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Abstract

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.

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... The MACOA searching capability is validated through experimental studies that employ the IEEE CEC2017 benchmark functions. The MACOA is compared with 10 popular algorithms across various dimensions (30,50, and 100), respectively. A comparative analysis of the convergence curves for all 12 algorithms across these dimensions, along with an examination of boxplots representing the outcomes from multiple runs and search history graphs, reveals that the MACOA demonstrates better optimization results over the other algorithms. ...
... Equation (12) can be optimized to address the problem of the global search capability. A dynamically adjusted step factor [30] is introduced, as shown in (13). ...
... Therefore, MACOA outperforms the comparison algorithms for most of the tested functions. Overall, MACOA works best in different dimensions (30,50, and 100) of the CEC-2017 tested functions. ...
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Optimization algorithms serve as a powerful instrument for tackling optimization issues and are highly valuable in the context of engineering design. The coati optimization algorithm (COA) is a novel meta-heuristic algorithm known for its robust search capabilities and rapid convergence rate. However, the effectiveness of the COA is compromised by the homogeneity of its initial population and its reliance on random strategies for prey hunting. To address these issues, a multi-strategy adaptive coati optimization algorithm (MACOA) is presented in this paper. Firstly, Lévy flights are incorporated into the initialization phase to produce high-quality initial solutions. Subsequently, a nonlinear inertia weight factor is integrated into the exploration phase to bolster the algorithm’s global search capabilities and accelerate convergence. Finally, the coati vigilante mechanism is introduced in the exploitation phase to improve the algorithm’s capacity to escape local optima. Comparative experiments with many existing algorithms are conducted using the CEC2017 test functions, and the proposed algorithm is applied to seven representative engineering design problems. MACOA’s average rankings in the three dimensions (30, 50, and 100) were 2.172, 1.897, and 1.759, respectively. The results show improved optimization speed and better performance.
... Diverse research has investigated the modular CMA-ES and DE algorithm families in various single-objective learning scenarios. This includes conducting empirical performance analysis of CMA-ES [198] and DE [199], predicting CMA-ES [200] and DE [201] algorithm performance, automated algorithm selection [202], and automated algorithm configuration [67], [203]. ...
... The empirical performance analysis [198], [199] has focused on providing empirical results through descriptive statistics of the performance achieved on a particular benchmark suite. Another way to compare algorithms' behavior using information from the performance space is to use performance2vec meta-representations [204]. ...
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The rapid advancements in Machine Learning (ML) and Black-Box Optimisation (BBO) have led to an increased reliance on benchmarking data for evaluating and comparing algorithms across diverse domain tasks. However, the effective exploitation of this data is hindered by challenges such as syntactic variability, semantic ambiguity, and lack of standardization. In this dissertation, we address these challenges by advocating for formal semantic representation of benchmarking data through the use of ontologies. By providing standardized vocabularies and ontologies, we improve knowledge sharing and promote data interoperability across studies in ML and BBO. In the ML domain, focusing on multi-label classification (MLC), we design an ontology-based framework for semantic annotation of benchmarking data, facilitating the creation of MLCBench – a semantic catalog that enhances data accessibility and reusability. In the BBO domain, we introduce the OPTION (OPTImization algorithm benchmarking ONtology) ontology to formally represent benchmarking data, including performance data, algorithm metadata, and problem landscapes. This ontology enables the automatic integration and interoperability of knowledge and data from diverse benchmarking studies. Building upon the semantically annotated benchmarking data, we conduct various empirical studies, including tasks such as algorithm performance prediction and automated algorithm selection (AAS). In the MLC domain, a data-driven AAS pipeline is proposed to exploit this MLC benchmarking data. We evaluate the predictive power of dataset meta-features for AAS and explore various ML approaches – including regression, classification, and pairwise methods – to identify the most effective one. In the BBO domain, we exploit benchmarking data about modular BBO algorithms to conduct a comprehensive analysis of how individual algorithm modules influence overall performance. We develop algorithm representations derived from performance and feature importance values, effectively linking algorithm behavior to problem landscape features. Using these representations, we also relate module configurations and performance, providing deeper insights into the impact of different modules on algorithm performance. Furthermore, the semantically annotated benchmarking data on modular BBO optimisation algorithms is used as a backbone for creating various knowledge graphs (KGs). The KGs are then examined for their predictive power in algorithm performance prediction. By applying scoring-based KG embedding methods and graph neural networks, we predict algorithm performance in transductive and inductive setups, respectively. Overall, the contributions of this dissertation include the development of ontology-based frameworks for managing benchmarking data in the ML and BBO domains, the creation of semantic data catalogs, and novel methodologies for algorithm selection and performance prediction. By addressing challenges in representation and exploitation, this work advances both ML and BBO. It provides tools for improved data management and algorithm selection, as well as insights into algorithm behavior.
... They are broadly classified as evolutionary, swarm intelligence, physics-based, or human-inspired algorithms. For example, evolutionary algorithms incorporate natural selection and genetic variation processes, illustrated by strategies such as evolutionary strategies [8], genetic algorithms [9], and differential evolution (DE) [10]. Similarly, swarm intelligence algorithms, such as particle swarm optimization (PSO) [11], the artificial bee colony (ABC) algorithm [12], and the cuckoo search algorithm (CSA) [13], replicate the collective behaviour of organisms. ...
... 1.09 × 10 3 ± 7.64 × 10 1 9.85 × 10 2 ± 1.12 × 10 2 8.70 × 10 2 ± 9.42 × 10 1 8.47 × 10 2 ± 6.38 × 10 1 F6 6.39 × 10 2 ± 5.52 6.31 × 10 2 ± 6.98 6.14 × 10 2 ± 9.03 6.12 × 10 2 ± 7.07 F7 2.06 × 10 3 ± 2.29 × 10 2 1.71 × 10 3 ± 2.94 × 10 2 1.35 × 10 3 ± 1. 25 In addition to evaluating PDDHBA-H against various HBA variants, we compared it with seven metaheuristic algorithms to further validate its performance. These algorithms include three classic algorithms, namely, particle swarm optimization (PSO), differential evolution (DE), and the cuckoo search algorithm (CSA), and four recent algorithms, namely, the grey wolf optimizer (GWO), whale optimization algorithm (WOA), sparrow search algorithm (SSA), and dung beetle optimizer (DBO), which have garnered significant attention [10,13,39,[43][44][45]. To ensure fair comparisons, all algorithms were configured with identical parameter settings derived from the relevant literature, as detailed in Table 7. ...
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The honey badger algorithm (HBA) has gained significant attention as a metaheuristic optimization method; however, despite these design strengths, it still faces challenges such as premature convergence, suboptimal exploration–exploitation balance, and low population diversity. To address these limitations, we integrate a power-law degree distribution (PDD) topology into the HBA population structure. Three improved versions of the HBA are proposed, with each employing different population update strategies: PDDHBA-R, PDDHBA-B, and PDDHBA-H. In the PDDHBA-R strategy, individuals randomly select neighbours as references, promoting diversity and randomness. The PDDHBA-B strategy allows individuals to select the best neighbouring individual, speeding up convergence. The PDDHBA-H strategy combines both approaches, using random selection for elite individuals and best selection for non-elite individuals. These algorithms were tested on 30 benchmark functions from CEC2017, 21 real-world problems from CEC2011, and four constrained engineering problems. The experimental results show that all three improvements significantly improve the performance of the HBA, with PDDHBA-H delivering the best results across various tests. Further analysis of the parameter sensitivity, computational complexity, population diversity, and exploration–exploitation balance confirms the superiority of PDDHBA-H, highlighting its potential for use in complex optimization problems.
... …………………… (1) K is the number of clusters [21], CK is the K th cluster, x is the data point in the cluster CK, µk is the centroid of k th cluster, || − || 2 represents the squared Euclidean distance between the data point x and the cluster centroid µk ...
... Differential Evolution (DE) is a global optimization algorithm designed to optimize complex, multi-dimensional functions (Storn & Price, 1997). It operates through mutation, crossover, and selection to iteratively refine candidate solutions (Das & Suganthan, 2011). In this research, DE is applied to optimize hotel selection by refining clustering processes and selecting the best OYO hotels based on pricing and rating attributes. ...
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This study evaluates a multi-swarm AI framework that embeds K-Means within Particle Swarm Optimization (PSO) and Differential Evolution (DE) to overcome classic clustering weaknesses. Across benchmark datasets, DE delivers the best balance of accuracy and speed: Silhouette = 0.67, Davies-Bouldin = 0.69, MSE = 0.045, RMSE = 0.212, and quicker convergence than PSO. PSO improves on plain K-Means (Silhouette = 0.61 vs 0.52; DBI = 0.75 vs 0.86; MSE = 0.052 vs 0.078) but converges slower than DE because of velocity-update dependence. K-Means remains the fastest computationally yet lags markedly in clustering quality. Overall, multi-swarm optimization boosts clustering performance but increases computational demands and complicates hyper-parameter tuning. Future work should devise adaptive mechanisms to trim runtime and automate parameter selection to broaden real-world applicability.
... Implementing IGPSO in TOD assessments could enhance spatial and transit suitability analysis by leveraging adaptive feature selection techniques. • Ensemble of Diferential Evolution (DE) for Optimization: DE is a powerful heuristic method used for global optimization, particularly in complex problemsolving [61]. Tis method has been successfully applied in urban transportation models to enhance MOO. ...
... Te integration of advanced optimization techniques, such as Gradient-Guided Evolutionary Neural Architecture Search, Self-Adaptive PSO, Importance-Based PSO with Deep Learning, and Ensemble DE, presents new opportunities for enhancing TOD assessments. Tese methods improve feature selection, optimize spatial relationships, and enhance decision-making accuracy, making TOD optimization more adaptable to real-time urban conditions [58,60,61]. Although this study does not empirically evaluate ridership changes, future research could apply the optimized TOD index to real-world transit networks and assess its impact on passenger behavior. ...
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This study explores transit-oriented development (TOD) in Dhaka City using optimization algorithms to provide urban planning and policy-making insights. The analysis examined the distribution of the TOD index values across the city and identified areas with varying levels of TOD potential. Two optimization algorithms, ant colony optimization (ACO) and particle swarm optimization (PSO), were employed to assess and compare the TOD index values. The results highlight the significance of transit infrastructure in promoting sustainable urban development, particularly in proximity to existing mass rapid transit (MRT) lines. PSO is more suitable for this study among the optimization algorithms because it offers a more precise TOD potential assessment. The findings suggest prioritizing investments in transit infrastructure and implementing TOD-friendly policies to foster sustainable urban growth and improve residents’ quality of life. Future studies can benefit from optimizing the algorithm parameters and incorporating real-world data to improve the accuracy of the TOD assessments.
... Compared to conventional methods, bio-inspired algorithms exhibit intelligence, efficiency, reduced complexity in testing, and a high degree of adaptability [2]. performance of SO is significantly influenced by the quality of the available data and the modeling approach applied to the problem [7], [8]. ...
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In recent years, various fields, including biology, mathematics, and computer science, have begun to use bio-inspired optimization techniques. When dealing with optimization issues, these methods emerge. Because of the difficulty of solving multi-objective optimization issues, scientists are looking to bio-inspired algorithms for a possible solution. This review paper looks at ten cutting-edge bio-inspired optimization algorithms, breaks them down into their contributions to bio-inspired computation and optimization, and reveals their advantages and disadvantages. Furthermore, it explores opportunities for substantial future study in the optimization domain and provides a bibliometric analysis of pertinent literature based on the Scopus databases. This paper delves into the idea of self-organization in bio-inspired algorithms and how they have been used in many studies. Along the way, we identify significant flaws that need further investigation, which will help future studies and bio-inspired optimization progress. Optimization strategies that draw inspiration from biological principles have recently become increasingly popular within computer science, mathematics, and biology, thanks to their capacity to provide novel approaches to solving difficult issues. Classical optimization methods have problems with nonlinearity and numerous restrictions; bio-inspired algorithms, on the other hand, give better answers.
... These evolutionary steps contribute to the strengthening of the population. Therefore, introducing differential evolution (DE) [29] operations into the original MOGWO can also enhance the search efficiency of the algorithm. The main steps of the evolutionary algorithm include mutation, crossover, and selection. ...
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In recent years, unmanned aerial vehicles (UAVs) reconnaissance task allocation are attracting more and more research attention. The efficient allocation of UAV resources is a fundamental and challenging problem. In this paper, the heterogeneous reconnaissance targets are categorized into point, line, and area targets. Considering the constraints of UAV flight path and remaining resources, we construct a multi-objective optimization model with fuel cost and total task time cost as the optimization objectives. To solve this model, an improved multi-objective gray wolf optimization (IMOGWO) algorithm is proposed, which employs three novel improved strategies to balance the exploration and exploitation abilities. Firstly, a nonlinear convergence factor is designed to strengthen the global search ability of the algorithm. Secondly, an evolutionary strategy is introduced to improve the population diversity to help the population jumps out of the local optimum. Finally, a Pareto front optimization strategy is adopted to remove the sub equivalent solutions and maintain the Pareto front set. Compared with the popular and classic multi-objective algorithms, the simulation results verify the effectiveness and superiority of the IMOGWO algorithm in solving the task allocation problem. Furthermore, its superiority becomes more pronounced as the problem scale increases.
... Метаевристичні підходи, включаючи генетичні алгоритми, диференціальну еволюцію та метод рою частинок [7][8][9], демонструють здатність уникати локальних мінімумів [10], але виявляються обчислювально дорогими для великих моделей [11]. ...
... DDE is a variant of the differential evolution (DE) algorithm designed for optimization problems with discrete decision variables. DE is a population-based algorithm used to improve solutions based on a fitness function iteratively (Das and Suganthan 2011;Pant et al. 2020;Ji et al. 2024;Majid et al. 2024;Molina-Pérez et al. 2024). The steps for executing DDE are well discussed by Davendra et al. (2016): ...
Article
This study introduces the group method of data handling with discrete differential evolution (GMDH-DDE) for estimating geothermal temperature and compares its performance with the generalized group method of data handling (GS-GMDH) and GMDH algorithms. GMDH-DDE outperforms accuracy, efficiency, and computational cost, achieving coefficient of determination (R2) values of 0.9999 and 0.9992 for training and testing, respectively. It also demonstrated minimal errors with root mean square error (RMSE) and mean absolute error (MAE) values of 0.0099 and 0.0032 during training and 0.1571 and 0.0099 during testing. Additionally, GMDH-DDE’s training time of 3.12 seconds highlights its computational efficiency, making it suitable for real-time applications and large datasets. Accurate geothermal temperature estimation is crucial for optimizing geothermal energy applications, such as drilling, power plant operations, and geothermal heat pump systems. In conclusion, GMDH-DDE offers a highly accurate, efficient, and computationally feasible method for geothermal temperature estimation, benefiting both research and practical applications in geothermal energy. The modified GMDH-DDE, as an enhanced version of GMDH, can serve and be adapted as a more effective alternative for geothermal temperature estimation across diverse geological settings worldwide.
... For additional information on the Differential Evolution (DE) algorithm, we can refer to the study [51], which is the first author. An in-depth study of the fundamental concepts, variants, and applications of algorithms [59]. The theoretical study of DE, including the analysis of convergence, differential change, crossroads, and the diversity of the population [60]. ...
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This study provides an innovative structure to diagnose the malfunction of the gridconnected photovoltaic energy systems (GPV), depending on the two bilateral improvements: the gray wolf (BGWO) and the differential development (BDE), as well as choosing the properties and classification of automatic learning (ELM and SVM). The proposed methodology relies on real data and includes the following steps: Firstly, we extract statistical parameters from all data sources. Second, the BGWO and BDE algorithms are used separately to choose the properties and reduce their number. Finally, the Extreme Learning Machine (ELM) and the support machine (SVM) are employed to identify seven main breakdowns, namely: nonhomogeneous partial shading, inverter fault, feedback sensor fault, MPPT controller fault, grid anomaly, open circuit in PV array, and boost converter controller fault. The results obtained indicate that the Extreme Learning Machine (ELM) algorithm associated with the BGWO chosen algorithm provides an optimal input vector that detects faults with high accuracy (99.16%) compared to other approaches.
... Both experiments were performed using MATLAB R2020a software on a computational platform with the following specifications: Intel i7 processor @3.70 GHz, 16 GB RAM, and Windows 10 operating system. In addition, the tuning parameters for DE were selected according to the recommendations in [27,28], taking the following values: mutation factor F = 0.6, crossover probability CR = 0.5, and number of individuals pop = 10 throughout all the generations. ...
Article
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Determining the position values of the effectors in a robot to enable its end effector to perform a specific task is a recurrent challenge in robotics. Diverse methodologies have been explored to address this problem, each with distinct advantages and limitations. This work proposes a metaheuristic-based approach to solve a sequence of optimization problems associated with the discretized trajectory of the end effector. Additionally, a method to identify a functional model that describes the effector trajectories is introduced using the same optimization technique. The key contribution lies in algorithmic adjustments that enhance the metaheuristic solutions by leveraging the behavior of the robot and the influence of the tracking task on the search space. Specifically, two operations are modified in the initialization process of the candidate solution. The proposed biased initialization with variable weights improves positional accuracy (72.5%) in relation to methods without dynamic updates. Additionally, the standard deviation was reduced by (89%). For industrial implementations, modern controllers can directly encode effector positions via parametric functions. The results of this proposal formulate optimization problems whose solutions yield the parameters of a time-dependent mathematical model describing the movement of the effector.
... The QP in v j (t + 1) is set to the maximum value of the range if it exceeds the preset range in (32), or to the minimum value if it is below the minimum value of the range. To ensure the randomness of mutation, the population size K must not be less than 4; otherwise, mutation cannot be performed [53]. After mutation, the mutant individual v j (t+1) and the target individual q j (t) exchange elements according to the crossover rate CR to form the trial individual u j (t + 1). ...
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Since the data volume of LiDAR point clouds is very huge, efficient compression is necessary to reduce their storage and transmission costs. However, existing learning-based compression methods do not exploit the inherent angular resolution of LiDAR and ignore the significant differences in the correlation of geometry information at different bitrates. The predictive geometry coding method in the geometry-based point cloud compression (G-PCC) standard uses the inherent angular resolution to predict the azimuth angles. However, it only models a simple linear relationship between the azimuth angles of neighboring points. Moreover, it does not optimize the quantization parameters for residuals on each coordinate axis in the spherical coordinate system. We propose a learning-based predictive coding method (LPCM) with both high-bitrate and low-bitrate coding modes. LPCM converts point clouds into predictive trees using the spherical coordinate system. In high-bitrate coding mode, we use a lightweight Long-Short-Term Memory-based predictive (LSTM-P) module that captures long-term geometry correlations between different coordinates to efficiently predict and compress the elevation angles. In low-bitrate coding mode, where geometry correlation degrades, we introduce a variational radius compression (VRC) module to directly compress the point radii. Then, we analyze why the quantization of spherical coordinates differs from that of Cartesian coordinates and propose a differential evolution (DE)-based quantization parameter selection method, which improves rate-distortion performance without increasing coding time. Experimental results on the LiDAR benchmark \textit{SemanticKITTI} and the MPEG-specified \textit{Ford} datasets show that LPCM outperforms G-PCC and other learning-based methods.
... To address the challenge of PID tuning in nonlinear systems, various metaheuristic algorithms have been employed. Differential evolution (DE) [9] and particle swarm optimization (PSO) [10] are among the most widely used, valued for their simplicity and convergence behavior. More recent methods like the slime mould algorithm (SMA) [11] and greater cane rat algorithm (GCRA) [12] offer improved exploration in complex search spaces. ...
Article
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Accurate temperature control of continuous stirred tank reactors (CSTRs) remains a major challenge due to the nonlinear dynamics and inherent time delay of the system. Conventional proportional-integral-derivative (PID) controllers often struggle to maintain optimal performance under such complexities, highlighting the need for more advanced control strategies. In this study, a two-degree-of-freedom (2-DOF) PID controller is designed and optimized using the quadratic interpolation optimization (QIO) to enhance temperature regulation in CSTRs. The proposed approach aims to minimize steady-state error, settling time, and overshoot. To implement this method, the nonlinear model of the CSTR is linearized around a stable operating point, and the controller parameters are tuned by minimizing a composite cost function consisting of normalized overshoot and instantaneous error. Simulation results demonstrate that the QIO-based 2-DOF PID controller significantly outperforms other metaheuristic approaches such as differential evolution, particle swarm optimization, slime mould algorithm, and greater cane rat algorithm. Furthermore, comparisons with recent works reveal substantial improvements in rise time, settling time, and steady-state accuracy.
... This structure supports multiple targets and accommodates scenarios where different etch rates are required across wafers or device layers. A differential evolution (DE) algorithm [17], [18] was selected to solve the optimization problem due to its simplicity, robustness, and suitability for black-box functions like neural networks. DE is a population-based metaheuristic that iteratively evolves a set of candidate solutions using mutation, crossover, and selection. ...
... Algorithms like a Linear Population Size Reduction (LPSR) success history (SH) adaptive DE (L-SHADE) [38] and the Distance-Based Success History Differential Evolution (DISH) [31] extend DE with population size reduction [38] that was already introduced to DE in continuous optimization [39], and real-world industry challenges [40], and a well-performing parameter control mechanism, named Success History (SH) [38]. The foundational concepts from DISH algorithm, the variants of algorithms L-SHADE, have won several evolutionary benchmarking competitions [38,[41][42][43][44]. Several recent surveys and insights exist with the DE algorithm's base name [18,19,32,[45][46][47][48] and its metaphors [49][50][51], stemming from the progress on computational mechanisms, mainly from the branches of the DE, as well as applications [18, 34-36, 52, 53]. More about the population-based optimization and DE development can be read in reviews like in Refs. ...
Chapter
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This chapter describes a range of foundational concepts in differential evolution (DE) algorithm, including distance-based success history differential evolution (DISH), and then tackles some challenges from real-world applications (RWAs) of DE. The DISH algorithm is described in more detail on how it self-adapts control parameters and how it is applied on evolutionary computation challenges, including recent 100-digit challenges. The chapter then continues with some RWA applications of self-adaptive DE by listing outcomes from benchmarks prepared in robotics, computer animation, energy, and document understanding, as well as other benchmarks from competitions on evolutionary computation. In robotics, a success history DE for underwater glider path planning is defined, in computer animation, a mixed-integer multi-objective optimization DE for tree geometry animation is listed, in energy, parallel constrained DE optimization for hydro-thermal scheduling, and in document understanding, a discrete constrained DE for text summarization. Main methods and results demonstrating their applicability are provided.
... However, DE has some shortcomings such as parameter sensitivity, selection of mutation strategy and early convergence. To address these shortcomings, many researchers have focused on improving the performance of classical DE. [7]. In this section, both classic DE and eight advanced DE variants are presented. ...
Article
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Since passive elements such as resistors and capacitors used in active filter design change the gain and phase of the filter, their selection is an important issue. The ability of the filter to achieve a targeted quality factor depends on the selection of these components. The filter sections are cascaded to get closer to the ideal filter response; in this case, as the number of components increases, the computational complexity in selecting the optimum values increases. Moreover, in practical applications, the values of the filter components should be fixed to the discrete component values in the industrial component series. Thus, the problem turns into a discrete optimization problem that becomes more difficult and time-consuming. The use of metaheuristic algorithms in solving the problem is an alternative approach. This work propounds a survey on the differential evolution (DE) algorithm and its advanced variants utilized for the selection of optimal component values in filter design. Nine DE algorithms have been used to determine the optimal component values of the tenth-order Multi-Feedback topology Bessel filter. The performance of each algorithm has been evaluated in terms of convergence rate and solution accuracy. Statistical results show that success-history based adaptive DE with linear population size reduction (LSHADE) is superior to other DE variants and can reduce the filter quality factor error value to 4.64E−02 for E12 series, 6.45E−02 for E96 series and 2.23E−02 for E192 series. The obtained results show that LSHADE algorithm are an effective tool for the selection of optimal discrete component values in filter design, increasing computational speed and solution accuracy.
... DE effectively is a population-based optimization technique that iteratively evolves a set of candidate solutions toward a better solution. By evaluating the fitness of each solution and applying genetic operators such as mutation and crossover, DE efficiently explores the solution space to find optimal or near-optimal solutions (Das and Suganthan 2011;Pant et al. 2020;Ji et al. 2024;Majid et al. 2024;Molina-Pérez et al. 2024;Mkono et al. 2025b). The procedure for executing DDE involves the following steps: ...
Article
Accurate estimation of the brittleness index (BI) is critical for optimizing hydraulic fracturing operations in shale gas reservoirs, as it directly influences fracture propagation and gas recovery efficiency. The BI quantifies the resistance of rock to fracturing, a key factor in determining the optimal depth for fracture stimulation. Prior methods of estimating BI, such as empirical correlations and other utilized machine learning (ML) techniques, often suffer from limited accuracy and generalizability, particularly in complex geological formations like the Fuling shale gas field. To address these limitations, ML techniques have gained prominence due to their ability to capture complex, nonlinear relationships within large data sets, improving predictive accuracy. In this study, we propose a novel approach that utilizes a hybrid group method of data handling based on discrete differential evolution (GMDH-DDE) to predict the BI. The GMDH-DDE model was compared with the group method of data handling (GMDH), random forest (RF), and multilayer perceptron (MLP). The results demonstrate that GMDH-DDE significantly outperforms these models, achieving a coefficient of determination (R2) of 0.9984, a root mean square error (RMSE) of 0.2895, and a mean absolute error (MAE) of 0.02543 to unseen data. The GMDH model ranked second in BI estimation, achieving an R2 of 0.9805, RMSE of 0.4635, and MAE of 0.04224. It was followed by the RF model, with an R2 of 0.9599, RMSE of 0.6034, and MAE of 0.0997. The MLP model, however, had the lowest performance, with an R2 of 0.9263, RMSE of 0.9566, and MAE of 0.1256. Additionally, the GMDH-DDE model demonstrates superior computational efficiency, requiring only 1.12 seconds. This is a significant advantage over other methods, with GMDH taking 4.82 seconds, RF requiring 11.23 seconds, and MLP taking 27.45 seconds. These findings highlight the potential of GMDH-DDE in providing accurate and computationally efficient BI estimations. The improved accuracy and efficiency of BI estimation by GMDH-DDE are expected to contribute to more effective and cost-efficient hydraulic fracturing operations, ultimately enhancing the economic viability of shale gas reservoirs.
... One of the first DE surveys was published by Neri and Tirronen in 2010 [9], and another in 2011 by Das and Sugathan [10]. The first one includes some experimental results obtained with the algorithms available at that time. ...
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Since the discovery of the Differential Evolution algorithm, new and improved versions have continuously emerged. In this paper, we review selected algorithms based on Differential Evolution that have been proposed in recent years. We examine the mechanisms integrated into them and compare the performance of algorithms. To compare their performances, statistical comparisons were used as they enable us to draw reliable conclusions about the algorithms’ performances. We use the Wilcoxon signed-rank test for pairwise comparisons and the Friedman test for multiple comparisons. Subsequently, the Mann–Whitney U-score test was added. We conducted not only a cumulative analysis of algorithms, but we also focused on their performances regarding the function family (i.e., unimodal, multimodal, hybrid, and composition functions). Experimental results of algorithms were obtained on problems defined for the CEC’24 Special Session and Competition on Single Objective Real Parameter Numerical Optimization. Problem dimensions of 10, 30, 50, and 100 were analyzed. In this paper, we highlight promising mechanisms for further development and improvements based on the study of the selected algorithms.
... In EAs, an iteration is referred to as a generation. The paradigm of evolutionary computing techniques follows Darwinian principles for automation problems (Das and Suganthan, 2011). ...
Article
Blasting mean fragment size, as a key indicator of blasting effectiveness, directly impacts the subsequent mineral processing efficiency and economic benefits. This study aimed to develop a machine learning-based model for predicting blasting mean fragment size to improve the accuracy and efficiency of blasting design. This study fine-tuned the XGBoost model using five metaheuristic optimization algorithms: ant colony optimization (ACO), differential evolution (DE), inverse diffusion optimization (IWO), particle swarm optimization (PSO), and simulated annealing (SA). The results showed that ACO, DE, and PSO produced better optimization results. Based on this, the study further introduced generative adversarial networks (GAN), integrating them with the three best-performing hybrid models. The results showed that the XGBoost hybrid model combining DE and GAN had the optimal prediction performance. The model’s root mean square error, mean absolute error, coefficient of determination, and variance explanation values were 0.0137, 0.0109, 0.9513, and 95.30%, respectively. Ultimately, this study developed an XGBoost hybrid model for predicting blast fragmentation, integrating DE and GAN.
Article
Purpose This study introduces a novel hybrid algorithm, equilibrium optimizer-singular value decomposition (EO-SVD), for structural damage detection in various bridge models. By combining the optimization capabilities of EO with the dimensionality reduction of SVD, the proposed approach achieves superior accuracy and computational efficiency compared to traditional algorithms. Design/methodology/approach By combining the optimization capabilities of EO with the dimensionality reduction of SVD, the proposed approach achieves superior accuracy and computational efficiency than traditional algorithms. Comprehensive evaluations were performed on multiple bridge models, including a reinforced concrete bridge, a steel truss bridge and a suspension bridge, under scenarios with noise. Findings The proposed algorithm achieved the highest accuracy in the three mentioned structures, with values of 2.98E−05, 2.97E−05 and 4.32E−04, demonstrating high accuracy as the highest standard deviation was only 7.97E−04. EO-SVD consistently delivered the lowest errors and fastest convergence. Utilizing finite element models and dynamic features, the algorithm effectively pinpointed damage locations and severities, even under complex scenarios. Research limitations/implications Although its performance may slightly decrease with highly intricate structures, EO-SVD remains highly robust and reliable, offering a solid foundation for the future development of structural health monitoring systems. Originality/value Utilizing finite element models and dynamic features, the algorithm effectively pinpointed damage locations and severities, even under complex scenarios.
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This study introduces a novel approach to addressing the challenges of high-dimensional variables and strong nonlinearity in reservoir production and layer configuration optimization. For the first time, relational machine learning models are applied in reservoir development optimization. Traditional regression-based models often struggle in complex scenarios, but the proposed relational and regression-based composite differential evolution (RRCODE) method combines a Gaussian naive Bayes relational model with a radial basis function network regression model. This integration effectively captures complex relationships in the optimization process, improving both accuracy and convergence speed. Experimental tests on a multi-layer multi-channel reservoir model, the Egg reservoir model, and a real-field reservoir model (the S reservoir) demonstrate that RRCODE significantly reduces water injection and production volumes while increasing economic returns and cumulative oil recovery. Moreover, the surrogate models employed in RRCODE exhibit lightweight characteristics with low computational overhead. These results highlight RRCODE’s superior performance in the integrated optimization of reservoir production and layer configurations, offering more efficient and economically viable solutions for oilfield development.
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This paper examines strategies aimed at improving search procedures in multimodal, low-dimensional domains. Here, low-dimensional domains refers to a maximum of five dimensions. The present analysis assembles strategies to form an algorithm named S-EPSO, which, at its core, locates and maintains multiple optima without relying on external niching parameters, instead adapting this functionality internally. The first proposed strategy assigns socio-emotional personalities to the particles forming the swarm. The analysis also introduces a technique to help them visit secluded zones. It allocates the particles of the initial distribution to subdomains based on biased decisions. The biases reflect the subdomain’s potential to contain optima. This potential is established from a balanced combination of the jaggedness and the mean-average interval descriptors developed in the study. The study compares the performance of S-EPSO to that of state-of-the-art algorithms over seventeen functions of the CEC benchmark, and S-EPSO is revealed to be highly competitive. It outperformed the reference algorithms 14 times, whereas the best of the latter outperformed the other two 10 times out of 30 relevant evaluations. S-EPSO performed best with the most challenging 5D functions of the benchmark. These results clearly illustrate the potential of S-EPSO when it comes to dealing with practical engineering optimization problems limited to five dimensions.
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Optimizing systems with an unknown number of critical homogenous components presents a significant challenge in many real-world applications. Traditional metaheuristic approaches often require predefined component counts, leading to suboptimal solutions when this number is uncertain. To address this, we propose a chaotic map-encoded metaheuristic framework that dynamically adjusts the number of components during optimization. This approach is applied to two complex problems: dendritic neuron model (DNM) optimization, where the goal is to determine the optimal number of dendritic branches for improved learning performance, and wind farm layout optimization (WFLOP), which seeks to optimize the placement and number of wind turbines to maximize energy output while minimizing wake effects. Experimental results show that this approach outperforms variable-length genetic algorithms in DNM optimization and demonstrates competitive performance in WFLOP. These findings highlight the potential of chaotic maps to improve metaheuristic efficiency in variable-length optimization problems.
Chapter
This paper presents the development of a Micro Differential Evolution algorithm with self-adaptation (μ\mu SADE) mechanisms for numerical optimization. The proposed μ\mu SADE algorithm incorporates self-adaptive mechanisms to update control parameters with the smaller population size to achieve the ability to both explore and exploit. One of the proposed features is the self-adaptive capability to adjust its mutation rate and crossover rate to improve the convergence rate of the needed solution. μ\mu SADE was applied to the benchmark functions of complex numerical optimization used by the Congress on Evolutionary Computation (CEC), and the results were statistically compared with those obtained by the classical Differential Evolution (DE), Micro Differential Evolution (μ\mu DE) and the Self-Adaptive Differential Evolution (SADE).
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This research investigates the impact of the Gurney flap on the aerodynamic performance of the NACA 0018 airfoil at a Reynolds number of Re = 1 × 105. A total of forty data sets are generated using the Halton sampling method, and computational fluid dynamics (CFD) simulations are performed on each set. The CFD outputs are then utilized to train a surrogate model based on the Kriging method. The optimization process employs the differential evolution algorithm to determine the optimal Gurney flap height, width and angle of attack values. The findings demonstrate that the optimized Gurney flap configuration leads to a significant enhancement in the lift coefficient, with an average increase of approximately 26.9%. These results underscore the effectiveness of the Gurney flap as a means to improve the aerodynamic performance of the NACA 0018 airfoil at the specified Reynolds number. Further investigations and experimental validations are recommended to validate the obtained results and explore potential applications in practical aerodynamic designs.
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Floating hybrid wind-wave systems combine offshore wind platforms with wave energy converters (WECs) to create cost-effective and reliable energy solutions. Adequately designed and tuned WECs are essential to avoid unwanted loads disrupting turbine motion while efficiently harvesting wave energy. These systems diversify energy sources, enhancing energy security and reducing supply risks while providing a more consistent power output by smoothing energy production variability. However, optimising such systems is complex due to the physical and hydrodynamic interactions between components, resulting in a challenging optimisation space. This study uses a 5-MW OC4-DeepCwind semi-submersible platform with three spherical WECs to explore these synergies. To address these challenges, we propose an effective ensemble optimisation (EEA) technique that combines covariance matrix adaptation, novelty search, and discretisation techniques. To evaluate the EEA performance, we used four sea sites located along Australia's southern coast. In this framework, geometry and power take-off parameters are simultaneously optimised to maximise the average power output of the hybrid wind-wave system. Ensemble optimisation methods enhance performance, flexibility, and robustness by identifying the best algorithm or combination of algorithms for a given problem, addressing issues like premature convergence, stagnation, and poor search space exploration. The EEA was benchmarked against 14 advanced optimisation methods, demonstrating superior solution quality and convergence rates. EEA improved total power output by 111%, 95%, and 52% compared to WOA, EO, and AHA, respectively. Additionally, in comparisons with advanced methods, LSHADE, SaNSDE, and SLPSO, EEA achieved absorbed power enhancements of 498%, 638%, and 349% at the Sydney sea site, showcasing its effectiveness in optimising hybrid energy systems.
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Monopulse antennas form an important methodology of realizing tracking radar. They are based on the simultaneous comparison of sum and difference signals to compute the angle-error and to steer the antenna patterns in the direction of the target (i.e., the boresight direction). In this study, we consider the synthesis problem of difference patterns of monopulse antennas in the framework of Multi-objective Optimization (MO). The synthesis problem is recast as an MO problem (for the first time, to the best of our knowledge), where the Maximum Side-Lobe Level (MSLL) and Beam Width (BW) of principal lobe are taken as the two objectives to be minimized simultaneously. The approximated Pareto Fronts (PFs) are obtained for different number of elements and sub-arrays using a recently developed and very competitive Multi-Objective Evolutionary Algorithm (MOEA) called MOEA/D-DE that uses a decomposition approach for converting the problem of approximation of the PF into a number of single objective optimization problems. This algorithm employs Differential Evolution (DE), one of the most powerful real parameter optimizers in current use, as the search method. The quality of solutions obtained is compared with the help of the trade-off graphs (plots of the approximated PF) generated by MOEA/D-DE on the basis of the two objectives to investigate the dependence of the number Corresponding author: S. Das (swagatamdas19@yahoo.co.in).
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The aim of this paper is to analyze some theoretical properties of differential evolution algorithms. The main result is a theoretical relationship between the expected population variance after mutation and crossover and the initial population variance. It allows us to obtain information on the explorative power of differential evolution algorithms. The theoretical result agrees with some empirical ones obtained by experimental studies and allows one to explain some of the behavior of differential evolution algorithms.
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In this paper we present experimental results to show deep view on how self- adaptive mechanism works in differential evolution algorithm. The results of the self-adaptive differential evolution algorithm were evaluated on the se t of 24 benchmark functions provided for the CEC2006 special session on constrained real parameter optimization. In this paper we especially focus on how the control parameters are being changed during the evolutionary process.
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A new heuristic approach for minimizing possibly nonlinear and non differentiable continuous space functions is presented. By means of an extensive testbed, which includes the De Jong functions, it will be demonstrated that the new method converges faster and with more certainty than Adaptive Simulated Annealing as well as the Annealed Nelder&Mead approach, both of which have a reputation for being very powerful. The new method requires few control variables, is robust, easy to use and lends itself very well to parallel computation.
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This paper presents a new multi-objective evolutionary algorithm based on differential evolution. The proposed approach adopts a secondary population in order to retain the non-dominated solutions found during the evolutionary process. Additionally, the approach also incorporates the concept of ε-dominance to get a good distribution of the solutions retained. The main goal of this work was to keep the fast convergence exhibited by Differential Evolution in global optimization when extending this heuristic to multi- objective optimization. We adopted standard test functions and performance measures reported in the specialized literature to validate our proposal. Our results are compared with respect to another multi-objective evolutionary algorithm based on differential evolution (Pareto Differential Evolution) and with respect to two approaches that are representative of the state-of-the-art in the area: the NSGA-II and ε-MOEA.
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Different constraint handling techniques have been used with multi-objective evolutionary algorithms (MOEA) to solve constrained multi-objective optimization problems. It is impossible for a single constraint handling technique to outperform all other constraint handling techniques always on every problem irrespective of the exhaustiveness of the parameter tuning. To overcome this selection problem, an ensemble of constraint handling methods (ECHM) is used to tackle constrained multi-objective optimization problems. The ECHM is integrated with a multi-objective differential evolution (MODE) algorithm. The performance is compared between the ECHM and the same single constraint handling methods using the same MODE (using codes available from http://www3.ntu.edu.sg/home/EPNSugan/index.htm). The results show that ECHM overall outperforms the single constraint handling methods.
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This paper presents a differential evolution algorithm to solve the permutaion flowshop sequencing problem with makespan criterion. Differential evolution is one of the latest evolutionary optmization algorithm applied to continuous optimization problems where members of population use chromosomes based on floating-point numbers to represent candidate solutions. In this paper we also present a heuristic rule, called smallest parameter value first in the permutation, which enables the differential evolution algorithm to be applied to all classes of sequencing scheduling problems. The results for the well known benchmark suite in the literature is presented and compared to the well known approaches such as genetic algorithm and partical swarm optimization algorithm.
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The social foraging behavior of Escherichia coli bacteria has recently been studied by several researchers to develop a new algorithm for distributed op-timization control. The Bacterial Foraging Optimization Algorithm (BFOA), as it is called now, has many features analogous to classical Evolutionary Algorithms (EA). Passino [1] pointed out that the foraging algorithms can be integrated in the framework of evolutionary algorithms. In this way BFOA can be used to model some key survival activities of the population, which is evolving. This article pro-poses a hybridization of BFOA with another very popular optimization technique of current interest called Differential Evolution (DE). The computational chemo-taxis of BFOA, which may also be viewed as a stochastic gradient search, has been coupled with DE type mutation and crossing over of the optimization agents. This leads to the new hybrid algorithm, which has been shown to overcome the problems of slow and premature convergence of both the classical DE and BFOA over several benchmark functions as well as real world optimization problems.
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A new heuristic approach for minimizing possiblynonlinear and non-differentiable continuous spacefunctions is presented. By means of an extensivetestbed it is demonstrated that the new methodconverges faster and with more certainty than manyother acclaimed global optimization methods. The newmethod requires few control variables, is robust, easyto use, and lends itself very well to parallelcomputation.
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This paper proposes the scale factor local search differential evolution (SFLSDE). The SFLSDE is a differential evolution (DE) based memetic algorithm which employs, within a self-adaptive scheme, two local search algorithms. These local search algorithms aim at detecting a value of the scale factor corresponding to an offspring with a high performance, while the generation is executed. The local search algorithms thus assist in the global search and generate offspring with high performance which are subsequently supposed to promote the generation of enhanced solutions within the evolutionary framework. Despite its simplicity, the proposed algorithm seems to have very good performance on various test problems. Numerical results are shown in order to justify the use of a double local search instead of a single search. In addition, the SFLSDE has been compared with a standard DE and three other modern DE based metaheuristic for a large and varied set of test problems. Numerical results are given for relatively low and high dimensional cases. A statistical analysis of the optimization results has been included in order to compare the results in terms of final solution detected and convergence speed. The efficiency of the proposed algorithm seems to be very high especially for large scale problems and complex fitness landscapes.
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Differential evolution (DE) is an efficient and powerful population-based stochastic search technique for solving global optimization problems over continuous space, which has been widely applied in many scientific and engineering fields. However, the success of DE to handle a specific problem crucially depends on the proper choice of various parameters including the size of the population. Employing the trial and error scheme to search for the most suitable parameter settings requires high computational costs. In this paper, we propose a DE algorithm with an ensemble of parallel populations in which the number of function evaluations allocated to each population is self-adapted by learning from their previous experiences in generating superior solutions. Consequently, a more suitable population size takes most of the function evaluations adaptively to match different phases of the search process/evolution. Although the evolutionary algorithms have been investigated for about five decades, to our best of knowledge so far no effective population adaptation scheme has been proposed. The performance of the DE algorithm with an ensemble of parallel populations is extensively evaluated on a suite of 14 bound-constrained numerical optimization problems and compares favorably with the conventional DE with different single population sizes.
Chapter
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The aim of this paper is to analyze the impact on the expected population mean and variance of several variants of mutation and crossover operators used in differential evolution algorithms. As a consequence of this analysis a simple variance based mutation operator which does not use differences but has the same impact on the population variance as classical differential evolution operators is proposed. A preliminary analysis of the distribution probability of the population in the case of a differential evolution algorithm for binary encoding is also presented.
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Differential evolution (DE) has been shown to be a simple, yet powerful, evolutionary algorithm for global optimization for many real problems. Adaptation, especially self-adaptation, has been found to be highly beneficial for adjusting control parameters, especially when done without any user interaction. This paper presents differential evolution algorithms, which use different adaptive or self-adaptive mechanisms applied to the control parameters. Detailed performance comparisons of these algorithms on the benchmark functions are outlined.
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In this chapter we present an overview of the major applications areas of differential evolution. In particular we pronounce the strengths of DE algorithms in tackling many difficult problems from diverse scientific areas, including single and multiobjective function optimization, neural network training, clustering, and real life DNA microarray classification. To improve the speed and performance of the algorithm we employ distributed computing architectures and demonstrate how parallel, multi–population DE architectures can be utilised in single and multiobjective optimization. Using data mining we present a methodology that allows the simultaneous discovery of multiple local and global minimizers of an objective function. At a next step we present applications of DE in real life problems including the training of integer weight neural networks and the selection of genes of DNA microarrays in order to boost predictive accuracy of classification models. The chapter concludes with a discussion on promising future extensions of the algorithm, and presents novel mutation operators, that are the result of a genetic programming procedure, as very interesting future research direction.
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A new heuristic approach for minimizing possiblynonlinear and non-differentiable continuous spacefunctions is presented. By means of an extensivetestbed it is demonstrated that the new methodconverges faster and with more certainty than manyother acclaimed global optimization methods. The newmethod requires few control variables, is robust, easyto use, and lends itself very well to parallelcomputation.
Chapter
The Differential Evolution Algorithm is a floating-point encoded evolutionary algorithm for global optimization over continuous spaces. This algorithm so far uses empirically chosen fixed search parameters. This study is to introduce dynamic parameter control using fuzzy logic controllers whose inputs incorporate the relative function values and individuals of the successive generations to adapt the search parameters for the mutation operation and the crossover operation. Standard test functions are used to demonstrate. Based on experimental results, the Fuzzy Adaptive Differential Evolution Algorithm results in a faster convergence.
Article
Linear antenna array design is one of the most important electromagnetic optimization problems of current interest. In contrast to a plethora of recently published articles that formulate the design as the optimization of a single cost function formed by combining distinct and often conflicting design-objectives into a weighted sum, in this work, we take a Multi-objective Optimization (MO) approach to solve the same problem. We consider two design objectives: the minimum average Side Lobe Level (SLL) and null control in specific directions that are to be minimized simultaneously in order to achieve the optimal spacing between the array elements. Our design method employs a recently developed and very competitive multi-objective evolutionary algorithm called MOEA/D-DE that uses a decomposition approach for converting the problem of approximation of the Pareto Fronts (PF) into a number of single objective optimization problems. This algorithm employs Differential Evolution (DE), one of the most powerful real parameter optimizers in current use, as the search method. As will be evident from the shape of the approximated PFs obtained with MOEA/D-DE, the two design-objectives are in conflict and usually, performance cannot be improved significantly for one without deteriorating the other. Unlike the single-objective approaches, the MO approach provides greater flexibility in the design by yielding a set of equivalent final solutions from which the user can choose one that attains a suitable trade-off margin as per requirements. We illustrate that the best compromise solution attained by MOEA/D-DE can comfortably outperform state-of-the-art single-objective algorithms like Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Tabu Search Algorithm (TSA), and Memetic Algorithm (MA). In addition, we compared the results obtained by MOEA/D-DE with those obtained by one of the most widely used MO algorithm called NSGA-2 and another generic multi-objective DE variant that uses non-dominated sorting, on the basis of the R-indicator, hypervolume indicator, and quality of the best trade-off solutions obtained.
Chapter
We’ve discussed a few traditional problem-solving strategies. Some of them guarantee finding the global solution, others don’t, but they all share a common pattern. Either they guarantee discovering the global solution, but are too expensive (i.e., too time consuming) for solving typical real-world problems, or else they have a tendency of “getting stuck” in local optima. Since there is almost no chance to speed up algorithms that guarantee finding the global solution, i.e., there is almost no chance of finding polynomial-time algorithms for most real problems (as they tend to be NP-hard), the other remaining option aims at designing algorithms that are capable of escaping local optima.
Conference Paper
Recent results show that the Differential Evolution algorithm has significant difficulty on functions that are not linearly separable. On such functions, the algorithm must rely primarily on its differential mutation procedure which, unlike its recombination strategy, is rotationally invariant. We conjecture that this mutation strategy lacks sufficient selective pressure when appointing parent and donor vectors to have satisfactory exploitative power on non-separable functions. We find that imposing pressure in the form of rank-based differential mutation results in a significant improvement of exploitation on rotated benchmarks.
Book
Differential evolution is arguably one of the hottest topics in today's computational intelligence research. This book seeks to present a comprehensive study of the state of the art in this technology and also directions for future research. The fourteen chapters of this book have been written by leading experts in the area. The first seven chapters focus on algorithm design, while the last seven describe real-world applications. Chapter 1 introduces the basic differential evolution (DE) algorithm and presents a broad overview of the field. Chapter 2 presents a new, rotationally invariant DE algorithm. The role of self-adaptive control parameters in DE is investigated in Chapter 3. Chapters 4 and 5 address constrained optimization; the former develops suitable stopping conditions for the DE run, and the latter presents an improved DE algorithm for problems with very small feasible regions. A novel DE algorithm, based on the concept of "opposite" points, is the topic of Chapter 6. Chapter 7 provides a survey of multi-objective differential evolution algorithms. A review of the major application areas of differential evolution is presented in Chapter 8. Chapter 9 discusses the application of differential evolution in two important areas of applied electromagnetics. Chapters 10 and 11 focus on applications of hybrid DE algorithms to problems in power system optimization. Chapter 12 applies the DE algorithm to computer chess. The use of DE to solve a problem in bioprocess engineering is discussed in Chapter 13. Chapter 14 describes the application of hybrid differential evolution to a problem in control engineering.
Conference Paper
In this paper, we propose an extension of Self-adaptive Differential Evolution algorithm (SaDE) to solve optimization problems with constraints. In comparison with the original SaDE algorithm, the replacement criterion was modified for handling constraints. The performance of the proposed method is reported on the set of 24 benchmark problems provided by CEC2006 special session on constrained real parameter optimization.
Article
Due to the growing complexity of todays technical systems optimization is becoming an important issue within the design phase. The applicability of optimization algorithms in automatic design processes is strongly dependent on the stopping criterion. It is important that the optimum is reliably found but furthermore no time or computational resources should be wasted. Therefore a run time analysis is conducted for several promising stopping criteria. Amongst others a new criterion incorporating a quicksort algorithm is examined. In former work it proved to be particularly beneficial with regards to the needed number of function evaluations for Particle Swarm Optimization. However, it is considered to produce additional computational effort because of the sorting. An estimation of the complexity of the stopping criteria calculations supports this assumption. Nevertheless, the results of the run time analysis confirm that the new criterion is the best choice for Particle Swarm Optimization, especially when optimizing real-worlds problems with computationally expensive objective functions. As most technical systems require complex simulations this assumption is generally met. For Differential Evolution a simpler criterion is sufficient.
Book
Problems demanding globally optimal solutions are ubiquitous, yet many are intractable when they involve constrained functions having many local optima and interacting, mixed-type variables.The differential evolution (DE) algorithm is a practical approach to global numerical optimization which is easy to understand, simple to implement, reliable, and fast. Packed with illustrations, computer code, new insights, and practical advice, this volume explores DE in both principle and practice. It is a valuable resource for professionals needing a proven optimizer and for students wanting an evolutionary perspective on global numerical optimization. A companion CD includes DE-based optimization software in several programming languages.
Conference Paper
Learnable Evolution Model (LEM) is a form of non-Darwinian evolutionary computation that employs machine learning to guide evolutionary processes. Its main novelty are new ty pe of operators for creating new individuals, specifically, hypothesis generation, which learns rules indicating subareas in the searc h space that likely contain the optimum, and hypothesis instantiation, which populates these subspaces with new individuals. Thi s paper briefly describes the newest and most advanced impl ementation of learnable evolution, LEM3, its novel features, and results from its comparison with a conventional, Darwinian-type evolutionary computation program (EA), a cultural evolution algo rithm (CA), and the estimation of distribution algorithm (EDA) on selected function optimization problems (with the number of variables varying up to 1000). In every experiment, LEM3 outperformed the compared programs in terms of the evolution len gth (the number of fitness evaluations needed to achieved a desired solution), sometimes more than by one order of magnitude.
Article
An abstract is not available.
Article
A technique is developed for the electromagnetic reconstruction of the location and shape of buried elliptical–cylindrical conductors or tunnels based on a differential evolution (DE) algorithm. Simulation results are presented which demonstrate that DE can offer a simple, yet efficient and robust method for the imaging of buried objects and voids. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 28: 164–169, 2001.
Article
Differential evolution (DE) has gained a lot of attention from the global optimization research community. It has proved to be a very robust algorithm for solving non-differentiable and non-convex global optimization problems. In this paper, we propose some modifications to the original algorithm. Specifically, we use the attraction-repulsion concept of electromagnetism-like (EM) algorithm to boost the mutation operation of the original differential evolution. We carried out a numerical study using a set of 50 test problems, many of which are inspired by practical applications. Results presented show the potential of this new approach.
Chapter
Differential Evolution (DE), a vector population based stochastic optimization method has been introduced to the public in 1995. During the last 10 years research on and with DE has reached an impressive state, yet there are still many open questions, and new application areas are emerging. This chapter introduces some of the current trends in DE-research and touches upon the problems that are still waiting to be solved.
Article
Previous studies have shown that differential evolution is an efficient, effective and robust evolutionary optimization method. However, the convergence rate of differential evolution in optimizing a computationally expensive objective function still does not meet all our requirements, and attempting to speed up DE is considered necessary. In this paper, a new local search operation, trigonometric mutation, is proposed and embedded into the differential evolution algorithm. This modification enables the algorithm to get a better trade-off between the convergence rate and the robustness. Thus it can be possible to increase the convergence velocity of the differential evolution algorithm and thereby obtain an acceptable solution with a lower number of objective function evaluations. Such an improvement can be advantageous in many real-world problems where the evaluation of a candidate solution is a computationally expensive operation and consequently finding the global optimum or a good sub-optimal solution with the original differential evolution algorithm is too time-consuming, or even impossible within the time available. In this article, the mechanism of the trigonometric mutation operation is presented and analyzed. The modified differential evolution algorithm is demonstrated in cases of two well-known test functions, and is further examined with two practical training problems of neural networks. The obtained numerical simulation results are providing empirical evidences on the efficiency and effectiveness of the proposed modified differential evolution algorithm.
Article
This paper studies the efficiency of a recently defined population-based direct global optimization method called Differential Evolution with self-adaptive control parameters. The original version uses fixed population size but a method for gradually reducing population size is proposed in this paper. It improves the efficiency and robustness of the algorithm and can be applied to any variant of a Differential Evolution algorithm. The proposed modification is tested on commonly used benchmark problems for unconstrained optimization and compared with other optimization methods such as Evolutionary Algorithms and Evolution Strategies.
Chapter
Modern power systems are very large, complex and widely distributed. Scarcity in energy resources, increasing power generation cost and ever-growing demand for electric energy necessitates optimal operation of power systems. Even a small reduction in production cost may lead to a large savings. Hence efficient algorithms for solving the power system scheduling are needed. New optimization methods based on evolutionary computation that abstract the principle of natural selection and genetics are employed for scheduling problems. They are easy to implement and have the capability to converge to global optimum at a relatively lesser computational effort. Differential Evolution (DE), a numerical optimization approach is simple, easy to implement, significantly faster and robust. It has been verified as a promising candidate for solving real-valued engineering optimization problems. This chapter is concerned with the applications of differential evolution and its variants for various power system scheduling problems like economic dispatch, dynamic economic dispatch and unit commitment. Different case studies have been conducted including nonlinearities such as the valve-point effects, prohibited operating zones and transmission losses. This chapter enumerates the advantages of differential evolution to determine the most economic conditions of the electric power system.
Chapter
Differential evolution (DE) and evolutionary programming (EP) are two major algorithms in evolutionary computation. They have been applied with success to many real-world numerical optimization problems. Neighborhood search (NS) is a main strategy underpinning EP.There have been analyses of different NS operators’ characteristics. Although DE might be similar to the evolutionary process in EP, it lacks the relevant concept of neighborhood search. In this chapter, DE with neighborhood search (NSDE) is proposed based on the generalization of NS strategy. The advantages of NS strategy in DE are analyzed theoretically. These analyses mainly focus on the change of search step size and population diversity after using neighborhood search. Experimental results have shown that DE with neighborhood search has significant advantages over other existing algorithms on a broad range of different benchmark functions. NSDE’s scalability is also evaluated on a number of benchmark problems, whose dimension ranges from 50 to 200.