In general, real-world applications and issues in artificial intelligence and machine learning are discrete, unconstrained, or discrete. Optimization approaches have a high success rate in tackling such situations. As a result, several sophisticated heuristic algorithms based on swarm intelligence have been presented in recent years. Various academics in the literature have worked on such algorithms and have effectively addressed many difficulties. Aquila Optimizer (AO) is one such algorithm. Aquila Optimizer (AO) is a recently suggested heuristic algorithm. It is a novel population-based optimization strategy. It was made by mimicking the natural behavior of the Aquila. It was created by imitating the behavior of the Aquila in nature in the process of catching its prey. The AO algorithm is an algorithm developed to solve continuous optimization problems in their original form. In this study, the AO structure has been updated again to solve binary optimization problems. Problems encountered in the real world do not always have continuous values. It exists in problems with discrete values. Therefore, algorithms that solve continuous problems need to be restructured to solve discrete optimization problems as well. Binary optimization problems constitute a subgroup of discrete optimization problems. In this study, a new algorithm is proposed for binary optimization problems (BAO). The most successful BAO-T algorithm was created by testing the success of BAO in eight different transfer functions. Transfer functions play an active role in converting the continuous search space to the binary search space. BAO has also been developed by adding candidate solution step crossover and mutation methods (BAO-CM). The success of the proposed BAO-T and BAO-CM algorithms has been tested on the knapsack problem, which is widely selected in binary optimization problems in the literature. Knapsack problem examples are divided into three different benchmark groups in this study. A total of sixty-three low, medium, and large scale knapsack problems were determined as test datasets. The performances of BAO-T and BAO-CM algorithms were examined in detail and the results were clearly shown with graphics. In addition, the results of BAO-T and BAO-CM algorithms have been compared with the new heuristic algorithms proposed in the literature in recent years, and their success has been proven. According to the results, BAO-CM performed better than BAO-T and can be suggested as an alternative algorithm for solving binary optimization problems.

Variational Quantum Algorithm Applied to Collision Avoidance of Unmanned Aerial Vehicles.

Mission planning for multiple unmanned aerial vehicles (UAVs) is a complex problem that is expected to be solved by quantum computing. With the increasing application of UAVs, the demand for efficient conflict management strategies to ensure airspace safety continues to increase. In the era of noisy intermediate-scale quantum (NISQ) devices, variational quantum algorithms (VQA) for optimizing parameterized quantum circuits with the help of classical optimizers are currently one of the most promising strategies to gain quantum advantage. In this paper, we propose a mathematical model for the UAV collision avoidance problem that maps the collision avoidance problem to a quadratic unconstrained binary optimization (QUBO) problem. The problem is formulated as an Ising Hamiltonian, then the ground state is solved using two kinds of VQAs: the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). We select conditional value-at-risk (CVaR) to further promote the performance of our model. Four examples are given to validate that with our method the probability of obtaining a feasible solution can exceed 90% based on appropriate parameters, and our method can enhance the efficiency of a UAVs' collision avoidance model.

An improved feature selection approach using global best guided Gaussian artificial bee colony for EMG classification

Electromyography (EMG) measures muscle relaxes or contractions during muscular activity through EMG signal. It plays a vital role in identifying muscle-related problems for clinical diagnosis. This paper presents an efficient EMG feature selection technique for classifying 17 different prosthetic hand movements recorded from 11 subjects. Two variants of the Artificial Bee Colony (ABC) algorithm, namely: i) Global Best Guided ABC (GbestABC) and ii) Gaussian ABC (GABC), are employed to propose an Improved Artificial Bee Colony (ABC) algorithm called Global Best Guided Gaussian ABC (GGABC) for solving global optimization problems. GbestABC performs better in the exploitation phase, whereas GABC performs better in the exploration phase in searching for the optimal solutions. The proposed GGABC takes advantage of GbestABC and GABC to counterbalance basic ABC's exploitation and exploration capability. Further, a binary version of GGABC known as binary GGABC (BGGABC) is developed to solve binary optimization problems and select optimal EMG signal classification features. Extensive experiments are carried out in three phases: i) GGABC for global optimization problems ii) BGGABC for EMG feature selection problems with other meta-heuristic-based competitors iii) BGGABC for EMG feature selection problems with well-known filter based techniques. K-nearest neighbor (KNN) classifier is used in experiments to validate and investigate the effectiveness of the proposed algorithm. Experimental result shows that the BGGABC-based EMG feature selection achieved 94.13% average classification accuracy and 97.06% best classification accuracy. Obtained results confirm that the proposed algorithm outperforms or is competitive with state-of-the-art algorithms in EMG feature selection and classification.

Practical and scalable decoder for topological quantum error correction with an Ising machine

Quantum error correction is one of the most important milestones for the realization of large-scale quantum computation. To achieve this, it is essential not only to integrate a large number of qubits with high fidelity but also to build a scalable classical system that can perform error correction. Here, we propose an efficient and scalable decoder for quantum error correction using ``Fujitsu Digital Annealer'' (DA). Specifically, the error correction problem of stabilizer codes is mapped into an Ising-type optimization problem, so-called quadratic unconstrained binary optimization (QUBO) problem, which is solved by DA. In particular, we implement the proposed DA decoder for the surface code and perform detailed numerical experiments for various code distances to see its performance and scalability. We observe that computational scaling for the DA decoder has a lower order of polynomials than the decoding methods using simulated annealing (SA) and minimum-weight perfect matching (MWPM) algorithm under all tested conditions. It is also shown that the DA decoder has advantages over the Union-Find (UF) decoder from a variety of perspectives including hardware implementation. Furthermore, the threshold behavior of the logical error probability for the DA decoder is analyzed and the resultant threshold lies between 9.4% and 9.8%, which is very close to that obtained by the MWPM decoder. This result clearly shows the high potential of the DA decoder for quantum error correction.

An improved binary manta ray foraging optimization algorithm based feature selection and random forest classifier for network intrusion detection

• Proposed a binary version of manta ray foraging optimization algorithm for binary optimization problems. • Applied the proposed binary manta ray foraging optimization algorithm for feature selection using NSL-KDD and CICIDS2017 network traffic datasets. • Developed network intrusion detection model with the selected features based on random forest classifier. • Examine performance analysis and comparison of the presented model with GA, PSO, GWO, and GOA using Accuracy, Recall, Precision, F-measure, and execution time. • Statistical justification of the results achieved compared to that of GA, PSO, GWO, and GOA using t -test. The growth within the Internet and communications areas have led to a massive surge in the dimension of network and data. Consequently, several new threats are being created and have posed difficulties for security networks to correctly discover intrusions. Intrusion Detection System (IDs) is one amongst the foremost essential events for security arrangements in network environments, and it is commonly applied to spot, track, and detect malevolent threats. Detecting intruders using metaheuristics and machine learning methodologies in recent trend offers improved discovery rate. Therefore, this paper presented an intrusion detection model using an improved Binary Manta Ray Foraging (BMRF) Optimization Algorithm based on adaptive S-shape function and Random Forest (RF) classifier. The BMFR is envisioned to identify the most relevant features and remove redundant and irrelevant ones from the intrusion detection datasets. Furthermore, the RF is used for feature evaluation and to build the intrusion detection model. The proposed method was validated and compared with other methods using two IDs benchmark datasets, which include NSL-KDD and CIC-IDS2017 datasets. The result indicates that the presented model selected 38 features with 99.6% precision, 94.3% recall, 96.9% f-measure, and 99.3% accuracy for the CIC-IDS2017 dataset. Moreover, for the NSL-KDD dataset, the presented model selected 22 features with 96.8%, 96.2%, 96.5%, and 98.8% for precision, recall, F-measure, and accuracy. In addition, a statistical significance test reveals a significance difference between the presented model and the compared methods in terms of F-measure.

Incorporate seagull optimization into ordinal optimization for solving the constrained binary simulation optimization problems

Incorporate seagull optimization into ordinal optimization for solving the constrained binary simulation optimization problems

Novel chaotic oppositional fruit fly optimization algorithm for feature selection applied on COVID 19 patients' health prediction.

The fast-growing quantity of information hinders the process of machine learning, making it computationally costly and with substandard results. Feature selection is a pre-processing method for obtaining the optimal subset of features in a data set. Optimization algorithms struggle to decrease the dimensionality while retaining accuracy in high-dimensional data set. This article proposes a novel chaotic opposition fruit fly optimization algorithm, an improved variation of the original fruit fly algorithm, advanced and adapted for binary optimization problems. The proposed algorithm is tested on ten unconstrained benchmark functions and evaluated on twenty-one standard datasets taken from the Univesity of California, Irvine repository and Arizona State University. Further, the presented algorithm is assessed on a coronavirus disease dataset, as well. The proposed method is then compared with several well-known feature selection algorithms on the same datasets. The results prove that the presented algorithm predominantly outperform other algorithms in selecting the most relevant features by decreasing the number of utilized features and improving classification accuracy.

Minimization of nth Order Rate Matching in Satellite Networks with One to Many Pairings

This paper studies the minimization of nth (positive integer) order rate matching in high-throughput multi-beam satellite systems, based on one-to-many capacity allocation pairings, for the first time in the literature. The offered and requested capacities of gateways and users’ beams are exploited, respectively. Due to the high complexity of the binary optimization problem, its solution is approached with a two-step heuristic scheme. Firstly, the corresponding continuous, in [0, 1], pairing problem is solved applying the difference of convex optimization theory, and then, a transformation from continuous to binary feasible allocation is provided to extract the pairings among gateways and users’ beams. Comparing with the exponential-time optimal exhaustive mechanism that investigates all possible pairs to extract the best matching for minimizing the rate matching, extended simulations show that the presented approximation for the solution of the non-convex optimization problem has fast convergence and achieves a generally low relative error for lower value of n. Finally, the simulation results show the importance of n in the examined problem. Specifically, pairings originated by the minimization of rate matching with larger n result in more fair rate matching among users’ beams, which is a valuable result for satellite and generally wireless systems operators.

Degeneracy engineering for classical and quantum annealing: A case study of sparse linear regression in collider physics

Classical and quantum annealing are computing paradigms that have been proposed to solve a wide range of optimization problems. In this paper, we aim to enhance the performance of annealing algorithms by introducing the technique of degeneracy engineering, through which the relative degeneracy of the ground state is increased by modifying a subset of terms in the objective Hamiltonian. We illustrate this novel approach by applying it to the example of $\ell_0$-norm regularization for sparse linear regression, which is in general an NP-hard optimization problem. Specifically, we show how to cast $\ell_0$-norm regularization as a quadratic unconstrained binary optimization (QUBO) problem, suitable for implementation on annealing platforms. As a case study, we apply this QUBO formulation to energy flow polynomials in high-energy collider physics, finding that degeneracy engineering substantially improves the annealing performance. Our results motivate the application of degeneracy engineering to a variety of regularized optimization problems.

A binary tree seed algorithm with selection-based local search mechanism for huge-sized optimization problems

Tree seed algorithm (TSA) is a recently proposed metaheuristic algorithm for solving continuous optimization problems. In order to use TSA in binary optimization problems, the SimLogicTSA method was developed by adding logic gates and Jaccard’s similarity measure to this algorithm by Cinar and Kiran. Although SimLogicTSA is generally successful in small, medium, and large size problems, it has not been successful in the huge-sized problems by stucking into local minima. To overcome this problem, a new local search mechanism called enhanced local search module (ELSM) is proposed and the SimLogicTSA-ELSM algorithm is suggested by implementing the ELSM mechanism to the original SimLogicTSA algorithm. The proposed ELSM mechanism consists of a swap operator and logic-based gates. To analyze the contribution of the ELSM mechanism to the algorithm, firstly, the original SimLogicTSA and SimLogicTSA-ELSM algorithms were compared on the Cap and M* problem sets. The obtained results showed that the proposed algorithm produced more successful results than the original SimLogicTSA. Then, the proposed SimLogicTSA-ELSM is compared with many state-of-art algorithms in the literature by using different performance metrics on Cap and M* problem sets. The results show that SimLogicTSA-ELSM outperforms the compared algorithms in nearly all cases. Especially, the performance of the SimLogicTSA-ELSM stands out in huge-sized problems.

Engineering Grover Adaptive Search: Exploring the Degrees of Freedom for Efficient QUBO Solving

Quantum computers have the potential to solve Quadratic Unconstrained Binary Optimization (QUBO) problems with lower computational complexity than classical ones. Considering the current limitations of quantum hardware, the joint use of classical and quantum paradigms could exploit both advantages. Quantum routines can make some complex tasks for classical computers feasible. For example, in the Grover Adaptive Search (GAS) procedure, the problem cost function is classically shifted iteratively, whenever a negative value is found through the quantum Grover Search (GS) algorithm, until the minimum is achieved. This quantum-classical approach is characterized by many degrees of freedom, e.g. the number of GS iterations in each call and the stop condition of the algorithm, which should be appropriately tuned for an effective and fast convergence to the optimal solution. The availability of software routines could permit the best management of the GAS parameters. This work proposes new mechanisms for GAS parameters management and compares them with the existing ones, like one available in the Qiskit framework. The proposed mechanisms can automatically arrange the parameters according to the algorithm evolution and their previous experience, thus ensuring a more frequent and faster achievement of the optimal solution. Even though these strategies can be further improved, the results are encouraging. The analysis is done to identify the best policy for different problems. It lays the foundation for designing an automatic toolchain for QUBO solving, which can obtain the best possible implementation of the GAS algorithm for each submitted problem.

Topology Optimization of Electromagnetic Devices Using Digital Annealer

Topology optimization (TO) has been formulated as a quadratic unconstrained binary optimization (QUBO) problem that can be solved by Digital Annealer (DA) and quantum computers, which can realize massive parallelization. It is shown that the 3-D TO of a permanent magnet (PM), with 600 unknowns, is successfully performed by the DA with the aid of the finite element method (FEM) for field computations. Moreover, it is shown to perform TO of a magnetic core, with 758 unknowns, in such a way that the QUBO and field problems are iteratively solved to determine the optimal solution in which the magnetic field and optimal core structure are self-consistent.

Capacity Allocation Mechanisms in High-Throughput Satellite Systems: One-to-Many Pairings

In this article, one-to-many suboptimal assignments, for various capacity allocation metrics, in high-throughput multibeam satellite systems, under the smart gateway diversity concept, are studied. Furthermore, in the analysis both the offered and requested capacities in the satellite network and the dynamic variations of the atmospheric satellite channels are considered. The objectives, from the literature, of maximization of both minimum and total system’s satisfaction ratios are investigated. Moreover, the dissatisfaction ratio, defined as the multiplicative inverse of satisfaction ratio, is examined as a new proposed metric under the objectives of minimization of both maximum and total system’s dissatisfaction ratios. In order to approach the optimal values of aforementioned binary optimization problems a two-step heuristic approach is described where first a continuous pairing solution is given based on fractional programming theory for the satisfaction problems and the difference of convex programming theory for the dissatisfaction problems. Then, a continuous to discrete feasible matching solution is provided for all cases. The proposed two-step schemes have very low complexity based on simulations and the latter show small relative error compared with the optimal performance of the exhaustive algorithms that have exponential time complexity.