Unimodal Functions Research Articles

FAST Observations of an Extremely Active Episode of FRB 20201124A. III. Polarimetry

As the third paper in the multiple-part series, we report the statistical properties of radio bursts detected from the repeating fast radio burst (FRB) source FRB 20201124A with the Five-hundred-meter Aperture Spherical radio Telescope during an extremely active episode between the 25th and 28th of September 2021 (UT). We focus on the polarization properties of 536 bright bursts with S/N > 50. We found that the Faraday rotation measures (RMs) monotonically dropped from −579 to −605 rad m−2 in the 4 day window. The RM values were compatible with the values (−300 to −900 rad m−2) reported 4 months ago. However, the RM evolution rate in the current observation window was at least an order of magnitude smaller than the one (∼500 rad m−2 day−1) previously reported during the rapid RM-variation phase, but is still higher than the one (≤1 rad m−2 day−1) during the later RM no-evolution phase. The bursts of FRB 20201124A were highly polarized with the total degree of polarization (circular plus linear) greater than 90% for more than 90% of all bursts. The distribution of linear polarization position angles (PAs), degree of linear polarization (L/I) and degree of circular polarization (V/I) can be characterized with unimodal distribution functions. During the observation window, the distributions became wider with time, i.e., with larger scatter, but the centroids of the distribution functions remained nearly constant. For individual bursts, significant PA variations (confidence level 5σ) were observed in 33% of all bursts. The polarization of single pulses seems to follow certain complex trajectories on the Poincaré sphere, which may shed light on the radiation mechanism at the source or the plasma properties along the path of FRB propagation.

The Power Zeghdoudi Distribution: Properties, Estimation, and Applications to Real Right-Censored Data

A new two-parameter power Zeghdoudi distribution (PZD) is suggested as a modification of the Zeghdoudi distribution using the power transformation method. As a result, the PZD may have increasing, decreasing, and unimodal probability density function and decreasing mean residual life function. In addition, other properties are presented, such as moments, order statistics, reliability measures, Bonferroni and Lorenz curves, Gini index, stochastic ordering, mean and median deviations, and quantile function. Following this, a section is devoted to the related model parameters which are estimated using the maximum likelihood estimation method, the weighted least squares and least squares methods, the maximum product of spacing method, the Cramer–von Mises method, and the right-tail and left-tail Anderson–Darling methods, and the Nikulin–Rao–Robson test statistic is considered. A simulation study is conducted to assess these methods and to investigate the distribution properties with right-censored data. The applicability of the proposed model is studied based on three real data sets of failure times, bladder cancer patients, and glass fiber data with a comparison with such competitors as the gamma, xgamma, Lomax, Darna, power Darna, power Lindley, and exponentiated power Lindley models. According to several established criteria, the comparative findings are overwhelmingly favorable to the suggested model.

A survey of recently developed metaheuristics and their comparative analysis

The aim of this study was to gather, discuss, and compare recently developed metaheuristics to understand the pace of development in the field of metaheuristics and make some recommendations for the research community and practitioners. By thoroughly and comprehensively searching the literature and narrowing the search results, we created with a list of 57 novel metaheuristic algorithms. Based on the availability of the source code, we reviewed and analysed the optimization capability of 26 of these algorithms through a series of experiments. We also evaluated the exploitation and exploration capabilities of these metaheuristics by using 50 unimodal functions and 50 multimodal functions, respectively. In addition, we assessed the capability of these algorithms to balance exploration and exploitation by using 29 shifted, rotated, composite, and hybrid CEC-BC-2017 benchmark functions. Moreover, we evaluated the applicability of these metaheuristics on four real-world constrained engineering optimization problems. To rank the algorithms, we performed a nonparametric statistical test, the Friedman mean rank test. Based on the statistical results for the unimodal and multimodal functions, we declared that the GBO, PO, and MRFO algorithms have better exploration and exploitation capabilities. Based on the results for the CEC-BC-2017 benchmark functions, we found the MPA, FBI, and HBO algorithms to be the most balanced. Finally, based on the results for the constrained engineering optimization problems, we declared that the HBO, GBO, and MA algorithms are the most suitable. Collectively, we confidently recommend the GBO, MPA, PO, and HBO algorithms for real-world optimization problems.

Attention-Based Sentiment Region Importance and Relationship Analysis for Image Sentiment Recognition.

Image sentiment recognition has attracted considerable attention from academia and industry due to the increasing tendency of expressing opinions via images and videos online. Previous studies focus on multilevel representation from global and local views to improve recognition performance. However, it is insufficient to research the importance and relationship of visual regions for image sentiment recognition. This paper proposes an attention-based sentiment region importance and relationship (ASRIR) analysis method, including important attention and relation attention for image sentiment recognition. First, we extract spatial region features using a multilevel pyramid network from the image. Second, we design important attention to exploring the sentiment semantic-related regions and relation attention to investigating the relationship between regions. In order to release the excessive concentration of attention, we employ a unimodal function as the objective function for regularization. Finally, the region features weighted by the attention mechanism are fused and input into a fully connected layer for classification. Extensive experiments on various commonly used image sentiment datasets demonstrate that our proposed method outperforms the state-of-the-art approaches.

An Improved Particle-Swarm-Optimization Algorithm for a Prediction Model of Steel Slab Temperature

Aiming at the problem of the low accuracy of temperature prediction, a mathematical model for predicting the temperature of a steel billet is developed. For the process of temperature prediction, an improved particle-swarm-optimization algorithm (called XPSO) is developed. XPSO was designed based on a multiple swarm scheme to improve the global search capability and robustness; thus, it can improve the low accuracy of prediction and overcome the problem of easy entrapment into local optima. In the XPSO, the multiple swarm scheme comprises four modified components: (1) the strategy of improving the positional initialization; (2) the mutation strategy for particle swarms; (3) the adjustment strategy of inertia weights; (4) the strategy of jumping out local optima. Based on widely used unimodal, multimodal and composite benchmark functions, the effectiveness of the XPSO algorithm was verified by comparing it with some popular variant PSO algorithms (PSO, IPSO, IPSO2, HPSO, CPSO). Then, the XPSO was applied to predict the temperatures of steel billets based on simulation data sets and measured data sets. Finally, the obtained results show that the XPSO is more accurate than other PSO algorithms and other optimization approaches (WOA, IA, GWO, DE, ABC) for temperature prediction of steel billets.

An Approximate MSE Expression for Maximum Likelihood and Other Implicitly Defined Estimators of Non-Random Parameters

An approximate mean square error (MSE) expression for the performance analysis of implicitly defined estimators of non-random parameters is proposed. An implicitly defined estimator (IDE) declares the minimizer/maximizer of a selected cost/reward function as the parameter estimate. The maximum likelihood (ML) and the least squares estimators are among the well known examples of this class. In this paper, an exact MSE expression for implicitly defined estimators with a symmetric and unimodal objective function is given. It is shown that the expression reduces to the Cramer-Rao lower bound (CRLB) and misspecified CRLB in the large sample size regime for ML and misspecified ML estimation, respectively. The expression is shown to yield the Ziv-Zakai bound (without the valley filling function) for the maximum a posteriori (MAP) estimator when it is used in a Bayesian setting, that is, when an a-priori distribution is assigned to the unknown parameter. In addition, extension of the suggested expression to the case of nuisance parameters is studied and some approximations are given to ease the computations for this case. Numerical results indicate that the suggested MSE expression not only predicts the estimator performance in the asymptotic region; but it is also applicable for the threshold region analysis, even for IDEs whose objective functions do not satisfy the symmetry and unimodality assumptions. Advantages of the suggested MSE expression are its conceptual simplicity and its relatively straightforward numerical calculation due to the reduction of the estimation problem to a binary hypothesis testing problem, similar to the usage of Ziv-Zakai bounds in random parameter estimation problems.

An Improved Nonlinear Tuna Swarm Optimization Algorithm Based on Circle Chaos Map and Levy Flight Operator

The tuna swarm optimization algorithm (TSO) is a new heuristic algorithm proposed by observing the foraging behavior of tuna populations. The advantages of TSO are a simple structure and fewer parameters. Although TSO converges faster than some classical meta-heuristics algorithms, it can still be further accelerated. When TSO solves complex and challenging problems, it often easily falls into local optima. To overcome the above issue, this article proposed an improved nonlinear tuna swarm optimization algorithm based on Circle chaos map and levy flight operator (CLTSO). In order to compare it with some advanced heuristic algorithms, the performance of CLTSO is tested with unimodal functions, multimodal functions, and some CEC2014 benchmark functions. The test results of these benchmark functions are statistically analyzed using Wilcoxon, Friedman test, and MAE analysis. The experimental results and statistical analysis results indicate that CLTSO is more competitive than other advanced algorithms. Finally, this paper uses CLTSO to optimize a BP neural network in the field of artificial intelligence. A CLTSO-BP neural network model is proposed. Three popular datasets from the UCI Machine Learning and Intelligent System Center are selected to test the classification performance of the new model. The comparison result indicates that the new model has higher classification accuracy than the original BP model.

IFA-EO: An improved firefly algorithm hybridized with extremal optimization for continuous unconstrained optimization problems

As one of the evolutionary algorithms, firefly algorithm (FA) has been widely used to solve various complex optimization problems. However, FA has significant drawbacks in slow convergence rate and is easily trapped into local optimum. To tackle these defects, this paper proposes an improved FA combined with extremal optimization (EO), named IFA-EO, where three strategies are incorporated. First, to balance the tradeoff between exploration ability and exploitation ability, we adopt a new attraction model for FA operation, which combines the full attraction model and the single attraction model through the probability choice strategy. In the single attraction model, small probability accepts the worse solution to improve the diversity of the offspring. Second, the adaptive step size is proposed based on the number of iterations to dynamically adjust the attention to the exploration model or exploitation model. Third, we combine an EO algorithm with powerful ability in local-search into FA. Experiments are tested on two group popular benchmarks including complex unimodal and multimodal functions. Our experimental results demonstrate that the proposed IFA-EO algorithm can deal with various complex optimization problems and has similar or better performance than the other eight FA variants, three EO-based algorithms, and one advanced differential evolution variant in terms of accuracy and statistical results.

Grey Wolf Optimization algorithm based on Cauchy-Gaussian mutation and improved search strategy

The traditional Grey Wolf Optimization algorithm (GWO) has received widespread attention due to features of strong convergence performance, few parameters, and easy implementation. However, in actual optimization projects, there are problems of slow convergence speed and easy to fall into local optimal solution. The paper proposed a Grey Wolf Optimization algorithm based on Cauchy-Gaussian mutation and improved search strategy (CG-GWO) in response to the above problems. The Cauchy-Gaussian mutation operator is introduced to increase the population diversity of the leader wolves and improve the global search ability of the algorithm. This work retains outstanding grey wolf individuals through the greedy selection mechanism to ensure the convergence speed of the algorithm. An improved search strategy was proposed to expand the optimization space of the algorithm and improve the convergence accuracy. Experiments are performed with 16 benchmark functions covering unimodal functions, multimodal functions, and fixed-dimension multimodal functions to verify the effectiveness of the algorithm. Experimental results show that compared with four classic optimization algorithms, particle swarm optimization algorithm (PSO), whale optimization algorithm (WOA), sparrow optimization algorithm (SSA), and farmland fertility algorithm (FFA), the CG-GWO algorithm shows better convergence accuracy, convergence speed, and global search ability. The proposed algorithm shows the same better performance compared with a series of improved algorithms such as the improved grey wolf algorithm (IGWO), modified Grey Wolf Optimization algorithm (mGWO), and the Grey Wolf Optimization algorithm inspired by enhanced leadership (GLF-GWO).

A dynamic model of adaptive consumers with endogenous unimodal preferences

We consider a discrete-time dynamic model to describe the repeated choices of adaptive consumers that at each time period adjust their request for a given good according to the discrepancies between the observed price and the fair price perceived on the basis of their utility function. Moreover, consumers’ preferences are endogenously modified on the basis of past consumption experience. The model considered is derived from the one proposed in D’Orlando and Rodano (2006), with a different assumption about the way the utility function changes according to the past consumption. In fact, in D’Orlando and Rodano (2006) the consumption preferences increase whenever past consumption increases, whereas in the model proposed in this paper a saturation effect is introduced, so that the same assumption holds for low and moderate past consumption, whereas current consumption decreases if the quantity consumed in the previous time period was too high. This leads to a unimodal preference function instead of an increasing one, which implies that the two-dimensional map, whose iteration represents the time evolution of the consumers’ choices, is transformed from an invertible map to a noninvertible one. Hence different global dynamic properties are obtained that influence the structure of the attractors and basins of attraction. These global dynamic features, described by the method of critical curves, interact with the property that the map is also characterized by the presence of a denominator that can vanish, giving rise to different kinds of singularities denoted as focal points and prefocal curves in Bischi et al. (1999), Bischi et al. (2003), Bischi et al. (2005), that strongly influence the structure of the basins of attraction. We describe the structure of the basins of attraction, and the contact bifurcations that change the qualitative properties of their global structure, by using geometric and numerical methods guided by the combined study of critical and prefocal curves.

Inverse estimation of hydraulic parameters of soils with rock fragments

The application of inverse modeling to determine the hydraulic properties of layered soils with rock fragments (RF > 2 mm) is associated with complex challenges such as selecting suitable hydraulic functions and defining a strategy to optimize many parameters. These two issues were addressed in this study by performing field drainage experiments in layered soil profiles (three layers) with different particle size distributions and different percentages of RF. Water contents (θ) and pressure heads (h) were monitored at different soil depths during drainage experiments (h ≥ −200 cm). Data of θ and h for a drier range (h < −5000 cm) were determined with a dew point potentiometer on disturbed soil samples. The unimodal and bimodal van Genuchten-Mualem functions were evaluated, and their parameters were optimized using the Hydrus-1D “Inverse solution”. The RETC curve fitting software was used to estimate the second set of parameters of the bimodal function. The parameters for the uni- and bimodal models (15 and 27 parameters, respectively) were repeatedly optimized by fixing some parameters while estimating others. The unimodal van Genuchten-Mualem function provided a satisfactory fit of θ and h measurements only when either drainage or dew point potentiometer measurements were used. On the other hand, the bimodal van Genuchten-Mualem function provided a satisfactory fit of θ and h measurements when both sets of data (drainage and dew point potentiometer measurements) were used simultaneously. Furthermore, the optimized parameters were physically consistent except for a few high saturated hydraulic conductivity values. Therefore, bimodal functions should be considered to represent the hydraulic properties of soils with RF. The problem of many calibrated parameters when using bimodal functions can be managed using sequential optimization, which allowed us to estimate 27 parameters for layered soils with RF successfully.

Young’s double-slit experiment optimizer : A novel metaheuristic optimization algorithm for global and constraint optimization problems

Due to the global progress, the optimization problems are becoming more and more complex. Hence, deterministic and heuristic approaches are no longer adequate for dealing with such sophisticated problems. subsequently, metaheuristics have recently emerged as an effective alternative for addressing the optimization problems. This paper proposes a novel metaheuristic called Young’s Double-Slit Experiment (YDSE) optimizer, derived from a physical backdrop. The YDSE optimizer is inspired by Young’s double-slit experiment, which is regarded as one of the most well-known classical physics experiments, revealing the wave nature of light. In YDSE optimizer, each fringe represents a possible solution in the population. Many concepts are modeled from the experiment, such as monochromatic light waves, Huygens’ principle, constructive and destructive interference, wave intensity, amplitude, and path difference. The YDSE optimizer strikes a balance between exploration and exploitation by selecting either a constructive interference or a destructive interference based on the order number of the fringe. During the optimization process, the solution moves in search space based on its order number. If the solution has an odd number, it moves in the dark regions towards the central bright region, which is expected to contain the optimal solution. The algorithm exploits the promising areas in the bright fringe areas, which are assumed to contain the optimum. The performance of the YDSE optimizer is compared with another twelve metaheuristics using CEC 2014, CEC 2017, and CEC 2022. The benchmarks cover different unimodal, multimodal, hybrid, and composite test functions. Also, we consider ten constrained and unconstrained engineering optimization design problems. YDSE proved its superiority over the CEC 2014 and CEC 2017 winners, such as L-SHADE, LSHADE-cnEpSin, and LSHADE-SPACMA. The results and the statistical analysis demonstrated the outperformance of the proposed YDSE optimizer at a 95% confidence interval.

Research on single cell membrane algorithm and engineering application based on membrane computing theory

Membrane computing is a new computing paradigm with great significance in the field of computer science. The Multi-membrane search algorithm (MSA) is proposed based on the membrane computational population optimization theory. It showed excellent performance in the test. This paper further studies the performance characteristics of a single individual (Single Cell Membrane Algorithm, SCA) of MSA. SCA can generate adaptive solution sets for problems of different dimensions. Through transcription and reprocessing rules, new weakly correlated feasible solutions are formed for global search and local exploration. This paper is based on the unimodal Sphere function and the multimodal Rastrigr function, at dim=3, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 300, 500, 1000 and Q=1.00, 0.75, 0.50, 0.40, 0.30, 0.20, 0.10, 0.005, 0.025, 0.010, the SCA was optimized for 1000 iterations. Analyze the impact of the key parameter Q of SCA on the search performance of the algorithm in problems of different dimensions. The results show that under the set conditions, SCA has better performance when Q is 0.010 and 0.025 in the unimodal function test. In the multimodal function test, SCA has better performance when dim≤100 and Q≤0.200, and when dim>100 and Q≥0.200. In addition, this paper employs one engineering problem: I-beams to perform engineering tests on SCA and obtain results superior to other algorithms participating in the comparison. The test and comparison results show that SCA can also be used as a derivative algorithm of MSA, and has good performance.

Make waiting not to seem like waiting: Capacity management of waiting-area entertainment

To operationalize the psychological principle that “occupied time feels shorter than unoccupied time”, it is common for service providers to offer entertainment options in the waiting areas. Typical examples that put in practice this mechanism include amusement parks, car dealers, airports, hospitals, restaurants, etc. In this paper, we study a queueing system where the server provides entertainment services to waiting customers. Assuming customers are strategic and delay-sensitive, we formulate a game-theoretical model and study customers' equilibrium behavior in response to this mechanism. Because offering waiting-area entertainment incurs extra operational costs, we discuss whether and when this option will benefit the service provider and obtain the optimal entertainment capacity that maximizes the system's profit. Our analysis reveals that this option is appealing if and only if the market size is intermediate and that the optimal capacity of the entertainment is a unimodal function in the market size. Our insights continue to remain valid when the service fee becomes endogenous.

Homonuclear Molecules Optimization (HMO) meta-heuristic algorithm

This study introduces a novel meta-heuristic algorithm known as Homonuclear Molecules Optimization (HMO) for optimizing complex and nonlinear problems. HMO is inspired by the arrangement of electrons around atoms given the Bohr atomic model and the structure of homonuclear molecules. This algorithm is based on creating the initial population of a set of atoms in the search space and the electrons associated with each atom (searching agents) given the quantum numbers. In each iteration, the best electron of each atom is selected as the new location of the nucleus, and a number of atoms move toward the atom with the best solution to form a homonuclear molecule. The results of applying the MHO algorithm were evaluated in comparison with three classical optimization algorithms of PSO, GA, and DE along with a novel algorithm called Equilibrium Optimizer (EO). The HMO was able to precisely solve unimodal functions and find global and local solutions for multimodal functions. The outcomes of Wilcoxon’s rank-sum test demonstrated that there is a significant difference between the final results of HMO and those of the other algorithms (a=0.05%). Overall, it was concluded that the HMO outperforms the classical algorithms and can compete with new and efficient algorithms such as EO.

Design and Analysis of FOPID-Based Damping Controllers Using a Modified Grey Wolf Optimization Algorithm

This study proposes a novel modified grey-wolf optimization algorithm (MGWOA) to enhance power system stability. The power system stabilizer and static synchronous series compensator (SSSC) are used as damping controllers. Additionally, fractional-order PID (FOPID) controller is used to handle the system nonlinearities and thus achieve better performance. The control parameters are tuned using the proposed MGWOA method which has been verified on unimodal and multimodal functions. Single-machine infinite bus (SMIB) and multimachine power system (MMPS) are taken as case studies to analyze the efficacy of the proposed controller. Minimization of rotor speed deviation is considered an objective function. The results obtained from the MGWOA-tuned FOPID-based damping controllers are compared with those obtained using recently developed efficient and competitive heuristic algorithms. It was observed that the MGWOA method is well-suited for damping low-frequency oscillations. Furthermore, statistical analysis is performed on the obtained results to justify the superiority of the MGWOA method. The simulation results suggest that the MGWOA exhibits superior performance characteristics when applied to a real power system.

Optimization of Oil Pipeline Operations to Reduce Energy Consumption Using an Improved Squirrel Search Algorithm

To achieve the goal of achieving carbon-neutral by 2060, the government of China has put forward higher requirements for energy conservation and consumption reduction in the energy industry. Therefore, it is necessary to reduce energy consumption in the process of transporting oil. In this paper, an optimization model that minimizes the total energy consumption of the entire pipeline system is proposed and the squirrel search algorithm (SSA) is used to solve the optimization model. Meanwhile, to improve the performance of the SSA, two strategies are proposed. One is the adaptive inertia weight strategy, and the other is the multi-group co-evolution strategy. The adaptive inertia weight can adjust the step size of the flying squirrels according to the difference of the objective function value and multi-group co-evolution is introduced to improve population diversity. The improved SSA is named multigroup coevolution-adaptive inertia weight SSA (MASSA). A total of 20 benchmark functions are used to test the performance of MASSA, including unimodal functions and multimodal functions. Compared with the other four algorithms, MASSA has better performance and convergence capabilities. In the case study experiment, an optimization model of the oil pipeline is built, which takes the minimum energy consumption of the whole pipeline as the objective function. Compared with the actual operating conditions, the electricity consumption optimized by MASSA decreases by 399,018.94 kgce, and the thermal energy dissipation decreases by 113,759.25 kgce. The total energy consumption is reduced by 512,778.19 kgce, which is 9.62%. These results indicate that the two improvement strategies are significant, and optimizing the operating parameters can reduce energy consumption.

When move acceptance selection hyper-heuristics outperform Metropolis and elitist evolutionary algorithms and when not

Selection hyper-heuristics (HHs) are automated algorithm selection methodologies that choose between different heuristics during the optimisation process. Recently, selection HHs choosing between a collection of elitist randomised local search heuristics with different neighbourhood sizes have been shown to optimise standard unimodal benchmark functions from evolutionary computation in the optimal expected runtime achievable with the available low-level heuristics. In this paper, we extend our understanding of the performance of HHs to the domain of multimodal optimisation by considering a Move Acceptance HH (MAHH) from the literature that can switch between elitist and non-elitist heuristics during the run. In essence, MAHH is a non-elitist search heuristic that differs from other search heuristics in the source of non-elitism.We first identify the range of parameters that allow MAHH to hillclimb efficiently and prove that it can optimise the standard hillclimbing benchmark function OneMax in the best expected asymptotic time achievable by unbiased mutation-based randomised search heuristics. Afterwards, we use standard multimodal benchmark functions to highlight function characteristics where MAHH outperforms elitist evolutionary algorithms and the well-known Metropolis non-elitist algorithm by quickly escaping local optima, and ones where it does not. Since MAHH is essentially a non-elitist random local search heuristic, the paper is of independent interest to researchers in the fields of artificial intelligence and randomised search heuristics.

Egret Swarm Optimization Algorithm: An Evolutionary Computation Approach for Model Free Optimization.

A novel meta-heuristic algorithm named Egret Swarm Optimization Algorithm (ESOA) is proposed in this paper, which is inspired by two egret species’ hunting behavior (Great Egret and Snowy Egret). ESOA consists of three primary components: a sit-and-wait strategy, aggressive strategy as well as discriminant conditions. The learnable sit-and-wait strategy guides the egret to the most probable solution by applying a pseudo gradient estimator. The aggressive strategy uses random wandering and encirclement mechanisms to allow for optimal solution exploration. The discriminant model is utilized to balance the two strategies. The proposed approach provides a parallel framework and a strategy for parameter learning through historical information that can be adapted to most scenarios and has well stability. The performance of ESOA on 36 benchmark functions as well as 3 engineering problems are compared with Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Differential Evolution (DE), Grey Wolf Optimizer (GWO), and Harris Hawks Optimization (HHO). The result proves the superior effectiveness and robustness of ESOA. ESOA acquires the winner in all unimodal functions and reaches statistic scores all above 9.9, while the scores are better in complex functions as 10.96 and 11.92.

Binary equilibrium optimizer: Theory and application in building optimal control problems

This study proposes a binary version of the recently developed Equilibrium Optimizer (EO) widely used in various applications. The performance of the proposed Binary Equilibrium Optimizer (BiEO) is evaluated against three classes of mathematical benchmark functions, including unimodal, multimodal, and composition functions. The results of BiEO are also compared to other binary optimizers, including Binary Particle Swarm Optimization with S-shape (BPSO/S) and V-shape (BPSO/V) transfer functions, Binary Dragonfly Algorithm (BDA), and Genetic Algorithm (GA). This study employs an advanced post-hoc analysis of Bonferroni–Dunn test to reveal the significant difference between BiEO and its competitors from the statistical point of view. BiEO has implications for various applications, specifically optimal control problems in buildings due to its rapid convergence rate and simplicity. To assess BiEO efficiency in the building and construction industry, three different test cases are selected: (i) control of switchable Ethylene tetrafluoroethylene (ETFE) cushions, (ii) operation of motorized shades, and (iii) schedule of window opening during natural ventilation. The results from the optimal control problems are analyzed from two perspectives of optimization and building energy performance. The proposed BiEO method shows a fast rate of convergence compared to its competitors in most mathematical and construction case studies (i.e., on average 5 times). This characteristic highlights the merits of BiEO and makes it a powerful binary optimizer specially when there are limited budget of time and iterations for solving an optimization problem and specifically for building applications it allows deploying it to real-time control of building systems and components. The source code of BiEO is publicly available at: https://github.com/afshinfaramarzi/Binary-Equilibrium-Optimizer, https://built-envi.com/portfolio/equilibrium-optimizer/, and https://seyedalimirjalili.com/eo.