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Global optimization techniques are increasingly preferred over human-driven methods in the design of electromagnetic structures such as metasurfaces, and careful construction and parameterization of the physical structure is critical in ensuring computational efficiency and convergence of the optimization algorithm to a globally optimal solution. While many design variables in physical systems take discrete values, optimization algorithms often benefit from a continuous design space. This work demonstrates the use of level set functions as a continuous basis for designing material distributions for metasurface arrays and introduces an improved parameterization which is termed the periodic level set function. We explore the use of alternate norms in the definition of the level set function and define a new pseudo-inverse technique for upsampling basis coefficients with these norms. The level set method is compared to the fragmented parameterization and shows improved electromagnetic responses for two dissimilar cost functions: a narrowband objective and a broadband objective. Finally, we manufacture an optimized level set metasurface and measure its scattering parameters to demonstrate real-world performance. [ABSTRACT FROM AUTHOR]

Many different aspects of software system development and verification rely on precise function identification in binary code. Recognition of the source Assembly functions in embedded systems is one of the fundamental challenges in binary program analysis. While numerous approaches assume that the functions are given a priori, correct identification of the functions in binaries remains a great issue. This contribution addresses the problem of uncertainty in binary code in identification of functions, which were optimized during compilation. This paper investigates the difference between debug and optimized functions via modeling of these functions. To do so, we introduce an extensible model-centred hands-on approach for examining similarities between binary functions. The main idea is to model each function using a set of predetermined, experimentally discovered features, and then find a suitable weight vector that could give impact factor to each such a feature. After finding the weight vector, the introduced models of such desired functions can be identified in binary software packages. It means that we reduce the similarity identification problem of the models to a classical version of optimization problems with one optimization criterion. Using our implementation, we found that the proposed approach works smoothly for functions, which contain at least ten Assembly instructions. Our tool guarantees success at a very high level. [ABSTRACT FROM AUTHOR]

The elastic optical network (EON) adopting virtual network function (VNF) is a new type of network, in which the routing, spectrum, and data center allocation are key and challenging problems, and solving these three problems simultaneously can not only improve the network efficiency for network providers, but also let users obtain better service. However, few existing works handle these three problems simultaneously. To tackle the three problems simultaneously, given a set of network function chains (i.e., a set of tasks), we set up a new multi-objective optimization model in which the total length of paths for all tasks is minimized, the totally occupied spectrums are minimized, and the loads on all data centers are most balanced, simultaneously. To solve the model, we design two new evolutionary algorithms. The experiments are conducted on 16 cases of 4 widely used types of networks, and the results indicate that the proposed model and algorithms are effective. [ABSTRACT FROM AUTHOR]

We propose a parameterized level set method (PLSM) for structural topology optimization based on reaction diffusion equation (RDE) and fuzzy PID control algorithm. By using the proposed method, the structural compliance minimization problem under volume constraints is studied. In this work, the RDE is used as the evolution equation of level set function, and the topological derivative of the material domain is used as the reaction term of the RDE to drive the evolution of level set function, which has little dependence on the initial design domain, and can generate holes in the material domain; the compactly supported radial basis function (CS-RBF) is used to interpolate the level set function and modify the RDE, which can improve the computational efficiency, and keep the boundary smooth in the optimization process. Meanwhile, the fuzzy PID control algorithm is used to deal with the volume constraints, so that the convergence process of the structure volume is relatively stable. Furthermore, the proposed method is applied to 3D structural topology optimization. Several typical numerical examples are provided to demonstrate the feasibility and effectiveness of this method. [ABSTRACT FROM AUTHOR]

In this article, an Interval Type-3 Fuzzy Logic System (IT3FLS) for enhancing the performance in Bee Colony Optimization (BCO) is outlined. The efficiency of the IT3FLS approach is verified with results on a set of benchmark mathematical functions. The IT3FLS provides an approach that helps to identify the optimal values in α and β parameters that allows to improve the performance in the original BCO. The IT3FLS approach exhibits advantages in the optimization of the benchmark functions. It can be noted that a IT3FLS exhibits better results in the minimal values of the set of mathematical functions. The experimentation demostrates that the implementation of the IT3FLS approach enhances the performance of BCO when compared with respect to the variants utilizing Generalized Type-2 FLS (GT2FLS), Interval Type-2 FLS (IT2FLS) and Type-1 FLS (T1FLS). [ABSTRACT FROM AUTHOR]

In order to separate the sub-signals and extract the feature frequency in the signal accurately, we proposed a parameter-adaptive time-varying filtering empirical mode decomposition (TVF-EMD) feature extraction method based on the improved grasshopper optimization algorithm (IGOA). The method not only improved the local optimal problem of GOA, but could also determine the bandwidth threshold and B-spline order of TVF-EMD adaptively. Firstly, a nonlinear decreasing strategy was introduced in this paper to adjust the decreasing coefficient of GOA dynamically. Then, energy entropy mutual information (EEMI) was introduced to comprehensively consider the energy distribution of the modes and the dependence between the modes and the original signal, and the EEMI was used as the objective function. In addition, TVF-EMD was optimized by IGOA and the optimal parameters matching the input signal were obtained. Finally, the feature frequency of the signal was extracted by analyzing the sensitive mode with larger kurtosis. The optimization experiments of 23 sets of benchmark functions showed that IGOA not only enhanced the balance between exploration and development, but also improved the global and local search ability and stability of the algorithm. The analysis of the simulation signal and bearing signal shows that the parameter-adaptive TVF-EMD method can separate the modes with specific physical meanings accurately. Compared with ensemble empirical mode decomposition (EEMD), variational mode decomposition (VMD), TVF-EMD with fixed parameters and GOA-TVF-EMD, the decomposition performance of the proposed method is better. The proposed method not only improved the under-decomposition, over-decomposition and modal aliasing problems of TVF-EMD, but could also accurately separate the frequency components of the signal and extract the included feature information, so it has practical significance in mechanical fault diagnosis. [ABSTRACT FROM AUTHOR]

To improve safety, parking efficiency, smoothness and riding comfort of parallel parking of driverless vehicles at roadside, the characteristics of parallel parking conditions were analyzed, and the path planning was carried out by quintic polynomial curve. The mathematical model of path planning curve parameters optimization design was established with the abscissa of parking starting position as design variable, and six equality constraints were established based on parking boundary conditions. Three inequality constraints were established based on the requirements of curvature, collision avoidance and reducing parking space, and the weighted sum of the maximum curvature and the absolute value of abscissa of parking starting position was set as objective function. By the particle swarm optimization algorithm, the abscissa of the parking starting position was obtained, and six polynomial undetermined coefficients were calculated. The optimized smooth and continuous curvature planning path curve expression was obtained. Parking path tracking was realized based on the pure pursuit algorithm. The results show that the vehicle can track the optimized path precisely without collision with obstacles, which meets the safety requirements. The steering wheel angle changes continuously to meet the requirements of smoothness and ride comfort. [ABSTRACT FROM AUTHOR]

The most important and demanding part of the artificial neural network is the training process which involves finding the most suitable values for the weights in the network architecture, a challenging optimization problem. Gradient approaches and the meta-heuristic approaches are two methods extensively used to optimize the weights in the network. Gradient approaches have serious disadvantages including getting stuck in local optima, inadequate exploration, etc. To overcome these disadvantages, meta-heuristic approaches are preferred in training the artificial neural network instead of gradient methods. Therefore, in this study, an improved animal migration optimization algorithm with the Lévy flight feature was proposed to train the multilayer perceptron. The proposed hybrid algorithm is named IAMO-MLP. The main contributions of this article are that the IAMO algorithm was developed, the IAMO-MLP algorithm can successfully escape from local optima, and the initial positions did not affect the performance of the IAMO-MLP algorithm. The enhanced algorithm was tested and validated against a wider set of benchmark functions and indicated that it substantially outperformed the original implementation. Afterward, the IAMO-MLP was compared with ten algorithms on five classification problems (xor, balloon, iris, breast cancer, and heart) and one real-world problem in terms of mean squared error, classification accuracy, and nonparametric statistical Friedman test. According to the results, the IAMO was successful in training the multilayer perceptron. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid level set method (HLSM) to design novelty functionally graded structures (FGSs) with complex macroscopic graded patterns. The hybrid level set function (HLSF) is constructed to parametrically model the macro unit cells by introducing the affine concept of convex optimization theory. The global weight coefficients on macro unit cell nodes and the local weight coefficients within the macro unit cell are defined as master and slave design variables, respectively. The local design variables are interpolated by the global design variables to guarantee the C0 continuity of neighboring unit cells. A HLSM-based topology optimization model for the FGSs is established to maximize structural stiffness. The optimization model is solved by the optimality criteria (OC) algorithm. Two typical FGSs design problems are investigated, including thin-walled stiffened structures (TWSSs) and functionally graded cellular structures (FGCSs). In addition, additively manufactured FGCSs with different core layers are tested for bending performance. Numerical examples show that the HLSM is effective for designing FGSs like TWSSs and FGCSs. The bending tests prove that FGSs designed using HLSM are have a high performance. [ABSTRACT FROM AUTHOR]

• A level-set based robust topology optimization method considering bounded field parameters is proposed. • A variable time step strategy based on the RBF gradient function is developed to realize the separation of time and space. • The bounded field parameters are characterized through the dimension reduction method and dimension-wise method. In this paper, a robust topology optimization method considering bounded field parameters with uncertainties based on the variable time step parametric level-set method is proposed. Firstly, a variable time step strategy for level set function evolution based on the gradient of the level set function that uses radial basis function interpolation to realize the separation of time and space is developed, which can achieve better design results during topology optimization. Beyond that, the dimension reduction method and dimension-wise method based on the polynomials are used for characterization and quantification of bounded field parameters with uncertainties. Finally, the sensitivity of the robust optimization model is derived based on the shape derivative principle, which provides the basis for the implementation of gradient based optimization algorithm. Three examples illustrate the effectiveness, necessity and influence of important parameters of the robust topology optimization method considering bounded field parameters with uncertainties based on the variable time step parametric level-set method from different aspects. [ABSTRACT FROM AUTHOR]

A real-valued set function is (additively) approximately submodular if it satisfies the submodularity conditions with an additive error. Approximate submodularity arises in many settings, especially in machine learning, where the function evaluation might not be exact. In this paper we study how close such approximately submodular functions are to truly submodular functions. We show that an approximately submodular function defined on a ground set of n elements is O (n 2) pointwise-close to a submodular function. This result also provides an algorithmic tool that can be used to adapt existing submodular optimization algorithms to approximately submodular functions. To complement, we show an Ω (n) lower bound on the distance to submodularity. These results stand in contrast to the case of approximate modularity, where the distance to modularity is a constant, and approximate convexity, where the distance to convexity is logarithmic. [ABSTRACT FROM AUTHOR]

Finite element-based crashworthiness optimization is extensively used to improve the safety of motor vehicles. However, the responses of crash simulations are characterized by a high level of numerical noise, which can hamper the blind use of surrogate-based design optimization methods. It is therefore essential to account for the noise-induced uncertainty when performing optimization. For this purpose, a surrogate, referred to as non-deterministic kriging (NDK), can be used. It models the noise as a non-stationary stochastic process, which is added to a traditional deterministic kriging surrogate. Based on the NDK surrogate, this study proposes an optimization algorithm tailored to account for both epistemic uncertainty, due to the lack of data, and irreducible aleatory uncertainty, due to the simulation noise. The variances are included within an extension of the well-known expected improvement infill criterion referred to as modified augmented expected improvement (MAEI). Because the proposed optimization scheme requires an estimate of the aleatory variance, it is approximated through a regression kriging, referred to as variance kriging, which is iteratively refined. The proposed algorithm is tested on a set of analytical functions and applied to the optimization of an occupant restraint system (ORS) during a crash. [ABSTRACT FROM AUTHOR]

In order to overcome the drawbacks of Archimedes optimization algorithm( AOA), such as weak global search ability, easily trapping into local optimum and prematurely converge, this paper put forward Archimedes optimization algorithm improved by multi-strategy collaborative( MAOA ) . Initially, it used the random Gaussian mutation strategy to increase the diversity of the population in the iterative process and strengthen the global search ability. Then, based on the randomness, ergodicity and diversity of multiple chaotic models, it introduced the local chaotic search strategy to expand the scope range of the chaotic space and enhance the local development capabilities of the algorithm. At the same time, it proposed a nonlinear dynamic density decreasing factor to coordinate the global exploration ability and local development ability of the algorithm. Finally, for the sake of increasing the diversity of the population during the iteration process, this paper adopted the golden sine strategy of the Levy flight guidance mechanism to perturb the population position and improve the ability of the algorithm to jump out of the local optimum. Through simulation experiments on 12 benchmark functions and part of the CEC2014 function set, the results show that the proposed algorithm can overcome the shortcomings of AOA' s weak global exploration ability and easy to fall into local optimality, and improve the accuracy and stability of AOA . In addition, the introduction of mechanical optimization design cases for testing and analysis will further verify the feasibility and applicability of MAOA on practical issues. [ABSTRACT FROM AUTHOR]

This research introduces a new probabilistic and meta-heuristic optimization approach inspired by the Corona virus pandemic. Corona is an infection that originates from an unknown animal virus, which is of three known types and COVID-19 has been rapidly spreading since late 2019. Based on the SIR model, the virus can easily transmit from one person to several, causing an epidemic over time. Considering the characteristics and behavior of this virus, the current paper presents an optimization algorithm called Corona virus optimization (CVO) which is feasible, effective, and applicable. A set of benchmark functions evaluates the performance of this algorithm for discrete and continuous problems by comparing the results with those of other well-known optimization algorithms. The CVO algorithm aims to find suitable solutions to application problems by solving several continuous mathematical functions as well as three continuous and discrete applications. Experimental results denote that the proposed optimization method has a credible, reasonable, and acceptable performance. [ABSTRACT FROM AUTHOR]

We introduce MathOptInterface, an abstract data structure for representing mathematical optimization problems based on combining predefined functions and sets. MathOptInterface is significantly more general than existing data structures in the literature, encompassing, for example, a spectrum of problems classes from integer programming with indicator constraints to bilinear semidefinite programming. We also outline an automated rewriting system between equivalent formulations of a constraint. MathOptInterface has been implemented in practice, forming the foundation of a recent rewrite of JuMP, an open-source algebraic modeling language in the Julia language. The regularity of the MathOptInterface representation leads naturally to a general file format for mathematical optimization we call MathOptFormat. In addition, the automated rewriting system provides modeling power to users while making it easy to connect new solvers to JuMP. Summary of Contribution: This paper describes a new abstract data structure for representing mathematical optimization models with a corresponding file format and automatic transformation system. The advances are useful for algebraic modeling languages, allowing practitioners to model problems more naturally and more generally than before. [ABSTRACT FROM AUTHOR]

In this article, we propose a new sparse neural ordinary differential equation (ODE) model to characterize flexible relations among multiple functional processes. We characterize the latent states of the functions via a set of ODEs. We then model the dynamic changes of the latent states using a deep neural network (DNN) with a specially designed architecture and a sparsity‐inducing regularization. The new model is able to capture both nonlinear and sparse‐dependent relations among multivariate functions. We develop an efficient optimization algorithm to estimate the unknown weights for the DNN under the sparsity constraint. We establish both the algorithmic convergence and selection consistency, which constitute the theoretical guarantees of the proposed method. We illustrate the efficacy of the method through simulations and a gene regulatory network example. [ABSTRACT FROM AUTHOR]

The rapid growth of distributed energy resources integrated in distribution systems leads to an increasing need of continuously and automatically changing the system topology to realize the economic operation of distribution networks. This paper proposes an optimization model of dynamic reconfiguration for distribution networks based on a new method of time series analysis. Equivalent daily curve considering time‐varying nature of distributed generator and load demands is divided by an improved fuzzy C‐means clustering algorithm, where the indicator of section function is set to find the optimal reconfiguration time intervals. The uncertainty of distributed generator outputs and load demands is described by the interval algorithm. Then the affine Taylor expansion is adopted to solve the interval power flow equations. The reconfiguration optimization model is solved with decimal particle swarm optimization algorithm based on loop search. The optimal dynamic reconfiguration of a modified 70‐bus test system with distributed generators is carried out and the simulation results demonstrate the effectiveness and superiority of the proposed method. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

In five-axis machining, tool orientation optimization is a critical problem that significantly affects machining quality, efficiency, and kinetic performance. In this paper, a tool orientation optimization method based on ruled surface is proposed. Through optimizing section selection algorithm, the region to be optimized is selected precisely, and a ruled surface is established at each cutter contact point (CC point). The tool orientation optimization range is limited to a certain level, and optimization objective function is set to minimize the vibration of rotary axes. The proposed method is of advantages over existing methods in three aspects. First, the influence on machining area and surface quality can be reduced to a lower level due to the tool orientation change is limited to a certain surface. Second, the efficiency of optimization algorithm is improved. Third, the nonlinear mapping between tool orientation and rotary axes position is avoided by setting the kinetic parameters of the rotary axes as optimization goal. Simulation and experiment are performed to verify the performance of the proposed method. [ABSTRACT FROM AUTHOR]

Aiming at the problems in the iterative process of seagull optimization algorithm ( SOA), such as local optimization, slow convergence speed and low optimization accuracy, this paper proposed a golden sine guide and sigmoid continuous seagull optimization algorithm( GSCSOA) . In the seagull migration stage, the algorithm used the sigmoid function as a nonlinear convergence factor to guide the seagull search process, so that the algorithm maintained a stronger global optimization ability in the early stage and converged faster in the later stage. In the seagull rushing stage, it introduced the idea of Taboo search, so that the seagulls always moved to the area with higher confidence, and the optimal position continued to change in one iteration, which improved the optimization accuracy. After that, it used the golden sine mechanism to guide the population position to update, which narrowed the search range, and improved the local optimization ability. Finally, this paper used 12 test functions and CEC2014 function set to test the improved algorithm, and the results prove that the improved seagull algorithm has better convergence speed and accuracy than original algorithm and other algorithms. [ABSTRACT FROM AUTHOR]

Robots with visual sensors have been used in various goods logistics, such as bin picking or uploading. However, there are more and more demands for the automatic blanking and loading, and it is necessary to solve the problem of object pose estimation in changing accommodation space. This paper proposes a method for pose estimation in the accommodation space using alpha-shape algorithm and improved fruit fly optimization algorithm (FOA). The alpha-shape volume variety of object and measured space is set to the objective function, and the pose variety of object is set to six variables of improved FOA. The experiments were performed by setting parameters of improved FOA and considering the four space types represented the common accommodation shapes. Compared with previous work using convex hull, the new study using alpha-shape algorithm not only keeps the object in the accommodation space, but also maintains the object pose which is at the bottom of the space and can meet the practical requirement of object placement by robot arms. [ABSTRACT FROM AUTHOR]

The flower pollination algorithm (FPA) is a highly efficient metaheuristic optimization algorithm that is inspired by the pollination process of flowering species. FPA is characterised by simplicity in its formulation and high computational performance. Previous studies on FPA assume fixed parameter values based on empirical observations or experimental comparisons of limited scale and scope. In this study, a comprehensive effort is made to identify appropriate values of the FPA parameters that maximize its computational performance. To serve this goal, a simple non-iterative, single-stage sampling tuning method is employed, oriented towards practical applications of FPA. The tuning method is applied to the set of 28 functions specified in IEEE-CEC'13 for real-parameter single-objective optimization problems. It is found that the optimal FPA parameters depend significantly on the objective functions, the problem dimensions and affordable computational cost. Furthermore, it is found that the FPA parameters that minimize mean prediction errors do not always offer the most robust predictions. At the end of this study, recommendations are made for setting the optimal FPA parameters as a function of problem dimensions and affordable computational cost. [ABSTRACT FROM AUTHOR]

A comprehensive methodology for semiparametric probability density estimation is introduced and explored. The probability density is modelled by sequences of mostly regular or steep exponential families generated by flexible sets of basis functions, possibly including boundary terms. Parameters are estimated by global maximum likelihood without any roughness penalty. A statistically orthogonal formulation of the inference problem and a numerically stable and fast convex optimization algorithm for its solution are presented. Automatic model selection over the type and number of basis functions is performed with the Bayesian information criterion. The methodology can naturally be applied to densities supported on bounded, infinite or semi-infinite domains without boundary bias. Relationships to the truncated moment problem and the moment-constrained maximum entropy principle are discussed and a new theorem on the existence of solutions is contributed. The new technique compares very favourably to kernel density estimation, the diffusion estimator, finite mixture models and local likelihood density estimation across a diverse range of simulation and observation data sets. The semiparametric estimator combines a very small mean integrated squared error with a high degree of smoothness which allows for a robust and reliable detection of the modality of the probability density in terms of the number of modes and bumps. [ABSTRACT FROM AUTHOR]

In this paper, a novel swarm-based metaheuristic algorithm is proposed, which is called tuna swarm optimization (TSO). The main inspiration for TSO is based on the cooperative foraging behavior of tuna swarm. The work mimics two foraging behaviors of tuna swarm, including spiral foraging and parabolic foraging, for developing an effective metaheuristic algorithm. The performance of TSO is evaluated by comparison with other metaheuristics on a set of benchmark functions and several real engineering problems. Sensitivity, scalability, robustness, and convergence analyses were used and combined with the Wilcoxon rank-sum test and Friedman test. The simulation results show that TSO performs better compared to other comparative algorithms. [ABSTRACT FROM AUTHOR]

Past present future (PPF) is a new stochastic optimization algorithm inspired by the phenomena of the way an individual learns from a successful person in society. PPF is based on the concept of "future improvement of a person's life depending on his/her past experience and present work." The influence of successful persons also affects the improvement of the future life of an individual. This work develops a mathematical model for PPF following the above facts. In this new algorithm, the population is divided into subpopulations and a switching mechanism is followed among the subpopulations to track the change in optimal positions of an individual thereby accelerating the convergence rate. In addition, this switching mechanism also prevents pre-mature convergence. PPF was found to possess low computational complexity with fast convergence characteristics. The proposed PPF is compared with 41 up-to-date meta-heuristic algorithms taking an extensive set of benchmark functions to verify the efficiency. In addition, five classical engineering design problems are simulated to estimate the efficacy of the PPF algorithm in optimizing engineering problems. The results confirm the superior performance of the proposed algorithm to get the optimal solution with less iteration and have shown the best competitive performance compared to all other algorithms. [ABSTRACT FROM AUTHOR]

All available thermodynamic properties and phase diagram data of the Sn-O system at 1 atm total pressure were critically evaluated and optimized to obtain a set of thermodynamic functions of all stable phases. The discrepancies among available experimental phase diagram data were resolved. In addition, new experiments were attempted to determine the melting temperature of SnO 2 using sealed Pt capsules. It was confirmed that the melting temperature of SnO 2 is higher than 1700 °C, which was taken into account in the present optimization. The Gibbs energies of the liquid solution of SnO-SnO 2 and all solid compounds were obtained. A new phase diagram at 1 atm total pressure was constructed from the optimized Gibbs energy functions of all phases. [ABSTRACT FROM AUTHOR]

Computational efficiency in simulation-based optimization algorithms is essential when the system objective functions are expensive to evaluate and computational resources are limited. This article proposes a hybrid Bayesian BFGS algorithm (HB2O) to address this efficiency problem. An adaptive expected improvement (AEI) acquisition function is developed to realize a self-adaptive sampling strategy by dynamically balancing the design space exploration and exploitation. A series of computational experiments is conducted on a diverse set of test functions to benchmark the optimization performance of the HB2O against six commonly used alternative optimizers, and to validate the effectiveness of AEI against four alternative acquisition functions. The computational results show that the proposed HB2O can robustly converge on the functions' optima with limited simulation samples, and it significantly outperforms other optimizers for various test functions. This article provides a sample-efficient solution to complex optimization problems where taking a large number of system simulations is computationally prohibitive. [ABSTRACT FROM AUTHOR]

This paper proposes a new dynamic multi-objective optimization algorithm by integrating a new fitting-based prediction (FBP) mechanism with regularity model-based multi-objective estimation of distribution algorithm (RM-MEDA) for multi-objective optimization in changing environments. The prediction-based reaction mechanism aims to generate high-quality population when changes occur, which includes three subpopulations for tracking the moving Pareto-optimal set effectively. The first subpopulation is created by a simple linear prediction model with two different stepsizes. The second subpopulation consists of some new sampling individuals generated by the fitting-based prediction strategy. The third subpopulation is created by employing a recent sampling strategy, generating some effective search individuals for improving population convergence and diversity. Experimental results on a set of benchmark functions with a variety of different dynamic characteristics and difficulties illustrate that the proposed algorithm has competitive effectiveness compared with some state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Consensus in multi-agent dynamical systems is prone to be sabotaged by the adversary, which has attracted much attention due to its key role in broad applications. In this paper, we study a new false data injection (FDI) attack design problem, where the adversary with limited capability aims to select a subset of agents and manipulate their local multi-dimensional states to maximize the consensus convergence error. We first formulate the FDI attack design problem as a combinatorial optimization problem and prove it is NP-hard. Then, based on the submodularity optimization theory, we provide the necessary and sufficient conditions to guarantee that the convergence error is a submodular function of the set of compromised agents, satisfying the property of diminishing marginal returns. In other words, the benefit of adding an extra agent to the compromised set decreases as that set becomes larger. With this property, we exploit the greedy scheme to find the optimal compromised agent set that can produce the maximum convergence error when adding one extra agent to that set each time. Thus, the FDI attack set selection algorithms are developed to obtain the near-optimal subset of the compromised agents. Furthermore, we derive the analytical suboptimality bounds and the worst-case running time under the proposed algorithm. Extensive simulation results are conducted to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In conventional level set methods for topology optimization, the evolution of level set function is solved by upwind scheme and needs to be reinitialized frequently throughout the optimization. The upwind scheme is complicated in numerical implementation and the reinitialization is time-consuming and slows down the optimization efficiency. This paper presents a level set method updated with finite difference scheme for structural topology optimization. The velocity field used to update the level set function is interpolated by piecewise basis function in order to incorporate the universal mathematical programming algorithm into the optimization. The diffusion is introduced into the Hamilton-Jacobi equation and the three-step splitting method is adopted to solve the equation. By applying the proposed method, the evolution of the level set can be updated by simple central difference scheme and the procedure of reinitialization is avoided without sacrificing the numerical stability. The classical mean compliance minimization problem with several numerical examples is used to test the validity of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we conduct a case study of a company that collects and processes used home appliances and sells them as new recycled resources based on the Home Appliance Recycling Law. The target company earns sales by selling multiple resources to multiple sales destinations with different selling prices. There are various restrictions on such sales, which creates complexity. Due to this complexity, the sales amount cannot be maximized using only the intuition and experience of employees. Therefore, we propose a model that maximizes the sales amount obtained from selling each resource. As a result, using the proposed model, different sales amounts and sales destinations of each resource were obtained, achieving better results. Specifically, compared to the current total sales amount, 3.6% better results are expected. Furthermore, as a sensitivity analysis, experiments were conducted in which the credit constraints of each sales destination were varied. It was found that risk management can be performed without affecting the objective function value by setting credit appropriately. [ABSTRACT FROM AUTHOR]

Reproducing kernel (RK) approximations are meshfree methods that construct shape functions from sets of scattered data. We present an asymptotically compatible (AC) RK collocation method for nonlocal diffusion models with Dirichlet boundary condition. The numerical scheme is shown to be convergent to both nonlocal diffusion and its corresponding local limit as nonlocal interaction vanishes. The analysis is carried out on a special family of rectilinear Cartesian grids for a linear RK method with designed kernel support. The key idea for the stability of the RK collocation scheme is to compare the collocation scheme with the standard Galerkin scheme, which is stable. In addition, assembling the stiffness matrix of the nonlocal problem requires costly computational resources because high-order Gaussian quadrature is necessary to evaluate the integral. We thus provide a remedy to the problem by introducing a quasi-discrete nonlocal diffusion operator for which no numerical quadrature is further needed after applying the RK collocation scheme. The quasi-discrete nonlocal diffusion operator combined with RK collocation is shown to be convergent to the correct local diffusion problem by taking the limits of nonlocal interaction and spatial resolution simultaneously. The theoretical results are then validated with numerical experiments. We additionally illustrate a connection between the proposed technique and an existing optimization based approach based on generalized moving least squares. [ABSTRACT FROM AUTHOR]

Given the outstanding effectiveness and efficiency performance in different fields such as image processing and energy dispatching, the virus optimization algorithm (VOA), a newly developed metaheuristic for general optimization purposes, has been further improved. Similar to other metaheuristic methods, VOA performance to some degree relies on proper parameter settings, which may require large numbers of experiments to determine. Therefore, this study proposes a self-adaptive version of VOA (SaVOA) to decrease the number of controllable parameters in the algorithm and thus reduce the time needed to determine proper parameter values by any sort of experimental design process. Having an SaVOA ensures the ease access of the algorithm for different types of continuous domain problems, whereas previous different optimization problems may have needed different parameter settings. To perform the comparison, SaVOA is tested by optimizing the same set of benchmark functions used when proposing the original VOA. Computational results indicate some major advances were achieved by the SaVOA in addition to competitive results obtained. Most importantly, SaVOA proved its superiority on functions where the original VOA was not powerful enough to perform well, such as Rosenbrock, Schwefel, Drop Wave, Levy, and Easom's functions. In terms of implementation, the number of controllable parameters in SaVOA was greatly reduced to only one—the stopping criterion. This promises a significant improvement in the utility of SaVOA for any type of continuous domain optimization problem. [ABSTRACT FROM AUTHOR]

Motivated by recent results relating synchronizing DFAs and primitive sets, we tackle the synchronization process and the related longstanding Černý conjecture by studying the primitivity phenomenon for sets of nonnegative matrices having neither zero-rows nor zero-columns. We formulate the primitivity process in the setting of a two-player probabilistic game and we make use of convex optimization techniques to describe its behavior. We develop a tool for approximating and upper bounding the exponent of any primitive set and supported by numerical results we state a conjecture that, if true, would imply a quadratic upper bound on the reset threshold of a new class of automata. [ABSTRACT FROM AUTHOR]

Initial thickness imperfections of thin membranes due to manufacturing are inevitable and commonly observed. This paper presents an experimental and numerical investigation on how thickness imperfections affect the wrinkling of stretched membrane structures. With the measured data from a limited number of samples, we model the uncertain deviation of membrane thickness from that of a perfect geometry as a non-probabilistic bounded field with spatial dependency. After representing the bounded field as a linear function of a reduced set of uncertain coefficients by using a series expansion, the effect of thickness imperfections on the membrane wrinkling is investigated. To this end, the upper and lower bounds of out-of-plane displacements for membranes with initial imperfections are evaluated by a mathematical programming. The proposed wrinkling evaluation problem is then solved efficiently by using the Kriging-based optimization algorithm, with validation done by Monte Carlo simulation. The results show that initial thickness imperfections play a critical role in the wrinkling behavior of membranes. [ABSTRACT FROM AUTHOR]

In this paper, a new optimization algorithm called the search and rescue optimization algorithm (SAR) is proposed for solving single-objective continuous optimization problems. SAR is inspired by the explorations carried out by humans during search and rescue operations. The performance of SAR was evaluated on fifty-five optimization functions including a set of classic benchmark functions and a set of modern CEC 2013 benchmark functions from the literature. The obtained results were compared with twelve optimization algorithms including well-known optimization algorithms, recent variants of GA, DE, CMA-ES, and PSO, and recent metaheuristic algorithms. The Wilcoxon signed-rank test was used for some of the comparisons, and the convergence behavior of SAR was investigated. The statistical results indicated SAR is highly competitive with the compared algorithms. Also, in order to evaluate the application of SAR on real-world optimization problems, it was applied to three engineering design problems, and the results revealed that SAR is able to find more accurate solutions with fewer function evaluations in comparison with the other existing algorithms. Thus, the proposed algorithm can be considered an efficient optimization method for real-world optimization problems. [ABSTRACT FROM AUTHOR]

• Stego distribution optimization achieves efficient adversarial steganography. • Optimizing embedding modification probabilities enables end-to-end gradient descent. • Cover enhancement and distortion optimization can be collaborated. • Pairing cover-stego in loss removes mode collapses in steganographic min-max games. Adversarial steganography aims to fool steganalysis models and enhance embedding security. Its application in the sequential min-max steganographic game has recently shown state-of-the-art embedding security. However, current methods suffer from high computational costs and inferior convergence. These issues could be caused by unnecessary optimization on distortions and the monotonous criterion for adversaries. This paper introduces a novel and concise scheme for conducting adversarial steganography and refines the criterion for adversaries. The suggested adversarial optimizations leave out distortions and focus on optimizing the stego distribution, whose difference with the intrinsic cover distribution is the primary factor affecting embedding security. These optimization techniques are accomplished by utilizing gradient descent on embedding modification probabilities and introducing a novel protocol for cover enhancement. Moreover, the proposed criteria for adversaries prioritize enhancing the similarity between each cover-stego pair, rather than evading steganalysis models, to break monotony and enhance convergence. The discussion and refinement of the loss function and termination setting of the optimization process are also provided. The proposed method demonstrates its benefits in increased security and computation efficiency in experiments. After collaborating with the steganographic min-max game, the state-of-the-art embedding security and stronger resistance to various and unexpected steganalysis models are seen. [ABSTRACT FROM AUTHOR]

This study constructs a reinforcement learning-based hybrid algorithm for Aquila Optimizer (AO) and improved Arithmetic Optimization Algorithm (IAOA). The point of the hybrid algorithm is that Q-learning can dynamically select the AO and the IAOA at different stages for different problems. In Arithmetic Optimization Algorithm (AOA), the mathematical optimization acceleration (MOA) function is restructured to balance global search and local exploitation, which can effectively stay away from the local optimum. Moreover, an improved reward function is modeled for Q-learning, which makes our hybrid algorithm more efficient and accurate. A set of benchmark functions and two engineering optimization problems are employed to test the performance of the proposed hybrid algorithm in this paper. Compared with other algorithms, the results show that the proposed hybrid algorithm has higher convergence speed and accuracy. [ABSTRACT FROM AUTHOR]

This paper develops an extended bi-directional evolutionary structural optimization (BESO) method for topology optimization of continuum structures with smoothed boundary representation. In contrast to conventional zigzag BESO designs and removal/addition of elements, the newly proposed evolutionary topology optimization (ETO) method, determines implicitly the smooth structural topology by a level-set function (LSF) constructed by nodal sensitivity numbers. The projection relationship between the design model and the finite element analysis (FEA) model is established. The analysis of the design model is replaced by the FEA model with various elemental volume fractions, which are determined by the auxiliary LSF. The introduction of sensitivity LSF results in intermediate volume elements along the solid-void interface of the FEA model, thus contributing to the better convergence of the optimized topology for the design model. The effectiveness and robustness of the proposed method are verified by a series of 2D and 3D topology optimization design problems including compliance minimization and natural frequency maximization. It has been shown that the developed ETO method is capable of generating a clear and smooth boundary representation; meanwhile the resultant designs are less dependent on the initial guess design and the finite element mesh resolution. [ABSTRACT FROM AUTHOR]

Consider the problem of selecting k items that maximize the value of a monotone submodular set function f, where f can be accessed using value queries. It is well known that polynomially many queries suffice in order to obtain an approximation ratio of $$1 - \frac{1}{e}$$ . We consider a variation on this problem in which the value queries are required to be of uniform size: each queried set, like the desired solution itself, must contain k items. We show that polynomially many uniform size queries suffice in order to obtain an approximation ratio of $$\frac{1}{2}$$ , and that an approximation ratio of $$\frac{1 + \epsilon }{2}$$ requires a number of queries that is exponential in $$\epsilon k$$ . For the interesting special case of coverage functions, we show that an approximation ratio strictly better than $$\frac{1}{2}$$ is attainable with polynomially many uniform size queries. The 'uniform size' requirement is motivated by situations in which a firm may offer a menu of exactly k items to its clients, where k is a parameter determined by external considerations. Performing a query corresponds to physically changing the identities of the items offered, and the reply to the query is deduced by observing the behavior of clients in response to the change. Queries that involve a number of items that differs from k may not be desirable due to these external considerations. In such situations it is natural to ask whether the same approximation ratios that can be guaranteed by general value queries can also be obtained by uniform size queries. [ABSTRACT FROM AUTHOR]

Finite element (FE) model of updating is the process of calibrating model parameters to improve the accuracy of numerical prediction. This goal is usually achieved by solving an optimization problem with the objective function measuring the misfit between simulated responses and experimental data. The sensitivity method is the predominate class of algorithms to FE model updating problems, and has opened a wide range of applications. However, this method often suffers from large errors due to linearization. To address this challenge, this paper proposes to utilize the unscented Kalman inversion (UKI) method to solve the FE model updating problems in a derivative-free manner. As an iterative optimization method, the UKI determines the new iterate using function values at a set of sample points rather than the derivative information. Implementation details, such as handling constraints during the optimization process, are presented in the paper. To validate the proposed UKI, model updating of a pedestrian bridge is conducted using the simulated and experimental data. Both validation examples show that the UKI is a competitive method for solving FE model updating problems. • The UKI method solves FE model updating problems in a derivative-free manner. • The UKI takes the effect of noises into account in a natural way. • Method is proposed to incorporate constraints during iterative process of the UKI. • The UKI is compared with the Levenberg–Marquardt algorithm. • The UKI is applied to updating a pedestrian bridge model using field test data. [ABSTRACT FROM AUTHOR]

PM 2.5 forecasting has always been difficult. Neural networks are widely used in the forecasting of PM 2.5 , however, the accuracy is not satisfactory due to uncertainty. In order to solve this problem, a new PM 2.5 forecasting system based on data preprocessing, combined neural network, and the unconstrained weighting method based on an improved multi-objective optimization algorithm is proposed. A new chaotic map is introduced to our model to improve the traditional population initialization. In addition, a new unconstrained weighting method was proposed, and a combination of MAPE value (prediction accuracy) and STD value (prediction stability) were set as the objective functions. The predicted results of each neural network were judged by statistical index and a dynamic weight was given to different neural networks to achieve the optimal prediction result. We demonstrated the superiority, accuracy and generalization ability of our proposed model through experiments on the PM 2.5 data of four cities around the Bohai Economic Belt in China: Beijing, Tianjin, Dalian, and Yantai. • VMD method is robust to the sampling and noise which can effectively avoid the mode aliasing. • The combination of ANN, RNN, CNN is adopted, which greatly improves the prediction ability of the model. • The unconstrained weighting algorithm is used to obtain the optimal weight of different neural networks. • A new chaotic mapping is proposed, which can effectively improve the global search ability. • The combination of point prediction and interval prediction can provide more effective information. [ABSTRACT FROM AUTHOR]

In the present paper, the task of designing a compliant mechanism is accomplished by solving a multi-objective topology optimization problem. The objective function includes a target displacement at the output port and compliances of two load cases. The design variables include two types of boundaries, i.e., the traction free boundary and the Dirichlet boundary. The topology optimization of compliant mechanism and its support is solved by using a level set method. Two level set functions are used to represent a compliant mechanism and the two types of boundaries. Each of the two boundaries is represented by a part of the zero level set of one level set function. Evolution of the two boundaries is modeled by two independent Hamilton–Jacobi equations, thus the shape and topology of the two boundaries change independently. The shape derivatives are derived by using a Lagrangian function and the adjoint method. The finite element analysis is done by modifying a fixed background mesh, and the artificial weak material is not used. Numerical examples in two dimensions are investigated. [ABSTRACT FROM AUTHOR]

A level-set based multi-material topology optimization method using a reaction diffusion equation is proposed in this paper. Each phase is represented by a combined formulation of different level set functions. This description model is modified from Multi-Material Level Set (MM-LS) topology description model. With a total number of M level set functions, this approach provides a representation of M materials and one void phase (totally M + 1 phases). By this approach, the mathematic model of the multi-material topology optimization problem using a reaction diffusion equation is established. With this model, the geometrical complexity of optimal solutions can be easily controlled by appropriately setting a regularization parameter. Some implementation details for solving this model are also presented in this paper. Finally, several typical numerical examples are shown to confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we study sub-topical functions in the framework of abstract convexity and examine the relevant properties such as support sets, polar sets and sub-differentials for these functions. Plus-radiant and plus-co-radiant sets, and their relations with sub-topical functions are studied. Applying sub-topical functions, we present some separation theorems for both plus-radiant and plus-co-radiant sets. [ABSTRACT FROM AUTHOR]

Decision support systems focus on their interpretability with a different caution. The majority of approaches utilize reliable optimization techniques to achieve high recognition accuracy. However, accuracy improvement is done at the cost of the readability of the decision support system. This paper proposes a novel technique of linguistic rule extraction focused on: explainability, interpretability, and reliability, called EasIeR. Proposed solution performs a direct analysis of the learning set without omitting real data imperfections. The proposed algorithm processes the imprecision of data with linguistic values described by fuzzy membership functions and the uncertainty of knowledge employing a fuzzy belief function. It describes the learning set with the most appropriate fuzzy if-then rules. For this purpose, a new method of evaluation of membership functions in a set of rules and their iterative refinement is proposed. EasIeR achieves the best results of trade-off criteria between the generalization quality and the interpretability of the knowledge base when compared with state-of-art fuzzy rule-based classification approaches. Achieving the simplest rule base and competitive generalization quality is verified by cross-validation experiments with benchmark data sets. The new method of rule evaluation allows for better determination of their quality in decision support, and the selection algorithm quickly provides a clear and easy to interpret knowledge base. This rule evaluation technique will be proficient for all fuzzy rule-based classification systems. • Efficient algorithm of rule extraction provides interpretable data-driven knowledge. • Fuzzy rules and belief measure ensure classification reliability and explainability. • New rule evaluation method allows extracting effective rule-based knowledge. • Approach achieves competitive generalization quality with the simplest knowledge base. [ABSTRACT FROM AUTHOR]

With the correction of the level set function by the use of Lagrangian maker particles, the particle level method has been proven to be an accurate and robust scheme to capture the evolution of moving interface [1] . In this work, together with the later improved version [2] , the drawbacks of the particle correction procedure in the original particle level set method were investigated in detail and an optimized particle correction procedure was developed to improve the accuracy and robustness of the implicitly represented moving interface. A refined grid point level set value selection process has been proposed and shown to effectively improve the interface location accuracy through a set of standard advection test cases when using a fast first order accurate semi-Lagrangian solver firstly proposed in [3] . With the implementation of our enhanced level set value selection procedure during the particle correction stage, it was observed that the particle reseeding was not required, which allowed for faster runtime performance of the fast particle level set method without compromising interface position accuracy. [ABSTRACT FROM AUTHOR]

This paper presents an accurate implicit re-initialization approach in the framework of a level set method. The improved method includes two schemes for keeping the zero level set unperturbed. The first scheme is to derive and use a new formula for the smoothing parameter in the conventional re-initialization equation based on the principle of the interface not moving. The second scheme is to reduce the local time step to avoid the interface moving across grid points when the sign of the level set function near the interface is changed. The example presented suggests that the new algorithm has a better approximation to the signed distance function and obtains a more accurate interface than the algorithm presented by Sussman et al. (1994). For shape and topology optimization of fluid, the effectiveness of the developed method in this paper was demonstrated by the internal and external flow examples. [ABSTRACT FROM AUTHOR]

• A novel index is proposed to evaluate the signal complexity. • The envelope signal is Fourier transformed twice in the objective function. • A novel adaptive VMD method based on the AOA is proposed. Variational mode decomposition (VMD) is widely used in rotating machinery fault diagnosis. However, the choice of its main parameters is often based on experience, affecting the decomposition results. Aiming to mitigate this drawback, an adaptive VMD method using the Archimedes optimization algorithm (AOA) is presented. Firstly, the computational domain of the objective function is set to the amplitude spectrum of the signal envelope spectrum. Secondly, a correlation waveform index (Cwi) is proposed to evaluate the complexity of the signal. The minimum average value of the Cwi of all intrinsic modal functions (IMFs) is taken as the objective function. Finally, the AOA is used to search for the optimal mode number and penalty factor to find IMFs which are sensitive to fault features. Compared to the other improved VMD methods, the proposed method has a better performance in extracting the fault characteristics from the simulated and actual cases. [ABSTRACT FROM AUTHOR]

Particle swarm optimization (PSO) is a popular method widely used in solving different optimization problems. Unfortunately, in the case of complex multidimensional problems, PSO encounters some troubles associated with the excessive loss of population diversity and exploration ability. This leads to a deterioration in the effectiveness of the method and premature convergence. In order to prevent these inconveniences, in this paper, a learning competitive swarm optimization algorithm (LCSO) based on the particle swarm optimization method and the competition mechanism is proposed. In the first phase of LCSO, the swarm is divided into sub-swarms, each of which can work in parallel. In each sub-swarm, particles participate in the tournament. The participants of the tournament update their knowledge by learning from their competitors. In the second phase, information is exchanged between sub-swarms. The new algorithm was examined on a set of test functions. To evaluate the effectiveness of the proposed LCSO, the test results were compared with those achieved through the competitive swarm optimizer (CSO), comprehensive particle swarm optimizer (CLPSO), PSO, fully informed particle swarm (FIPS), covariance matrix adaptation evolution strategy (CMA-ES) and heterogeneous comprehensive learning particle swarm optimization (HCLPSO). The experimental results indicate that the proposed approach enhances the entropy of the particle swarm and improves the search process. Moreover, the LCSO algorithm is statistically and significantly more efficient than the other tested methods. [ABSTRACT FROM AUTHOR]