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The parameters of a lithium-ion battery are important to construct an effective battery management system. Parameter estimation assisted by the pseudo-two-dimensional (P2D) model is much more cost-effective than direct measurement methods. However, this is a nontrivial task, because the simulation of the P2D model is time-consuming. Alternatively, surrogate models such as reduced-order/data-driven models are often used to accelerate the parameter estimation process. Each category of surrogate models has its own strengths and weaknesses. Traditionally, reduced-order models run faster than data-driven models, while data-driven models are more accurate than reduced-order models. To leverage the complementary advantages of these two kinds of surrogate models, we make an interesting attempt to combine them compactly, thus proposing a two-phase surrogate model-assisted parameter estimation algorithm (TPSMA-PEAL). In the first phase, a fast reduced-order model is designed for parameter prescreening. In the second phase, a high-fidelity data-driven model is developed for fine estimation. In TPSMA-PEAL, except the time-consuming simulation, the other two challenges (i.e., the overfitting problem and the low observability of some parameters) are also considered from the perspective of optimization. Note that TPSMA-PEAL takes advantage of differential evolution and parameter sensitivity analysis to address them. Simulations and experiments verify that TPSMA-PEAL is efficient and accurate. [ABSTRACT FROM AUTHOR]

This work presents an automated design methodology for time-mode proportional and integral (PI) controllers aimed for an on-chip switched-capacitor (SC) dc/dc converter system. The basis of this design is the use of evolutionary optimization algorithms to find the near-optimal set of sizings for the time-mode PI controller. It is motivated due to the difficulty faced when tuning the controller parameters at a circuit level, which arise as a result of the presence of modeling inaccuracies and the small region for the linearized model where it is defined. Moreover, this design proposes the required modifications for the original design presented for the inductor-based dc/dc converter. These modifications are necessary to operate the SC dc/dc converter in slow switching limit (SSL). The addition of a pulse-width-modulated (PWM)-to-pulse frequency-modulated (PFM) conversion block is presented and elaborated in this article. The controller is codesigned using the differential evolution algorithm for the circuit level implementation to mitigate the issues prior mentioned. The optimized controller is then tested in a simulation environment using TSMC $0.18~\mu \text{m}$ technology. The results of the optimized controller were superior to those of a conventional controller. The optimized system achieved an overall efficiency of 79.1%. [ABSTRACT FROM AUTHOR]

Nonlinear equation systems (NESs) are ubiquitous, and solving them is an important yet challenging task in numerical computation. Most of the NESs usually contain multiple roots. To locate multiple roots, the use of evolutionary algorithms attracts more attention recently. For the purpose of finding different roots within a limited computational budget in a single run simultaneously, in this article, a hybrid niching-based differential evolution with two archives, referred to as HNDE/2A, is proposed. It can be featured as: 1) two niching techniques, i.e., crowding and speciation, are combined to balance the diversity and convergence; 2) a root archive is used to save the found roots during the run. Additionally, if a root is saved into the root archive, it will be reinitialized immediately to further promote the population diversity; and 3) an inferior offspring archive is presented to utilize the useful information of the inferior offspring. To evaluate the performance of our proposal, 30 problems are chosen as the test suite. Moreover, HNDE/2A is also used to solve two real-world problems. Compared with other algorithms, HNDE/2A yields better results in terms of the root ratio and the success rate with a less computational budget. [ABSTRACT FROM AUTHOR]

Recent studies show that deep neural networks are vulnerable to adversarial attacks in the form of subtle perturbations to the input image, which leads the model to output wrong prediction. Such an attack can easily succeed by the existing white-box attack methods, where the perturbation is calculated based on the gradient of the target network. Unfortunately, the gradient is often unavailable in the real-world scenarios, which makes the black-box adversarial attack problems practical and challenging. In fact, they can be formulated as high-dimensional black-box optimization problems at the pixel level. Although evolutionary algorithms are well known for solving black-box optimization problems, they cannot efficiently deal with the high-dimensional decision space. Therefore, we propose an approximated gradient sign method using differential evolution (DE) for solving black-box adversarial attack problems. Unlike most existing methods, it is novel that the proposed method searches the gradient sign rather than the perturbation by a DE algorithm. Also, we transform the pixel-based decision space into a dimension-reduced decision space by combining the pixel differences from the input image to neighbor images, and two different techniques for selecting neighbor images are introduced to build the transferred decision space. In addition, six variants of the proposed method are designed according to the different neighborhood selection and optimization search strategies. Finally, the performance of the proposed method is compared with a number of the state-of-the-art adversarial attack algorithms on CIFAR-10 and ImageNet datasets. The experimental results suggest that the proposed method shows superior performance for solving black-box adversarial attack problems, especially nontargeted attack problems. [ABSTRACT FROM AUTHOR]

A growing number of organizations are hosting their software applications in distributed data centers (DCs) in the cloud, for faster response time and higher energy efficiency. The dramatic increase of user tasks, however, poses a significant challenge on DC providers to retain users’ expectations on both aspects. To tackle this challenge, this work first formulates the problem into a constrained biobjective optimization problem. A biobjective algorithm, named simulated-annealing-based adaptive differential evolution (SADE), is presented to simultaneously reduce both the response time of tasks and energy cost. Meanwhile, a method of minimal Manhattan distance is adopted to search for a final knee, for achieving a good balance between response time minimization and energy cost reduction. Experimental results on real-life datasets, i.e., the electricity prices and tasks collected from a Google cluster trace, have proved that SADE yields less task response time and lower energy cost compared with state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Bistatic synthetic aperture radar (BiSAR) has received more and more attention because of its forward-looking imaging capability and configuration flexibility. For BiSAR moving target imaging (MTIm), its noncooperative motion leads to unknown range cell migration (RCM) and additional phase modulation. Consequently, MTIm in BiSAR faces two main challenges: 1) the unknown RCM correction and Doppler parameter estimation are tightly coupled and 2) the Doppler parameters of the extended moving target’s different scattering points are different, i.e., the Doppler parameters are spatially variant. To cope with these problems, an optimal polar format refocusing method for bistatic SAR MTIm is proposed. First, the main part of tight coupling and spatial variation effects caused by the BiSAR platforms is eliminated, while the moving target is 2-D defocused and shifted. Then, we analyze the characteristics of 2-D defocused and shifted of the moving target in BiSAR and give the analytical expressions. Basis this, a new bistatic polar format transformation is introduced, in which the degree of freedom of defocusing result is reduced from 2-D to only 1-D. After that, the parameter estimation and refocusing issues are transformed into a constrained optimization problem (COP), and differential evolution (DE) is applied to solve the COP and obtain the refocusing results. Finally, considering the spatial variation of the extended moving target, compensation processing is performed to relocate each scattering point. Numerical simulations verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Solving constrained multiobjective optimization problems brings great challenges to an evolutionary algorithm, since it simultaneously requires the optimization among several conflicting objective functions and the satisfaction of various constraints. Hence, how to adjust the tradeoff between objective functions and constraints is crucial. In this article, we propose a dynamic selection preference-assisted constrained multiobjective differential evolutionary (DE) algorithm. In our approach, the selection preference of each individual is suitably switching from the objective functions to constraints as the evolutionary process. To be specific, the information of objective function, without considering any constraints, is extracted based on Pareto dominance to maintain the convergence and diversity by exploring the feasible and infeasible regions; while the information of constraint is used based on constrained dominance principle to promote the feasibility. Then, the tradeoff in these two kinds of information is adjusted dynamically, by emphasizing the utilization of objective functions at the early stage and focusing on constraints at the latter stage. Furthermore, to generate the promising offspring, two DE operators with distinct characteristics are selected as components of the search algorithm. Experiments on four test suites including 56 benchmark problems indicate that the proposed method exhibits superior or at least competitive performance, in comparison with other well-established methods. [ABSTRACT FROM AUTHOR]

One of the most promising technologies to be employed in beyond 5G networks is based on the concept of cell-free (CF) massive MIMO, in which a predetermined set of access points (APs) jointly cooperate in the data transmission and reception to/from the user equipment (UE). In order to efficiently manage radio resources, the CF central processing unit implement uplink power control policies. These policies aim to optimize a given network utility function. In this paper, we investigate the max-min fairness optimization problem, in which the spectral efficiency performance of the UE with the worst channel conditions is prioritized, taking into account a per-UE power constraint and assuming linear maximum ratio combining at APs. Existing solutions have typically relied on second-order cone programming with convex approximations, which exhibit high computational complexity and scalability issues. Therefore, meta-heuristics (MHs) are explored as alternative optimization schemes, capable of providing (near)-optimal solutions with reasonable computational effort. Three MH approaches with different operation principles are compared. Numerical results show that the differential evolution algorithm exhibits the best trade-off between solution quality and run time, being able to reach (near)-optimal solutions faster than the bisection approach while coping with the scalability issues of the geometric programming-based algorithm. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms (EAs) have been recognized as a promising approach for bilevel optimization. However, the population-based characteristic of EAs largely influences their efficiency and effectiveness due to the nested structure of the two levels of optimization problems. In this article, we propose a transfer learning-based parallel EA (TLEA) framework for bilevel optimization. In this framework, the task of optimizing a set of lower level problems parameterized by upper level variables is conducted in a parallel manner. In the meanwhile, a transfer learning strategy is developed to improve the effectiveness of each lower level search (LLS) process. In practice, we implement two versions of the TLEA: the first version uses the covariance matrix adaptation evolutionary strategy and the second version uses the differential evolution as the evolutionary operator in lower level optimization. The experimental studies on two sets of widely used bilevel optimization benchmark problems are conducted, and the performance of the two TLEA implementations is compared to that of four well-established evolutionary bilevel optimization algorithms to verify the effectiveness and efficiency of the proposed algorithm framework. [ABSTRACT FROM AUTHOR]

This research presents an original and efficient elite archive-assisted adaptive memetic algorithm (EAMA) to deal with a realistic hybrid differentiation flowshop scheduling problem (HDFSP) with the objective of total completion time minimization. In this scheduling problem, each job consists of multiple parts and the jobs are divided into different types. The manufacturing of a job is comprised of three consecutive stages: 1) parts fabrication on first-stage parallel machines; 2) parts assembly on second-stage single machine; and 3) job differentiation on one of third-stage dedicated machines. We provide a mixed-integer programming model, derive three lower bounds, and further present the EAMA metaheuristic for HDFSP. The EAMA is initialized heuristically, and its global exploration is performed by a differential evolution, which includes three newly designed operators: 1) elite-driven discretized differential mutation; 2) probability crossover; and 3) biased selection. To enhance the local search, an external elite archive is set and evolved in parallel with global exploration by a meta-Lamarckian learning-based adaptive multistage local search and a variable length-based adaptive block-insertion local search. After the global exploration and local exploitation, an elite sharing strategy is used to exchange the excellent information between population and elite archive, and an adaptive restart strategy is used to diversify the population. The influence of parameter setting on EAMA is surveyed by using an improved design-of-experiment. The statistical results from extensive computational experiments demonstrate the effectiveness of the special designs and show that EAMA performs more efficient than the existing algorithms in solving the problem under consideration. [ABSTRACT FROM AUTHOR]

Differential evolution is a powerful nature-inspired real-parameter optimization algorithm that has been successfully used to solve a number of hard optimization problems. It has been used to tackle both continuous and discrete optimization problems. The application of a continuous method to discrete problems involves several challenges, including solution representation and search space–solution space mapping. In this work, we study random key encoding, a popular encoding scheme that is used to represent permutations in high-dimensional continuous spaces. We analyze the search space it constitutes, study its structure and properties, and introduce two novel modifications of the encoding. We investigate the proposed encoding strategies in the context of four variants of the differential evolution algorithm and demonstrate their usefulness for two widespread permutation problems: 1) the linear ordering problem and 2) the traveling salesman problem. [ABSTRACT FROM AUTHOR]

Acoustic remote sensing with multibeam echo-sounder systems (MBESs) has been extensively used for coastal and ocean survey works. The imperfect integration of multibeam echo sounder and motion sensor can introduce integration errors, which manifest as high-frequency wobbles in swaths and hinder the accurate expression of high-resolution seabed topographic maps. To address this issue, a precise method is developed to calibrate these integration errors based on a simplified georeferenced model. First, an equivalent attitude coordinate (EAC) system is defined to represent mutual transformation between equivalent attitudes and the beam launch vector; then, with the help of equivalent attitudes, a simplified footprint georeferenced model is deduced that considers the effect of the parameterized integration errors (including time delay, motion scale, yaw misalignment, and lever arm errors); finally, in a selected flat region, integration errors are inverted by regressing the bathymetric data to the corresponding fitted plane via the differential evolution (DE) algorithm. The results indicate that the proposed method can effectively eliminate wobbles in multibeam bathymetries caused by single or multiple integration errors in both shallow- and deep-water areas. By comparing the data before and after calibration with the in situ measurements, the accuracy of the calibrated shallow- and deep-water data is controlled within approximately 0.15% and 0.06% of the water depth, respectively. [ABSTRACT FROM AUTHOR]

In this article, a method for solving cable layout optimization problems in electronic systems based on ensemble learning (EL) and improved differential evolution (DE) algorithm is proposed. Using this method, we produced two cable layout schemes with the considerations of the electromagnetic compatibility performance and the total length of cables. First, several different individual machine learning (ML) models for all output variables were established. On this basis, we established EL models with better performance than previous individual ML models. Then, aiming at the optimization problem presented in this article, an improved DE algorithm was proposed. On this basis, a method for solving cable layout optimization problems in electronic systems based on EL and the improved DE algorithm was proposed. Finally, the effectiveness of the proposed method was verified by two examples of electronic system cable layout optimization with different routing modes. Each example problem was solved using four different methods. The results indicate that the method proposed here outperformed existing methods. [ABSTRACT FROM AUTHOR]

In this article, a 2-D bistatic attributed scattering center (BASC) model is developed to represent the bistatic return from a perfect electric conducting (PEC) target, based on the derived analytic scattering solutions of seven canonical primitives. Because of its unified and concise form, the BASC model is useful for extracting the geometrical features of targets from synthetic aperture radar (SAR) echoes. However, estimating the parameters of the BASC model is an ill-posed inverse problem. To reduce the ill-posedness, we present a sparse method for bistatic inverse scattering that incorporates differential evolution (DE) into doubly orthogonal matching pursuit (DOMP). The experimental results not only verify the validity of the parameter inversion method but also demonstrate the applicability of the proposed model. [ABSTRACT FROM AUTHOR]

JADE is a differential evolution (DE) algorithm and has been shown to be very competitive in comparison with other evolutionary optimization algorithms. However, it suffers from the premature convergence problem and is easily trapped into local optima. This article presents a novel JADE variant by incorporating chaotic local search (CLS) mechanisms into JADE to alleviate this problem. Taking advantages of the ergodicity and nonrepetitious nature of chaos, it can diversify the population and thus has a chance to explore a huge search space. Because of the inherent local exploitation ability, its embedded CLS can exploit a small region to refine solutions obtained by JADE. Hence, it can well balance the exploration and exploitation in a search process and further improve its performance. Four kinds of its CLS incorporation schemes are studied. Multiple chaotic maps are individually, randomly, parallelly, and memory-selectively incorporated into CLS. Experimental and statistical analyses are performed on a set of 53 benchmark functions and four real-world optimization problems. Results show that it has a superior performance in comparison with JADE and some other state-of-the-art optimization algorithms. [ABSTRACT FROM AUTHOR]

Real-time taxi–passenger matching plays a critical role in modern taxi dispatch systems. Currently, the greedy strategy is widely adopted, which limits the quality of the service (QoS) and the profit of the entire system. There are two crucial tasks in this system: 1) the pairwise prioritization and 2) the matching of taxi–passenger pairs. In this paper, we develop a two-stage taxi–passenger matching system to deal with these two tasks. In the first stage, we design a fuzzy controller to assign a priority score to each taxi–passenger pair in real time. To ensure its performance on providing good QoS and profit, the fuzzy controller is optimized by an offline differential evolution algorithm. New individual representation is designed to optimize the membership functions and fuzzy rule base simultaneously. To accelerate the optimization process, the algorithm is implemented in a parallel way. Then, in the second stage, considering the priority scores as weights in the bipartite graph of taxi and passenger sets, we further apply a polynomial Kuhn–Munkres algorithm to find the maximum weight perfect matching in the bipartite graph. Simulated results validate the effectiveness of the proposed algorithm, which is able to enhance the QoS provided by the taxi system and improve the profit gained by the taxi service company. [ABSTRACT FROM AUTHOR]

A new technique for fast and accurate extraction of faulty element position from multipatterned time-modulated arrays (TMAs) has been proposed in this article. The strategy incorporates a novel rank-based population (RBP) for generating nonrepeated integers from the continuous population set of differential evolution (DE) algorithm. This enables to solve the discrete optimization problem of finding the defective elements in antenna arrays. Instead of considering the conventionally used single pattern, the degraded dual-beam patterns of TMA are utilized to enhance the convergence speed in detecting the faulty elements. Finally, a phasor matrix that stores the phasor components of the array factor is defined for the fast computation of error-free and failed array factors. Through rigorous simulation results, it is shown that the combination of the two—the RBP-based DE (DE-RBP) and fast computation of array factor—are more efficient in diagnosing faulty elements in multipattern TMA. This brings forth higher convergence speed, improved success rate, and less computation time than the previously reported methods. [ABSTRACT FROM AUTHOR]

Economic dispatching of generating units in a power system can significantly reduce the energy cost of the system. However, the economic dispatch (ED) problem is highly constrained, and often has disconnected feasible regions because of various physical features. Enhancing population diversity is critical for the evolutionary approach to fully explore and exploit the feasible regions. In this article, we propose a density-enhanced multiobjective evolutionary approach to solve ED problem. An ED problem is first transformed into a tri-objective optimization problem, and then multiobjective optimization techniques are employed to fully optimize the constraints and cost function simultaneously. The first two objectives are derived from the original ED problem, while the third one is a novel density objective constructed by niching methods to enhance population diversity. These three objectives are optimized simultaneously by a dynamic dominance relation, which can make a good balance among feasibility, diversity, and convergence. To evaluate the performance of this proposed approach, 22 benchmark problems and seven real-world ED problems with different features are tested in this article. The experimental results show that our approach performs better than or at least competitive to the state-of-the-art algorithms, especially on large-scale ED problems. [ABSTRACT FROM AUTHOR]

The emergence of fuzzy sets makes job-shop scheduling problem (JSSP) become better aligned with the reality. This article addresses the JSSP with fuzzy execution time and fuzzy completion time (FJSSP). We choose the classic differential evolution (DE) algorithm as the basic optimization framework. The advantage of the DE algorithm is that it uses a special evolutionary strategy of difference vector sets to carry out mutation operation. However, DE is not very effective in solving some instances of FJSSP. Therefore, we propose a novel selection mechanism augmenting the generic DE algorithm (NSODE) to achieve better optimization results. The proposed selection operator adopted in this article aims at a temporary retention of all children generated by the parent generation, and then selecting N better solutions as the new individuals from N parents and N children. Various examples of fuzzy shop scheduling problems are experimented with to test the performance of the improved DE algorithm. The NSODE algorithm is compared with a variety of existing algorithms such as ant colony optimization, particle swarm optimization, and cuckoo search. Experimental results show that the NSODE can obtain superior feasible solutions compared with solutions produced by several algorithms reported in the literature. [ABSTRACT FROM AUTHOR]

To deal with the multimodality, nonlinearity, and nonconvexity of the maximum likelihood (ML) cost function when solving the localization problem with received signal strength (RSS) in wireless sensor networks, we propose a localization approach based on the differential evolution algorithm, opposition-based learning, and adaptive redirection in a unified way. In the proposed approach, we need neither to approximate the ML cost function nor to provide a good initial point while most conventional approaches, including those based on the semidefinite programming, second-order cone programming, and unscented transformation. The performance and computational complexity of the proposed approach are analyzed and compared with those of other approaches for three practical scenarios. Simulation results confirm that the proposed approach performs better than other approaches with relatively low computational complexity. Note to Practitioners—This article was motivated by the problem of localization in wireless sensor networks that can be found in different areas, such as intelligent farming, health care monitoring, and environmental monitoring. In this article, a technique is proposed, which exploits the RSS measurements to estimate the position of a target node. This technique is quite popular due to its simplicity and low cost. Most of the techniques based on the ML formulation approximate the ML cost function due to its high nonlinearity and nonconvexity. This article suggests a new approach using differential evolution and opposition-based learning a redirection, which does not require approximating the ML cost function to find the location of a target. In addition, in this article, we analyze the sensor nodes’ placement and its effect on localization accuracy. Numerical results in three practical scenarios are provided to demonstrate the effectiveness of the proposed approach and its superiority compared with state-of-the-art algorithms. In future research, we will address a more realistic scenario with multiple targets. [ABSTRACT FROM AUTHOR]

Locating more peaks and refining the solution accuracy on the found peaks are two challenging issues in solving multimodal optimization problems (MMOPs). To deal with these two challenges, a distributed individuals differential evolution (DIDE) algorithm is proposed in this article based on a distributed individuals for multiple peaks (DIMP) framework and two novel mechanisms. First, the DIMP framework provides sufficient diversity by letting each individual act as a distributed unit to track a peak. Based on the DIMP framework, each individual uses a virtual population controlled by an adaptive range adjustment strategy to explore the search space sufficiently for locating a peak and then gradually approach it. Second, the two novel mechanisms named lifetime mechanism and elite learning mechanism (ELM) cooperate with the DIMP framework. The lifetime mechanism is inspired by the natural phenomenon that every organism will gradually age and has a limited lifespan. When an individual runs out of its lifetime and also has good fitness, it is regarded as an elite solution and will be added to an archive. Then the individual restarts a new lifetime, so as to bring further diversity to locate more peaks. The ELM is proposed to refine the accuracy of those elite solutions in the archive, being efficient in dealing with the solution accuracy issue on the found peaks. The experimental results on 20 multimodal benchmark test functions show that the proposed DIDE algorithm has generally better or competitive performance compared with the state-of-the-art multimodal optimization algorithms. [ABSTRACT FROM AUTHOR]

This article presents a differential evolution algorithm with a new encoding mechanism and Cauchy mutation (DE-NEM-CM) for optimizing large unequally spaced planar array layouts with the minimum element spacing constraint. In the new encoding mechanism, each individual represents a certain element position rather than an entire array layout used in traditional stochastic optimization algorithms. Such an encoding mechanism has the following advantages: 1) in each individual updating, the array pattern can be efficiently evaluated by only considering the radiation contribution variation from one element movement, which can greatly reduce the computational time; 2) it naturally facilitates the generated new array layout in population updating to meet the minimum element spacing constraint, and 3) each individual is searched always in 2-D space as the array size increases. These advantages enable it to be very suitable for synthesizing large arrays. Besides, DE serves as a search engine, and Cauchy mutation with chaotic mapping is proposed to enhance the local search while preserving the diversity of the population. A set of experiments for synthesizing different types of unequally spaced planar arrays in both narrow-and broadband applications are conducted. Synthesis results show that the proposed method achieves much lower sidelobe level than some state-of-the-art stochastic optimization methods for all the test cases. Importantly, the proposed method is much more efficient than conventional stochastic optimization algorithm especially for the case of synthesizing large unequally spaced planar array layouts. A array layout optimization with more than 1000 elements can be achieved within acceptable CPU time cost, which has not yet been reported for the existing stochastic optimization methods without resorting to supercomputing facilities. [ABSTRACT FROM AUTHOR]

Various mutation strategies show distinct advantages in differential evolution (DE). The cooperation of multiple strategies in the evolutionary process may be effective. This article presents an underestimation-assisted global and local cooperative DE to simultaneously enhance the effectiveness and efficiency. In the proposed algorithm, two phases, namely, the global exploration and the local exploitation, are performed in each generation. In the global phase, a set of trial vectors is produced for each target individual by employing multiple strategies with strong exploration capability. Afterward, an adaptive underestimation model with an self-adapted slope control parameter is proposed to evaluate these trial vectors, the best of which is selected as the candidate. In the local phase, the better-based strategies guided by individuals that are better than the target individual are designed. For each individual accepted in the global phase, multiple trial vectors are generated by using these strategies and filtered by the underestimation value. The cooperation between the global and local phases includes two aspects. First, both of them concentrate on generating better individuals for the next generation. Second, the global phase aims to locate promising regions quickly while the local phase serves as a local search for enhancing convergence. Moreover, a simple mechanism is designed to determine the parameter of DE adaptively in the searching process. Finally, the proposed approach is applied to predict the protein 3-D structure. The experimental studies on classical benchmark functions, CEC test sets, and protein structure prediction problem show that the proposed approach is superior to the competitors. [ABSTRACT FROM AUTHOR]

Artificial intelligence evolved as a powerful tool in condition monitoring of the induction motor for early diagnosis of bearing faults. This paper attempted to identify the features to improve the accuracy of diagnosis using the benchmark database of the Case Western Reserve University (CWRU) and the Machinery Fault Prevention Technology (MFPT). In this paper, 18 time-domain features are extracted constituting six proposed time-dependent spectral features (TDSFs) and 12 statistical time-domain features. For the first time, a set of six TDSFs are extracted to diagnose the bearing faults. This involves extracting frequency-domain features using the relationship between Parseval’s theorem and the Fourier transform directly from the time domain. Particle swarm optimization (PSO) and wheel-based differential evolution (WBDE) feature selection algorithms are also implemented to identify four prominent features. It is found that three of the four selected features are TDSF features, and results of selected features revealed the attainment of 90.92% for 48 class identifications of CWRU database and 100% for 17 class identifications of the MFPT database, respectively. [ABSTRACT FROM AUTHOR]

The steelmaking process in the iron and steel industry involves complicated physicochemical reactions. The main aim of steelmaking is to adjust the quality of molten steel. During the steel-tapping process, the temperature and carbon content are the most essential quality indices for end-point prediction. This article presents a novel machine learning framework for the end-point prediction problems in the smelting process. Considering the importance of data representation in modeling, the original data are inputted to a stacked autoencoder (SAE) to extract the essential features in an unsupervised manner. The top layer is then designed as a sparse Bayesian regression (SBR) layer to obtain the predicted mean values and error bars that measure the uncertainty in the prediction. To improve the generalization ability of the prediction model, an intelligent optimization algorithm based on improved differential evolution (DE) is used to optimize the hyperparameters of the model. The main advantage of this model is that the underlying characteristics of the samples can be learned automatically layer by layer, instead of designing them manually. Finally, the effectiveness of the proposed method is verified using real data collected from two steel plants. The experimental results show that the proposed model gives a more precise prediction than other existing models and can provide error bars for the end-point prediction. Note to Practitioners—The end-point prediction is critical to the quality of products produced in the iron and steel production process. Because of the complexity of the physiochemical reactions during smelting, it is difficult to build mechanism models for the complex environment. Generally, expert knowledge and experience are needed for real production. The motivation behind this article was to establish a data-driven model through machine learning methods to solve end-point prediction problems. First, a stacked autoencoder (SAE) was used to extract the essential information from the original data. Second, sparse Bayesian regression (SBR) was applied to the top layer. Thus, the predicted mean values and error bars could be obtained to improve the robustness of the prediction model. Furthermore, an improved differential evolution (DE) algorithm was designed to adaptively optimize the hyperparameters of the model. In the experiments, the proposed method was applied to two real steelmaking production processes. The results verify the effectiveness of the proposed model. This article can be extended to other processes such as continuous casting and reheating furnace. The model can also be generalized for other practical industries to improve the product quality and enable safer production. [ABSTRACT FROM AUTHOR]

Finding multiple roots of nonlinear equation systems (NESs) in a single run is one of the most important challenges in numerical computation. We tackle this challenging task by combining the strengths of the repulsion technique, diversity preservation mechanism, and adaptive parameter control. First, the repulsion technique motivates the population to find new roots by repulsing the regions surrounding the previously found roots. However, to find as many roots as possible, algorithm designers need to address a key issue: how to maintain the diversity of the population. To this end, the diversity preservation mechanism is integrated into our approach, which consists of the neighborhood mutation and the crowding selection. In addition, we further improve the performance by incorporating the adaptive parameter control. The purpose is to enhance the search ability and remedy the trial-and-error tuning of the parameters of differential evolution (DE) for different problems. By assembling the above three aspects together, we propose a repulsion-based adaptive DE, called RADE, for finding multiple roots of NESs in a single run. To evaluate the performance of RADE, 30 NESs with diverse features are chosen from the literature as the test suite. Experimental results reveal that RADE is able to find multiple roots simultaneously in a single run on all the test problems. Moreover, RADE is capable of providing better results than the compared methods in terms of both root rate and success rate. [ABSTRACT FROM AUTHOR]

Coupling matrix (CM) synthesis methods for all-resonator diplexers and multiplexers are far from mature. For complex coupling topologies, the existing methods are often not able to find the appropriate CMs that satisfy the S-parameter specifications. To address this challenge, a new synthesis method, which hybridizes analytical and optimization techniques, called general all-resonator diplexer/multiplexer CM synthesis (GACMS) method, is proposed in this article. The two main innovations of GACMS are: 1) an optimization framework incorporating filter design knowledge, which effectively reduces the search space for CM synthesis and 2) a new memetic algorithm-based optimizer, which tackles the challenges from the complex landscape (function characteristics) of CM synthesis problems. GACMS is tested by six complex practical problems and CMs are successfully obtained for all of them. Comparisons with the existing methods demonstrate the advantages of GACMS in terms of solution quality and robustness. [ABSTRACT FROM AUTHOR]

In this paper, a new method is proposed for directly evaluating approximate lightning channel-base-current (CBC) parameters ($I_{m}$ , (di/dt)max, tFD, and tSD) and analytical function parameters (AFPs) of the CBC based on the measured lightning magnetic fields using a deconvolution and differential evolution (DE) method. This proposed method comprises two sequential steps. The first step is for determining the lightning CBC based on the measured magnetic field using modified transmission line model with exponential current decaying with height (MTLE) through deconvolution, while the second step is for evaluating the AFPs (Heidler's function) corresponding to the lightning CBC obtained from the first step. Data from the measured magnetic field above ground level (z = 10 m) at different horizontal distances (r = 9 km, 4.6 km, 2 km, and 50 m) from the lightning channel are considered for testing the proposed method. The sum of two Heidler's functions is used to represent the lightning CBC; and its parameters, namely I01, I02, τ11, τ12, τ21, τ22, n1, and n2 are identified using DE as a tool. Further, this methodology is helpful in the evaluation of the CBC parameters and mathematical modeling of the lightning CBC and the estimation of the lightning current through the channel using data from the measured magnetic field for different engineering return stroke models. [ABSTRACT FROM AUTHOR]

Niching techniques have been widely incorporated into evolutionary algorithms (EAs) for solving multimodal optimization problems (MMOPs). However, most of the existing niching techniques are either sensitive to the niching parameters or require extra fitness evaluations (FEs) to maintain the niche detection accuracy. In this paper, we propose a new automatic niching technique based on the affinity propagation clustering (APC) and design a novel niching differential evolution (DE) algorithm, termed as automatic niching DE (ANDE), for solving MMOPs. In the proposed ANDE algorithm, APC acts as a parameter-free automatic niching method that does not need to predefine the number of clusters or the cluster size. Also, it can facilitate locating multiple peaks without extra FEs. Furthermore, the ANDE algorithm is enhanced by a contour prediction approach (CPA) and a two-level local search (TLLS) strategy. First, the CPA is a predictive search strategy. It exploits the individual distribution information in each niche to estimate the contour landscape, and then predicts the rough position of the potential peak to help accelerate the convergence speed. Second, the TLLS is a solution refine strategy to further increase the solution accuracy after the CPA roughly predicting the peaks. Compared with the other state-of-the-art DE and non-DE multimodal algorithms, even the winner of competition on multimodal optimization, the experimental results on 20 widely used benchmark functions illustrate the superiority of the proposed ANDE algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a method for generating new individuals such that their mean vector and the covariance matrix are defined by formulas analogous to the covariance matrix adaptation evolution strategy (CMA-ES). In contrast to CMA-ES, which generates new individuals using multivariate Gaussian distribution with an explicitly defined covariance matrix, the introduced method uses combinations of difference vectors between archived individuals and univariate Gaussian random vectors along directions of past shifts of the population midpoints. We use this method to formulate the differential evolution strategy (DES)—an algorithm that is a crossover between differential evolution (DE) and CMA-ES. The numerical results presented in this paper indicate that DES is competitive against CMA-ES in performing both local and global optimization. [ABSTRACT FROM AUTHOR]

This article compares various design techniques for torque ripple reduction using a commercial industrial interior permanent magnet machine (IPMM). These design techniques include the traditional skewing, radial pole shaping, and the proposed axial pole shaping. The new axial pole shaping technique achieves a particular flux concentration pattern on the rotor surface along the axial direction through shaping the pole arc radially and axially. The flux concentration pattern was optimized using the differential evolution algorithm. All three design techniques are implemented individually in the same commercial IPMM design. The performance of all the techniques was simulated using finite element method. The comparative study shows that the proposed axial pole shaping can reduce the torque ripple effectively with minimum torque reduction compared to the other two traditional techniques. The predicted results were validated experimentally through a variety of tests in which the measurements show reasonably good agreement with the predicted performance. [ABSTRACT FROM AUTHOR]

As the mutation strategy and algorithmic parameters in differential evolution (DE) are sensitive to the problems being solved, a hot research topic is to adaptively control the strategy and parameters according to the requirements of the problem. In the literature, most adaptive DE use either historical experiences of the population or heuristic information of the individuals to promote adaptation. In this paper, we develop a novel variant of adaptive DE, utilizing both the historical experience and heuristic information for the adaptation. In this novel historical and heuristic DE (HHDE), each individual dynamically adjusts its mutation strategy and associated parameters not only by learning from previous successful experience of the whole population, but also according to heuristic information related with its own current state. These help the algorithm select a more suitable mutation strategy and determinate better parameters for each individual in different evolutionary stages. The performance of the proposed HHDE is extensively evaluated on 30 benchmark functions with different dimensions. Experimental results confirm the competitiveness of the proposed algorithm to a number of DE variants. [ABSTRACT FROM AUTHOR]

Recent research has revealed that the output of deep neural networks (DNNs) can be easily altered by adding relatively small perturbations to the input vector. In this paper, we analyze an attack in an extremely limited scenario where only one pixel can be modified. For that we propose a novel method for generating one-pixel adversarial perturbations based on differential evolution (DE). It requires less adversarial information (a black-box attack) and can fool more types of networks due to the inherent features of DE. The results show that 67.97% of the natural images in Kaggle CIFAR-10 test dataset and 16.04% of the ImageNet (ILSVRC 2012) test images can be perturbed to at least one target class by modifying just one pixel with 74.03% and 22.91% confidence on average. We also show the same vulnerability on the original CIFAR-10 dataset. Thus, the proposed attack explores a different take on adversarial machine learning in an extreme limited scenario, showing that current DNNs are also vulnerable to such low dimension attacks. Besides, we also illustrate an important application of DE (or broadly speaking, evolutionary computation) in the domain of adversarial machine learning: creating tools that can effectively generate low-cost adversarial attacks against neural networks for evaluating robustness. [ABSTRACT FROM AUTHOR]

This paper presents a novel method for optimizing a planar elliptical dipole antenna with elliptical slots, for ultrawideband electromagnetic compatibility applications. The antenna is required to achieve minimum return loss and boresight realized gain with an adequate gain flatness across the frequency range of 1–5 GHz. Such an antenna is a powerful tool for electromagnetic measurements, due to its very compact size and its wide operating bandwidth. The main optimization method used in this paper is the invasive weed optimization (IWO), which is a nature-inspired metaheuristic evolutionary algorithm. The conventional and a modified version of IWO are compared to other prior-art evolutionary algorithms, such as the particle swarm optimization and differential evolution. The comparison is performed by applying all the methods on a set of mathematical test functions and also on the specific antenna design problem presented in this paper. The comparative results demonstrate the superiority of the modified IWO over the other optimization methods. [ABSTRACT FROM AUTHOR]

Recently, magnetic gears have drawn wide attention due to their inherent merits, such as noncontact operation, high torque density, and intrinsic overload protection. In this paper, an analytical calculation based on magnet magnetomotive force permeance theory is adopted to analyze the modulation effect in a magnetic gear. After that, the effects of some key parameters on magnetic gear performance are investigated, including the air-slot-opening-to-pole-pitch ratio $c_0$ , the magnet-arc-to-permanent-magnet-pole-pitch ratio $\alpha$ , and the permanent magnet thickness $h_m$. In particular, three types of steel pole pieces are considered: radial slots, parallel teeth, and parallel slots. A global optimization design is then carried out by using the differential evolution algorithm, and some useful suggestions are derived from the optimal Pareto range. Finally, the determination of outer rotor yoke thickness is discussed considering the iron saturation, and the iron loss distribution is investigated. This paper will be helpful for the design and optimization of a coaxial magnetic gear. [ABSTRACT FROM AUTHOR]

Multimodal optimization problem (MMOP), which targets at searching for multiple optimal solutions simultaneously, is one of the most challenging problems for optimization. There are two general goals for solving MMOPs. One is to maintain population diversity so as to locate global optima as many as possible, while the other is to increase the accuracy of the solutions found. To achieve these two goals, a novel dual-strategy differential evolution (DSDE) with affinity propagation clustering (APC) is proposed in this paper. The novelties and advantages of DSDE include the following three aspects. First, a dual-strategy mutation scheme is designed to balance exploration and exploitation in generating offspring. Second, an adaptive selection mechanism based on APC is proposed to choose diverse individuals from different optimal regions for locating as many peaks as possible. Third, an archive technique is applied to detect and protect stagnated and converged individuals. These individuals are stored in the archive to preserve the found promising solutions and are reinitialized for exploring more new areas. The experimental results show that the proposed DSDE algorithm is better than or at least comparable to the state-of-the-art multimodal algorithms when evaluated on the benchmark problems from CEC2013, in terms of locating more global optima, obtaining higher accuracy solution, and converging with faster speed. [ABSTRACT FROM AUTHOR]

Switched reluctance (SR) machines are attractive because they present relatively high efficiency and torque density in spite of lacking permanent magnets. This paper focuses on a two-objective optimization of an external rotor SR motor with a stator that has concentrated coils and a rotor with magnetically isolated modules. The objectives are minimum loss and mass, and 11 independent dimensionless geometric variables are considered as inputs that affect them. A combined design of experiments (DOE) and differential evolution (DE) approach is proposed. The DOE methodology is used to reduce the search space by eliminating from consideration input variable values, leading to poor-performing designs. Following this initial DOE study, an optimization study based on DE is run over the reduced search space, which leads to significant savings in computation time. Furthermore, a directed graph-based method for comparing different designs on the Pareto front to rank the best compromise designs is proposed. [ABSTRACT FROM AUTHOR]

In synthetic aperture radar (SAR) imagery, images of ground moving targets (GMTs) are smeared, distorted, and shifted. Current GMT imaging methods are mostly based on range-Doppler algorithms, which have two main drawbacks: 1) coupling between range cell migration correction (RCMC) and Doppler parameter estimation and 2) cross terms degrade the performance of the nonlinear estimation methods. In this paper, an optimal 2-D spectrum matching method for SAR GMT imaging is proposed. The main innovation or advantage of this method is that the GMT imaging problem is transformed into a constrained optimization problem, and differential evolution is applied to guarantee a high-processing efficiency. As they are associated with the Doppler centroid variation compensation and range shift compensation processing, all GMT point scatterers can be well focused and well located. Compared with the current methods, the improvements exhibited by this method include three main benefits: 1) RCMC and Doppler parameter estimation can be simultaneously accomplished; 2) both along- and cross-track GMT velocities can be simultaneously estimated; and 3) this method can be applied to both monostatic and bistatic SARs. Numerical simulations and experimental data processing have verified the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a three-dimensional (3-D) performance analysis and multiobjective design optimization of coreless-type permanent magnet linear synchronous motors. The average of open circuit magnetic field distribution is analytically predicted by solving two Laplace's equations. The winding factor calculation, which requires an approach different from conventional slotted motors, is provided to evaluate the motor performances. As a result, average thrust and thrust ripple can be obtained without loss of accuracy compared with results of 2-D finite element analysis (FEA). The 3-D leakage influences are subsequently incorporated into the analysis using lumped parameter magnetic circuit model because end effects are not neglected due to a relatively large air gap. Consequently, two meaningful contributions of this paper are summarized as follows: first, 3-D electromagnetic performances can be accurately predicted by the proposed analytical method. Second, with no need for the time-consuming 3-D FEA, differential evolution, a practical approach to global optimization, can simply be employed to search for solutions which belong to the Pareto optimal set. Finally, the validity of the analytical results is confirmed with the experimental results. [ABSTRACT FROM PUBLISHER]

This paper presents a method for reducing computational time in constrained single objective optimization problems related to permanent magnet motors modeled using computationally intensive finite element method. The method is based on differential evolution algorithm. The principal approach is to interrupt the evaluation of inequality constraints after encountering the constraint which is violated and continue their evaluation only if better solutions are obtained in comparison with the candidate vector from the previous generation both in terms of inequality constraints and the cost function. This approach avoids unnecessary time consuming finite element calculations required for solving the inequality constraints and saves the overall optimization time without affecting the convergence rate. The main features of this approach and how it complements the existing method for handling inequality constraints in Differential Evolution algorithm is demonstrated on design optimization of an interior permanent magnet motor for the low-floor tram TMK 2200. The motor geometry is optimized for maximum torque density. [ABSTRACT FROM PUBLISHER]

Diplexer coupling matrix synthesis often involves both analytical methods and optimization techniques. At present, general purpose optimization algorithms are used, but they need strong supporting information (e.g., high-quality starting points and very narrow search ranges) from analytical methods, which is not available or too complex to be obtained in many cases. Aiming to obtain the desired coupling matrix with highly reduced supporting information to relieve the pressure of analytical methods, a new optimization algorithm, called self-adaptive differential evolution for coupling matrix synthesis (SADEC), is proposed. Considering the landscape characteristics of diplexer coupling matrix synthesis problems, a new self-adaptive multipopulation search framework and a self-adaptive algorithm parameter control strategy are proposed and organized in a particular way. The performance of SADEC is demonstrated by two all-resonator-based narrowband diplexers using large search ranges only with the requirement of matching the diplexer topology and no ad hoc analysis is included. Experiments and comparisons show the high performance of SADEC and clear advantages compared with the state-of-the-art global optimization methods. SADEC is also applicable to filter coupling matrix synthesis and is downloadable. [ABSTRACT FROM PUBLISHER]

A single-fed low-profile millimeter-wave substrate-integrated waveguide (SIW) cavity-backed slot antenna for dual-band circular polarization (CP) applications is proposed. First, by employing two annular exponential slots carved on the surface of a circular SIW cavity, dual-band CP radiation is achieved. Two different modes, that is, the cavity mode and the surface mode, separately modulated by the cavity field distribution and the surface current, are investigated. They are utilized to achieve the dual-band CP radiation. Next, a two-order matching circuit using inductor windows is introduced to achieve dual-band matching at the low-profile antenna design with the help of the differential evolution method. Finally, for the dual-band CP application at 37.5 and 47.8 GHz, an antenna prototype is fabricated and its performance is evaluated. Simulation and measurement results agree very well. [ABSTRACT FROM PUBLISHER]

This paper presents a method to compute the magnetic liquid-free surface shape of a single spike in a quasi-homogeneous magnetic field produced by the Helmholtz coil. In the Rosensweig instability, the magnetic liquid-free surface deforms in a spike-like shape pattern as a magnetic field above some critical value is applied to the liquid. The free surface of the magnetic liquid is described as a polynomial function in cylindrical coordinates with the applied cylindrical symmetry. To obtain the shape deformation, the system of nonlinear magnetically augmented Young-Laplace equations is solved iteratively. The approach to the solution is executed in two steps. In the first step, magnetic field distribution along the surface is computed by the finite-element method. When magnetic field distribution is known, the second step occurs in which the system of Young-Laplace equations, defined as an optimization problem, is solved by differential evolution. [ABSTRACT FROM AUTHOR]

This paper proposes an improved hybrid method to compute the parameters of the two-diode model of photovoltaic (PV) module. Unlike previous methods, it attains the speed of the analytical approach by utilizing only datasheet information. Furthermore, its accuracy is not compromised as it does not require simplifications in its computation. Four parameters are determined analytically, while the remaining three are optimized by using an evolutionary algorithm, i.e., the differential evolution. The speed is improved because the parameters are optimized only once, i.e., at standard test condition, while the values at other conditions are computed analytically. Furthermore, a procedure to guide the initial conditions of the Newton–Raphson iteration is introduced. For validation, the algorithm is compared to other established computational methods for mono-, polycrystalline, and thin film modules. When evaluated against the experimental data, the mean absolute error is improved by one order of magnitude, while the speed is increased by approximately threefold. The standard deviation of the decision parameters over 100 independent runs is less than 0.1—which suggests that the optimization process is very consistent. Due to its speed and accuracy, the method is envisaged to be useful as a computational engine in PV simulator. [ABSTRACT FROM PUBLISHER]

This paper introduces an evolutionary optimization procedure for the design of permanent-magnet motors (PMMs) for electric vehicle (EV) applications, considering a specific drive cycle with multiple operating points. For the purposes of the analysis, the New European Drive Cycle (NEDC) has been employed with two alternative PMM configurations. Energy distribution over the NEDC for a small passenger's EV has been calculated and the equivalent multiple operating points have been extracted, using appropriate weights, in order to maintain an equal energy consumption basis, resulting in reduced computational cost. The proposed optimization technique is constituted of an adaptive differential evolution (DE) algorithm involving dynamic variation of the mutation factor, combined with finite-element (FE) and circuit models. The procedure is based on the precise calculation of the two axes input current components for each candidate solution and operating condition. The methodology introduced presents stable and fast convergence characteristics and has been applied to optimize the geometry of both surface-mounted and interior PMM configurations. The proposed motor is based on the thorough tradeoff among the two alternative optimized geometries and has been validated through measurements on a prototype. [ABSTRACT FROM PUBLISHER]

Evolutionary algorithms (EAs) have recently been suggested as a candidate for solving big data optimization problems that involve a very large number of variables and need to be analyzed in a short period of time. However, EAs face a scalability issue when dealing with big data problems. Moreover, the performance of EAs critically hinges on the utilized parameter values and operator types, thus it is impossible to design a single EA that can outperform all others in every problem instance. To address these challenges, we propose a heterogeneous framework that integrates a cooperative co-evolution method with various types of memetic algorithms. We use the cooperative co-evolution method to split the big problem into subproblems in order to increase the efficiency of the solving process. The subproblems are then solved using various heterogeneous memetic algorithms. The proposed heterogeneous framework adaptively assigns, for each solution, different operators, parameter values and a local search algorithm to efficiently explore and exploit the search space of the given problem instance. The performance of the proposed algorithm is assessed using the Big Data 2015 competition benchmark problems that contain data with and without noise. Experimental results demonstrate that the proposed algorithm, with the cooperative co-evolution method, performs better than without the cooperative co-evolution method. Furthermore, it obtained very competitive results for all tested instances, if not better, when compared to other algorithms using lower computational times. [ABSTRACT FROM AUTHOR]

A novel automated design optimization procedure based on the application of an ultrafast computationally efficient finite-element analysis (CE-FEA) for current-regulated synchronous reluctance machines supplied from power electronic converters is proposed. The CE-FEA uses only a minimum number of magnetostatic solutions in order to comprehensively evaluate performance, including ripple torque and core losses. The optimization algorithm is based on differential evolution, and uses as independent variables the torque angle and ratios for a generic rotor topology with four flux barriers. Two problems, one with two and the other with three objectives, are studied and results are compared. Global performance indices and objectives incorporate the effect of average torque output, losses, torque ripple, and power factor at fixed cost. It is shown that through optimal studies with more than 5000 candidate designs, high output power, high efficiency, and low torque ripple can be achieved, while the relatively low power factor remains an inherent limitation of synchronous reluctance technology. Simulations are validated versus tests from a 10-hp 1800-r/min prototype. [ABSTRACT FROM AUTHOR]

This paper introduces an original algebraic approach to differential evolution (DE) algorithms for combinatorial search spaces. An abstract algebraic differential mutation for generic combinatorial spaces is defined by exploiting the concept of a finitely generated group. This operator is specialized for the permutations space by means of an original randomized bubble sort algorithm. Then, a discrete DE algorithm is derived for permutation problems and it is applied to the permutation flowshop scheduling problem with the total flowtime criterion. Other relevant components of the proposed algorithm are: a crossover operator for permutations, a novel biased selection strategy, a heuristic-based initialization, and a memetic restart procedure. Extensive experimental tests have been performed on a widely accepted benchmark suite in order to analyze the dynamics of the proposed approach and to compare it with the state-of-the-art algorithms. The experimental results clearly show that the proposed algorithm reaches state-of-the-art performances and, most remarkably, it is able to find some new best known results. Furthermore, the experimental analysis on the impact of the algorithmic components shows that the two main contributions of this paper, i.e., the discrete differential mutation and the biased selection operator, greatly contribute to the overall performance of the algorithm. [ABSTRACT FROM PUBLISHER]