Binary Optimization Research Articles

A Modified Binary Arithmetic Optimization Algorithm for Feature Selection

Feature selection chooses the optimal subset from the feature set without scarifying the information carried by the dataset. It is considered a complex combinatorial problem, so classical optimization techniques fail to solve it when the feature set becomes larger. Meta-heuristic approaches are well known to solve complex optimization problems; hence these algorithms have been successfully applied to extract optimal feature subsets. The arithmetic Optimization Algorithm is a newly proposed mathematics-based meta-heuristic search algorithm successfully applied to solve optimization problems. However, it has been observed that AOA experiences a poor exploration phase. Hence in the present work, a Modified Binary Arithmetic Optimization Algorithm (MB-AOA) is proposed, which solves the poor exploration problem of standard AOA. In the MB-AOA, instead of utilizing a single best solution, an optimal solution set that gradually shrinks after each successive iteration is applied for better exploration during initial iterations. Also, instead of a fixed search parameter (μ), the MB-AOA utilizes a variable parameter suitable for binary optimization problems. The proposed method is evaluated over seven real-life datasets from the UCI repository as a feature selection wrapper method and compared with standard AOA over two performance metrics, Average Accuracy, F-score, and the generated feature subset size. MB-AOA has performed better in six datasets regarding F-score and average accuracy. The obtained results from the simulation process demonstrate that the MB-AOA can select the relevant features, thus improving the classification task’s overall accuracy levels.

Intrusion detection in internet of things using improved binary golden jackal optimization algorithm and LSTM

Intrusion detection in internet of things using improved binary golden jackal optimization algorithm and LSTM

Binary well placement optimization using a decomposition-based multi-objective evolutionary algorithm with diversity preservation

Binary well placement optimization using a decomposition-based multi-objective evolutionary algorithm with diversity preservation

Network Bandwidth Utilization Optimization with Quantum-Inspired Approach

As the popularity of mobile devices and services continues to increase, the demand for more efficient and effective algorithms to manage network utility is increased. Here, we aim to optimize Network Bandwidth Utilization (NBU) by managing user equipments (UEs) and base stations (BSs) association in 5G ORAN architecture. We consider the network total throughput as an objective function and try to find the suitable Cell Individual Offset (CIO) to trigger UE handover with the A3 event such that the network throughput is optimal. We formulate this problem into a Quadratic Unconstrained Binary Optimization (QUBO) problem such that we can explore the power of Quantum Annealing (QA), which is a promising approach to finding the optimal solution for the NP-Hard problem. We also analyze the penalty coefficients setting problem which impacts the outcome of QA significantly. We test our QUBO formulation on a dataset of 7 BSs and 150 UEs with Fujitsu’s third generation Digital Annealer (DA3). Using our QUBO formulation with DA3 solver with fine-tuning, we can improve the throughput with 60% hit rate on this dataset.

Emended Harris Hawk Optimizer for Mixed Energy Generation Scheduling Problem

This paper proposes an emended Harris hawk optimizer (EHHO) to solve the mixed energy generation scheduling problem with available resources from hydrothermal, pumped storage hydro, solar, and wind units while minimizing the operating cost, utilizing the available water, and satisfying the other operational constraints. Direct heuristics are applied to solve the constraints imposed on the generation scheduling problem. An optimistic binary optimizer is utilized to commit solar and wind units so that solar and wind units share a certain percentage of power demand to meet the uncertainty of renewable power. The hunting behavior of the hawks for the desired prey inspires the Harris hawk optimizer (HHO) because of its flexibility, sturdiness, and scalability features. Despite HHO giving premature convergence as it tends to trap into the local optima while solving complex non-linear optimization problems. Hence, the local search technique (LST) is employed with the HHO to overcome it. LST also empowers the exploitation phase of HHO. Two practical electric power test systems are successfully solved using the proposed EHHO. On implementing the proposed EHHO, with the penetration of pumped storage hydro units, savings in the cost of thermal units range from 3.90 to 11.44%. Further, with the penetration of wind and solar power, the savings in operating costs of thermal units have increased from 12.15 to 20.19%. The main idea and contribution of the proposed work is the thermal fuel cost reduction using renewable energy sources by utilizing EHHO. The convergence curves and whisker box plots demonstrate the EHHO’s robustness while solving the electric power test systems.

Optimal control of a grid-connected photovoltaic agricultural water pumping system

Optimization of water pumping systems has been studied using various techniques which include classical, mathematical, and heuristics. Few studies have explored use of optimal controllers in agricultural water pumping applications. Some studies also ignore the interconnection between the water demand and energy used. Introduction of renewable energy sources such as photovoltaic (PV) necessitates different geographical studies as the intensity of the renewable energy varies widely with location. In this paper, an optimal controller for a batteryless grid-connected photovoltaic system to power water supply system for irrigation purposes was developed. The aim was to minimize the operational cost of grid energy by maximizing utilization of photovoltaic power and minimizing the utilization of grid power. A case study was done at a farm in Kajiado (−1.6033257^{circ } latitude and 36.7863352^{circ } longitude). The farm photovoltaic, grid power, water pumps (underground and booster pump), and storage tanks were modelled into a binary linear programming optimization problem and solved using intlinprog solver on MATLAB. Energy demand data was collected using a three-phase power logger, while water demand data was collected using onsite water meter and stopwatch timer. Photovoltaic power produced was estimated using Photovoltaic Geographical Information System (PVGIS). Simulation results obtained show that the use of an optimal controller results in reduced cost of energy by 44.4%. Better utilization of renewable photovoltaic energy by 24% was observed, and 3.6% more water was pumped.

Performance Optimization and Comprehensive Analysis of Binary Nutcracker Optimization Algorithm: A Case Study of Feature Selection and Merkle–Hellman Knapsack Cryptosystem

In this paper, a binary variant of a novel nature-inspired metaheuristic algorithm called the nutcracker optimization algorithm (NOA) is presented for binary optimization problems. Because of the continuous nature of the classical NOA and the discrete nature of the binary problems, two different families of transfer functions, namely S-shaped and V-shaped, are extensively investigated for converting the classical NOA into a binary variant, namely BNOA, applicable for various binary problems. Additionally, BNOA is improved using a local search strategy based on effectively integrating some genetic operators into the BNOA’s exploitation and exploration; this additional variant is called BINOA. Both BNOA and BINOA are evaluated using three common binary optimization problems, including feature selection, 0-1 knapsack, and the Merkle–Hellman knapsack cryptosystem (MHKC), and are compared to several robust binary metaheuristic optimizers in terms of statistical information, statistical tests, and convergence speed. The experiential findings show that BINOA is better than the classical BNOA and the other rival optimizers for both the 0-1 knapsack problem and attacking MHKC and is on par with some algorithms, like the genetic algorithm for feature selection.

An enhanced binary artificial rabbits optimization for feature selection in medical diagnosis

An enhanced binary artificial rabbits optimization for feature selection in medical diagnosis

Binary Sand Cat Swarm Optimization Algorithm for Wrapper Feature Selection on Biological Data.

In large datasets, irrelevant, redundant, and noisy attributes are often present. These attributes can have a negative impact on the classification model accuracy. Therefore, feature selection is an effective pre-processing step intended to enhance the classification performance by choosing a small number of relevant or significant features. It is important to note that due to the NP-hard characteristics of feature selection, the search agent can become trapped in the local optima, which is extremely costly in terms of time and complexity. To solve these problems, an efficient and effective global search method is needed. Sand cat swarm optimization (SCSO) is a newly introduced metaheuristic algorithm that solves global optimization algorithms. Nevertheless, the SCSO algorithm is recommended for continuous problems. bSCSO is a binary version of the SCSO algorithm proposed here for the analysis and solution of discrete problems such as wrapper feature selection in biological data. It was evaluated on ten well-known biological datasets to determine the effectiveness of the bSCSO algorithm. Moreover, the proposed algorithm was compared to four recent binary optimization algorithms to determine which algorithm had better efficiency. A number of findings demonstrated the superiority of the proposed approach both in terms of high prediction accuracy and small feature sizes.

High-Dimensional Feature Selection Based on Improved Binary Ant Colony Optimization Combined with Hybrid Rice Optimization Algorithm

In the realm of high-dimensional data analysis, numerous fields stand to benefit from its applications, including the biological and medical sectors that are crucial for computer-aided disease diagnosis and prediction systems. However, the presence of a significant number of redundant or irrelevant features can adversely affect system accuracy and real-time diagnosis efficiency. To mitigate this issue, this paper proposes two innovative wrapper feature selection (FS) methods that integrate the ant colony optimization (ACO) algorithm and hybrid rice optimization (HRO). HRO is a recently developed metaheuristic that mimics the breeding process of the three-line hybrid rice, which is yet to be thoroughly explored in the context of solving high-dimensional FS problems. In the first hybridization, ACO is embedded as an evolutionary operator within HRO and updated alternately with it. In the second form of hybridization, two subpopulations evolve independently, sharing the local search results to assist individual updating. In the initial stage preceding hybridization, a problem-oriented heuristic factor assignment strategy based on the importance of the knee point feature is introduced to enhance the global search capability of ACO in identifying the smallest and most representative features. The performance of the proposed algorithms is evaluated on fourteen high-dimensional biomedical datasets and compared with other recently advanced FS methods. Experimental results suggest that the proposed methods are efficient and computationally robust, exhibiting superior performance compared to the other algorithms involved in this study.

Simple odd β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-cycle inequalities for binary polynomial optimization

We consider the multilinear polytope which arises naturally in binary polynomial optimization. Del Pia and Di Gregorio introduced the class of odd β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-cycle inequalities valid for this polytope, showed that these generally have Chvátal rank 2 with respect to the standard relaxation and that, together with flower inequalities, they yield a perfect formulation for cycle hypergraph instances. Moreover, they describe a separation algorithm in case the instance is a cycle hypergraph. We introduce a weaker version, called simple odd β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-cycle inequalities, for which we establish a strongly polynomial-time separation algorithm for arbitrary instances. These inequalities still have Chvátal rank 2 in general and still suffice to describe the multilinear polytope for cycle hypergraphs. Finally, we report about computational results of our prototype implementation. The simple odd β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-cycle inequalities sometimes help to close more of the integrality gap in the experiments; however, the preliminary implementation has substantial computational cost, suggesting room for improvement in the separation algorithm.

BE-GWO: Binary extremum-based grey wolf optimizer for discrete optimization problems

Since most metaheuristic algorithms for continuous search space have been developed, a number of transfer functions have been proposed including S-shaped, V-shaped, linear, U-shaped, and X-shaped to convert the continuous solution to the binary one. However, most existing transfer functions do not provide exploration and exploitation required to solve complex discrete problems. Thus, in this study, an improved binary GWO named extremum-based GWO (BE-GWO) algorithm is introduced. The proposed algorithm proposes a new cosine transfer function (CTF) to convert the continuous GWO to the binary form and then introduces an extremum (Ex) search strategy to improve the efficiency of converted binary solutions. The performance of the BE-GWO was evaluated through solving two binary optimization problems, the feature selection and the 0-1 multidimensional knapsack problem (MKP). The results of feature selection problems were compared with several well-known binary metaheuristic algorithms such as BPSO, BGSA, BitABC, bALO, bGWO, BDA, BSSA, and BinABC. Moreover, the results were compared with four versions of the binary GWO, the binary PSO, and the binary ABC. In addition, the BE-GWO algorithm was evaluated to solve the 0-1 MKP with difficult and very difficult benchmark instances and the results were compared with several binary GWO variants. The results of two binary problems were statistically analyzed by the Friedman test. The experimental results showed that the proposed BE-GWO algorithm enhances the performance of binary GWO in terms of solution accuracy, convergence speed, exploration, and balancing between exploration and exploitation.

Quantum annealing solution for the unrelated parallel machine scheduling with priorities and delay of task switching on machines

Quantum computing has emerged in recent years as an alternative to classical computing, which could improve the latter in solving some types of problems. One of the quantum programming models, Adiabatic Quantum Computing, has been successfully used to solve problems such as graph partitioning, traffic routing, and task scheduling. In this paper, the focus is on the scheduling of the problem of unrelated parallel machines, where the processing time of tasks on any of the available processing elements is known. Moreover, the proposed model is extended in two relevant aspects for this kind of problem: the existence of some degree of priority of tasks, and the introduction of a delay or penalty every time a processing unit or machine changes the type of task that executes.In all cases, the problem is expressed as Quadratic Unconstrained Binary Optimization, which can be subsequently solved using quantum annealers. The quantum nonlinear programming framework discussed in this work consists of three steps: quadratic approximation of cost function, a binary representation of parameter space, and solving the resulting Quadratic Unconstrained Binary Optimization on the quantum annealer platform D-Wave. One of the novelties in tackling this problem is the compaction of the model bearing in mind the repetitions of each task, to allow solving larger scheduling problems with the quantum resources available in the experimentation platform. An estimation of the number of qubits required in relation to the scheduling parameters is analyzed. The models have been implemented on the D-Wave platform and validated with respect to other traditional methods. Furthermore, the proposed extensions to consider priorities and to switch the delay of tasks have been analyzed using a case study.

A quantum computing approach for minimum loss problems in electrical distribution networks

This paper presents an application of a novel quadratic unconstrained binary optimization (QUBO) formulation to the minimum loss problem in distribution networks. The proposed QUBO formulation was conceived to be employed in quantum annealing—a quantum computing paradigm useful for solving combinatorial optimization problems. Quantum annealing is expected to provide better and/or faster solutions to optimization problems when compared to the ones provided by classical computers. With the problem at stake, better solutions result in lower energy losses, and faster solutions contribute to the same outcome given the future need for frequent reconfiguration of distribution networks to accommodate highly volatile demand, as anticipated by recent low-carbon solutions. The paper presents the results obtained through a hybrid quantum-classical solver for a standard 33-node test network and compares them with the ones obtained from classical solvers. Our main conclusion is that quantum annealing has potential to show advantage in the near future in terms of solution quality and time-to-solution, as quantum annealers and hybrid solvers continue to improve their performance.

A Binary Archimedes Optimization Algorithm and Weighted Sum Method for UFLS in Islanded Distribution Systems Considering the Stability Index and Load Priority

This study proposes an under-frequency load-shedding (UFLS) scheme based on a binary Archimedes Optimization Algorithm (BAOA) and the Weighted Sum Method (WSM) to maintain the stability of an islanded distribution system. These methods consider stability indices and load priorities to ensure effective load shedding during frequency deviations. The BAOA determines the optimal load shedding based on the stability index and power mismatch that minimizes the impact on critical loads while maintaining system stability in an islanded distribution system. The WSM determines the rank of the load to be shed based on four criteria: the load priority, the load category, the stability index, and the load size. Each load is assigned a weight based on its priority. These weight variables determine the order in which loads are shed during frequency deviations. The effectiveness of the proposed UFLS was tested on an 11 kV Malaysian distribution network with two mini hydro distributed generation systems. A comparative study was conducted based on five result outputs, including the number of loads shed, the size of the loads shed, the frequency undershoot, the frequency overshoot, and the time taken to achieve a stable frequency in three cases: base load, peak load, and peak load with photovoltaics (PV). The proposed UFLS showed the best results for 11 of 15 outputs (73.3%) for islanding events and 9 of 15 outputs (60%) for overloading events. The voltage profile and stability index, also, were improved after the proposed UFLS was applied.

Quantum computing for a profusion of postman problem variants

In this paper we study the viability of solving the Chinese Postman Problem, a graph routing optimization problem, and many of its variants on a quantum annealing device. Routing problem variants considered include graph type, directionally varying weights, number of parties involved in routing, among others. We put emphasis on the explanation of how to convert such problems into quadratic unconstrained binary optimization (QUBO) problems. QUBO is one of two equivalent natural paradigms for quantum annealing devices, the other being the Ising Model. We also expand upon a previously discovered algorithm for solving the Chinese Postman Problem on a closed undirected graph to decrease the number of constraints and variables used in the problem. Optimal annealing parameter settings and constraint weight values are discussed based on results from implementation on the D-Wave 2000Q and Advantage. Results from classical, purely quantum, and hybrid algorithms are compared.

Solving the capacitated vehicle routing problem with time windows via graph convolutional network assisted tree search and quantum-inspired computing

Vehicle routing problems are a class of NP-hard combinatorial optimization problems which attract a lot of attention, as they have many practical applications. In recent years there have been new developments solving vehicle routing problems with the help of machine learning, since learning how to automatically solve optimization problems has the potential to provide a big leap in optimization technology. Prior work on solving vehicle routing problems using machine learning has mainly focused on auto-regressive models, which are connected to high computational costs when combined with classical exact search methods as the model has to be evaluated in every search step. This paper proposes a new method for approximately solving the capacitated vehicle routing problem with time windows (CVRPTW) via a supervised deep learning-based approach in a non-autoregressive manner. The model uses a deep neural network to assist finding solutions by providing a probability distribution which is used to guide a tree search, resulting in a machine learning assisted heuristic. The model is built upon a new neural network architecture, called graph convolutional network, which is particularly suited for deep learning tasks. Furthermore, a new formulation for the CVRPTW in form of a quadratic unconstrained binary optimization (QUBO) problem is presented and solved via quantum-inspired computing in cooperation with Fujitsu, where a learned problem reduction based upon the proposed neural network is applied to circumvent limitations concerning the usage of quantum computing for large problem instances. Computational results show that the proposed models perform very well on small and medium sized instances compared to state-of-the-art solution methods in terms of computational costs and solution quality, and outperform commercial solvers for large instances.

An Optimal Selection and Placement of Distributed Energy Resources Using Hybrid Genetic Local Binary Knowledge Optimization

In recent times, the virtual power plant (VPP) is gaining more attention in power system engineering due to its tremendous potential in enhancing sustainable urbanism, in which, it supplies clean energy from distributed generators. Electricity is deemed a basic requirement for future automotive and ultra-modern technologies. The deficiency of traditional energy resources and their complex generation process make the production cost of electricity increase dramatically. Moreover, traditional power distribution systems are encountering issues in distributing electrical energy to fulfill customer demands. Therefore, this paper proposes a novel power management system named ‘the hybrid genetic local binary knowledge (HGLBK) algorithm’ to manage power distribution in the transmission lines and to optimize the total operation cost of the network. The hybrid optimization algorithm effectively controls the load by supplying the surplus power load to the adjacent feeders thereby optimally selecting and placing the distributed energy resource (DER). The proposed concept is implemented at Kayathar, Tamil Nadu in India, and their real-time data are utilized for modeling the VPP. The proposed VPP concept is implemented in the IEEE-9 bus system and the performance of VPP is simulated using the MATLAB software. The performance of the proposed HGLBK algorithm is assessed by comparing its effectiveness with the existing approaches.

Boosted local dimensional mutation and all-dimensional neighborhood slime mould algorithm for feature selection

The slime mould algorithm (SMA) is a population-based optimization algorithm that mimics the foraging behavior of slime moulds with a simple structure and few hyperparameters. However, SMA has some limitations, such as getting trapped in local optima when dealing with multimodal or combinatorial functions. To overcome these limitations and improve the algorithm's exploration and exploitation abilities, a local dimensional mutation strategy and an all-dimensional neighborhood search strategy for SMA, known as LASMA, were introduced. To evaluate the performance of LASMA, experiments were conducted on 30 benchmark functions from the CEC2014 competition, and the results were compared with up to 27 peers. The experimental results were then synthesized, and the Wilcoxon signed-rank test was used to evaluate the performance of LASMA. The results showed that LASMA outperformed other algorithms in terms of solution accuracy, stability, and convergence speed, with at least a 53.3% improvement in optimization performance on the 30 tested functions. Moreover, to demonstrate the applicability of LASMA to feature selection problems, a binary version of LASMA called bLASMA was developed and compared with eight binary classification algorithms on 18 datasets from the UCI repository. The experimental results showed that bLASMA not only had faster convergence speed and higher convergence accuracy in handling optimization problems but also performed well in feature selection applications. Thus, LASMA is a promising optimization tool for handling global and binary optimization problems, and its binary version, bLASMA, can be used for feature selection tasks. By addressing the limitations of SMA and improving the algorithm's exploration and exploitation abilities, LASMA provides a robust and effective solution for various optimization problems.

A Binary Grey Wolf Optimization based Hybrid Convolutional Neural Network (BGWOHCNN) framework for hyperspectral image classification

A Binary Grey Wolf Optimization based Hybrid Convolutional Neural Network (BGWOHCNN) framework for hyperspectral image classification