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W-band frequency selective digital metasurface using active learning-based binary optimization

NANOPHOTONICS 2025年

作者： Kim, Young-Bin Park, Jaehyeon Kim, Jun-Young Seo, Seok-Beom Kim, Sun-Kyung Lee, Eungkyu Kyung Hee Univ Dept Appl Phys Yongin 17104 Gyeonggi Do South Korea Kyung Hee Univ Dept Elect Engn Yongin 17104 Gyeonggi Do South Korea

The W-band is essential for applications like high-resolution imaging and advanced monitoring systems, but high-frequency signal attenuation leads to poor signal-to-noise ratios, posing challenges for compact and multi-channel systems. This necessitates distinct frequency selective surfaces (FSS) on a single substrate, a complex task due to inherent substrate resonance modes. In this study, we use a digital metasurface platform to design W-band FSS on a glass substrate, optimized through binary optimization assisted by active learning. The digital metasurface is composed of a periodic array of sub-wavelength unit cells, each containing hundreds of metal or dielectric pixels that act as binary states. By utilizing a machine learning model, we apply active learning-aided binary optimization to determine the optimal binary state configurations for a given target FSS profile. Specifically, we identify optimal designs for distinct FSS on a conventional glass substrate, with transmittance peaks at 79.3 GHz and Q-factors of 32.7.

关键词： digital metasurface frequency selective surface active learning binary optimization

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Efficiency analysis of binary metaheuristic optimization algorithms for uncapacitated facility location problems

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APPLIED SOFT COMPUTING 2025年 174卷

作者： Sag, Tahir Ihsan, Aysegul Selcuk Univ Dept Comp Engn TR-42075 Konya Turkiye Selcuk Univ Dept Informat Technol Engn TR-42075 Konya Turkiye

This paper introduces binary adaptations of four metaheuristic optimization algorithms: the binary Coati optimization Algorithm (BCOA), binary Mexican Axolotl optimization Algorithm (BMAO), binary Dynamic Hunting Leadership optimization (BDHL), and binary Aquila Optimizer (BAO). These algorithms were evaluated for their effectiveness in solving Uncapacitated Facility Location (UFL) problems, which aim to minimize total costs associated with customer-facility allocations and facility opening expenses by determining the optimal number of open facilities. Using 15 UFL problem instances from the OR-Lib dataset, the study assessed algorithm performance across 17 transfer functions (TFs), including S-shaped, V-shaped, and other variants, to address the binary nature of these problems. Performance metrics such as the best, worst, average, standard deviation, and GAP values were analyzed for each binary algorithm. Additionally, statistical analyses were conducted to further assess algorithmic performance. The Kolmogorov-Smirnov (KS) normality test was applied to determine the distribution characteristics of the results, followed by either ANOVA or Kruskal-Wallis tests, depending on the normality of the distributions. These statistical tests revealed significant differences in algorithm performance across different problem instances. Rank values were calculated based on GAP values and CPU times to facilitate comparisons across algorithm versions for the 15 UFL problems. Results underscored the critical role of TF selection in optimizing algorithm efficiency: BCOA performed best with TF11, BMAO with TF16 and TF17, BAO with TF10, and BDHL with TF15. Finally, a performance comparison on GAP values was conducted with two state-of-the-art PSO variants adapted for binary optimization. The proposed algorithms demonstrated either superior or competitive performance in solving UFL problems, validating their efficacy in complex optimization tasks and highlighting the influence of TFs

关键词： Aquila optimizer binary optimization Coati optimization Dynamic hunting leadership optimization Mexican axolotl optimization

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A binary grasshopper optimization algorithm for solving uncapacitated facility location problem

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ENGINEERING SCIENCE AND TECHNOLOGY-AN INTERNATIONAL JOURNAL-JESTECH 2025年 65卷

作者： Babalik, Ahmet Babadag, Aybuke Konya Tech Univ Fac Engn & Nat Sci Dept Comp Engn TR-42075 Konya Turkiye

The Uncapacitated Facility Location Problem (UFLP) is a real-world binary optimization problem that aims to find the number of facilities to open, minimizing the total cost of exchange between customers and facilities, as well as the opening costs of these facilities. UFLP is classified as an NP-Hard problem. Metaheuristic methods are often preferred to solve UFLP due to their ability to find acceptable solutions in a reasonable time and its NPHard characteristics. Grasshopper optimization Algorithm (GOA) is a continuous metaheursitics optimization algorithm. In the literature, although some binary versions of the GOA algorithm have been used to solve problems such as feature selection, knapsack, scheduling and cluster covering, its performance analysis has not been conducted on UFLP which is pure binary optimization problem. In this study, a novel binary version of the GOA integrated with a novel binarization procedure is proposed for solving the UFLP. In the binarization procedure, a probability-based update strategy has been developed for generating new candidate solutions. This approach ensures the probability of determining the effect of the global best solution on the candidate solution. Besides, during the population update phase, there are two different mechanisms to update the global best solution and other grasshoppers. To enhance diversity in the grasshopper population, an alpha parameter has been integrated into the original algorithm. It was aimed to improve the quality of the candidate solutions by the integration of the alpha parameter. The performance of the proposed algorithm is assessed on the CAP and M* datasets. The obtained GAP values for the CAP 71-CAP A, CAP B, and CAP C problems are 0, 0.14, and 0.18, respectively. The GAP is 0 for the MO1-MO5, MP2, MP3, and MQ1-MQ3 problems, and GAP <= 0.24 for the remaining problems. The results were compared with other state-of-the-art binary optimization algorithms. The experimental results show that the

关键词： binary optimization Discrete optimization Grasshopper optimization algorithm Uncapacitated facility location problem

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binary optimization using hybrid particle swarm optimization and gravitational search algorithm

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NEURAL COMPUTING & APPLICATIONS 2014年第6期25卷 1423-1435页

作者： Mirjalili, Seyedali Wang, Gai-Ge Coelho, Leandro dos S. Griffith Univ Sch Informat & Commun Technol Brisbane Qld 4111 Australia Jiangsu Normal Univ Sch Comp Sci & Technol Xuzhou 221116 Jiangsu Peoples R China Pontifical Catholic Univ Parana PUCPR Ind & Syst Engn Grad Program PPGEPS Curitiba Parana Brazil Fed Univ Parana UFPR Dept Elect Engn Elect Engn Grad Program PPGEE Polytech Ctr Curitiba Parana Brazil

The PSOGSA is a novel hybrid optimization algorithm, combining strengths of both particle swarm optimization (PSO) and gravitational search algorithm (GSA). It has been proven that this algorithm outperforms both PSO and GSA in terms of improved exploration and exploitation. The original version of this algorithm is well suited for problems with continuous search space. Some problems, however, have binary parameters. This paper proposes a binary version of hybrid PSOGSA called BPSOGSA to solve these kinds of optimization problems. The paper also considers integration of adaptive values to further balance exploration and exploitation of BPSOGSA. In order to evaluate the efficiencies of the proposed binary algorithm, 22 benchmark functions are employed and divided into three groups: unimodal, multimodal, and composite. The experimental results confirm better performance of BPSOGSA compared with binary gravitational search algorithm (BGSA), binary particle swarm optimization (BPSO), and genetic algorithm in terms of avoiding local minima and convergence rate.

关键词： binary optimization binary algorithms PSOGSA Particle swarm optimization Gravitational search algorithm

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binary optimization for source localization in the inverse problem of ECG

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MEDICAL & BIOLOGICAL ENGINEERING & COMPUTING 2014年第9期52卷 717-728页

作者： Potyagaylo, Danila Cortes, Elisenda Gil Schulze, Walther H. W. Doessel, Olaf Karlsruhe Inst Technol Inst Biomed Engn D-76021 Karlsruhe Germany

The goal of ECG-imaging (ECGI) is to reconstruct heart electrical activity from body surface potential maps. The problem is ill-posed, which means that it is extremely sensitive to measurement and modeling errors. The most commonly used method to tackle this obstacle is Tikhonov regularization, which consists in converting the original problem into a well-posed one by adding a penalty term. The method, despite all its practical advantages, has however a serious drawback: The obtained solution is often over-smoothed, which can hinder precise clinical diagnosis and treatment planning. In this paper, we apply a binary optimization approach to the transmembrane voltage (TMV)-based problem. For this, we assume the TMV to take two possible values according to a heart abnormality under consideration. In this work, we investigate the localization of simulated ischemic areas and ectopic foci and one clinical infarction case. This affects only the choice of the binary values, while the core of the algorithms remains the same, making the approximation easily adjustable to the application needs. Two methods, a hybrid metaheuristic approach and the difference of convex functions (DC), algorithm were tested. For this purpose, we performed realistic heart simulations for a complex thorax model and applied the proposed techniques to the obtained ECG signals. Both methods enabled localization of the areas of interest, hence showing their potential for application in ECGI. For the metaheuristic algorithm, it was necessary to subdivide the heart into regions in order to obtain a stable solution unsusceptible to the errors, while the analytical DC scheme can be efficiently applied for higher dimensional problems. With the DC method, we also successfully reconstructed the activation pattern and origin of a simulated extrasystole. In addition, the DC algorithm enables iterative adjustment of binary values ensuring robust performance.

关键词： Inverse problem of ECG binary optimization Non-smooth source localization

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Inverse binary optimization of convolutional neural network in active learning efficiently designs nanophotonic structures

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Scientific Reports 2025年第1期15卷 1-10页

作者： Park, Jaehyeon Xu, Zhihao Park, Gyeong-Moon Luo, Tengfei Lee, Eungkyu Department of Electronic Engineering Kyung Hee University Gyonggi-do Yongin-si 17104 South Korea Department of Aerospace and Mechanical Engineering University of Notre Dame Notre Dame 46556 IN United States Department of Artificial Intelligence Korea University Seongbuk-gu Seoul 02841 South Korea

binary optimization using active learning schemes has gained attention for automating the discovery of optimal designs in nanophotonic structures and material configurations. Recently, active learning has utilized factorization machines (FM), which usually are second-order models, as surrogates to approximate the hypervolume of the design space, benefiting from rapid optimization by Ising machines such as quantum annealing (QA). However, due to their second-order nature, FM-based surrogate functions struggle to fully capture the complexity of the hypervolume. In this paper, we introduce an inverse binary optimization (IBO) scheme that optimizes a surrogate function based on a convolutional neural network (CNN) within an active learning framework. The IBO method employs backward error propagation to optimize the input binary vector, minimizing the output value while maintaining fixed parameters in the pre-trained CNN layers. We conduct a benchmarking study of the CNN-based surrogate function within the CNN-IBO framework by optimizing nanophotonic designs (e.g., planar multilayer and stratified grating structure) as a testbed. Our results demonstrate that CNN-IBO achieves optimal designs with fewer actively accumulated training data than FM-QA, indicating its potential as a powerful and efficient method for binary optimization. © The Author(s) 2025.

关键词： Active learning binary optimization Convolutional neural network Inverse optimization Nanophotonics

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binary optimization: A relation between the depth of a local minimum and the probability of its detection

Binary optimization: A relation between the depth of a local...

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4th International Conference on Informatics in Control, Automation and Robotics

作者： Kryzhanovsky, B. V. Kryzhanovsky, V. M. Mikaelian, A. L. SR Inst Syst Analisys RAS Ctr Opt Neural Technol Moscow 119333 Russia

ISBN: (纸本)9789728865825

The standard method in optimization problems consists in a random search of the global minimum: a neuron network relaxes in the nearest local minimum from some randomly chosen initial configuration. This procedure is to be repeated many times in order to find as deep an energy minimum as possible. However the question about the reasonable number of such random starts and whether the result of the search can be treated as successful remains always open. In this paper by analyzing the generalized Hopfield model we obtain expressions describing the relationship between the depth of a local minimum and the size of the basin of attraction. Based on this, we present the probability of finding a local minimum as a function of the depth of the minimum. Such a relation can be used in optimization applications: it allows one, basing on a series of already found minima, to estimate the probability of finding a deeper minimum, and to decide in favor of or against further running the program. The theory is in a good agreement with experimental results.

关键词： binary optimization neural networks local minimum

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STOCHASTIC LEARNING APPROACH FOR binary optimization: APPLICATION TO BAYESIAN OPTIMAL DESIGN OF EXPERIMENTS*

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2022年第2期44卷 B395-B427页

作者： ATTIA, A. H. M. E. D. LEYFFER, S. V. E. N. MUNSON, T. O. D. D. S. Argonne Natl Lab Math & Comp Sci Div Lemont IL 60439 USA

We present a novel stochastic approach to binary optimization suited for optimal experimental design (OED) for Bayesian inverse problems governed by mathematical models such as partial differential equations. The OED utility function, namely, the regularized optimality criterion, is cast into a stochastic objective function in the form of an expectation over a multivariate Bernoulli distribution. The probabilistic objective is then solved by using a stochastic optimization routine to find an optimal observational policy. This formulation (a) is generally applicable to binary optimization problems with soft constraints and is ideal for OED and sensor placement problems;(b) does not require differentiability of the original objective function (e.g., a utility function in OED applications) with respect to the design variable, and thus it enables direct employment of sparsityenforcing penalty functions such as \ell 0, without needing to utilize a continuation procedure or apply a rounding technique;(c) exhibits much lower computational cost than traditional gradient-based relaxation approaches;and (d) can be applied to both linear and nonlinear OED problems with proper choice of the utility function. The proposed approach is analyzed from an optimization perspective with detailed convergence analysis of the optimization approach and is also analyzed from a machine learning perspective with correspondence to policy gradient reinforcement learning. The approach is demonstrated numerically by using an idealized two-dimensional Bayesian linear inverse problem and validated by extensive numerical experiments carried out for sensor placement in a parameter identification setup.

关键词： design of experiments binary optimization Bayesian inverse problem reinforcement learning stochastic optimization

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Tabu search exploiting local optimality in binary optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第3期308卷 1037-1055页

作者： Hanafi, Said Wang, Yang Glover, Fred Yang, Wei Hennig, Rick Univ Polytech Hauts Defrance CNRS UMR 8201 LAMIHINSA Hauts De France F-59313 Valenciennes France Northwestern Polytech Univ Sch Management 127 Youyi West Rd Xian 710072 Peoples R China Entanglement Inc Boulder CO USA

A variety of strategies have been proposed for overcoming local optimality in metaheuristic search. This paper examines characteristics of moves that can be exploited to make good decisions about steps that lead away from a local optimum and then lead toward a new local optimum. We introduce strategies to identify and take advantage of useful features of solution history with an adaptive memory metaheuris-tic, to provide rules for selecting moves that offer promise for discovering improved local optima. Our approach uses a new type of adaptive memory based on a construction called exponential extrapolation. The memory operates by means of threshold inequalities that ensure selected moves will not lead to a specified number of most recently encountered local optima. Associated thresholds are embodied in choice rule strategies that further exploit the exponential extrapolation concept and open a variety of research possibilities for exploration. The considerations treated in this study are illustrated in an imple-mentation to solve the Quadratic Unconstrained binary optimization (QUBO) problem. We show that the AA algorithm obtains an average objective gap of 0.0315% to the best known values for the 21 largest Palubeckis instances. This solution quality is considered to be quite attractive because less than 20 s on average are taken by AA, which is 1 to 2 orders of magnitude less than the time required by most algo-rithms reporting the best known results.(c) 2023 Elsevier B.V. All rights reserved.

关键词： Metaheuristics Local optimality Adaptive memory Tabu search binary optimization QUBO

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An artificial algae algorithm with stigmergic behavior for binary optimization

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APPLIED SOFT COMPUTING 2018年 64卷 627-640页

作者： Korkmaz, Sedat Kiran, Mustafa Servet Selcuk Univ Fac Engn Dept Comp Engn TR-42075 Konya Turkey

In this study, we focus on modification of the artificial algae algorithm (AAA), proposed for solving continuous optimization problems, for binary optimization problems by using exclusive-or (xor) logic operator and stigmergic behavior. In the algorithm, there are four processes sequentially realized for solving continuous problems. In the binary version of the algorithm, three of them are adapted in order to overcome the structure of binary optimization problems. In the initialization, the colonies of AAA are set to either zero or one with equal probability. Secondly, helical movement phase is used for obtaining candidate solutions and in this phase, the xor operator and stigmergic behavior are utilized for obtaining binary candidate solutions. The last modified phase is adaptation, and randomly selected binary values in the most starved solution are likened to biggest colony obtained so far. The proposed algorithm is applied to solve well-known uncapacitated facility location problems and numeric benchmark problems. Obtained results are compared with state-of-art algorithms in swarm intelligence and evolutionary computation field. Experimental results show that the proposed algorithm is superior to other techniques in terms of solution quality, convergence characteristics and robustness. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Artificial algae algorithm binary optimization Stigmergy Benchmark problem

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