Ranking-based Mutation Operator Research Articles

An Enhanced Symmetric Sand Cat Swarm Optimization with Multiple Strategies for Adaptive Infinite Impulse Response System Identification

An infinite impulse response (IIR) system might comprise a multimodal error surface and accurately discovering the appropriate filter parameters for system modeling remains complicated. The swarm intelligence algorithms facilitate the IIR filter’s parameters by exploring parameter domains and exploiting acceptable filter sets. This paper presents an enhanced symmetric sand cat swarm optimization with multiple strategies (MSSCSO) to achieve adaptive IIR system identification. The principal objective is to recognize the most appropriate regulating coefficients and to minimize the mean square error (MSE) between an unidentified system’s input and the IIR filter’s output. The MSSCSO with symmetric cooperative swarms integrates the ranking-based mutation operator, elite opposition-based learning strategy, and simplex method to capture supplementary advantages, disrupt regional extreme solutions, and identify the finest potential solutions. The MSSCSO not only receives extensive exploration and exploitation to refrain from precocious convergence and foster computational efficiency; it also endures robustness and reliability to facilitate demographic variability and elevate estimation precision. The experimental results manifest that the practicality and feasibility of the MSSCSO are superior to those of other methods in terms of convergence speed, calculation precision, detection efficiency, regulating coefficients, and MSE fitness value.

Training Feedforward Neural Networks Using an Enhanced Marine Predators Algorithm

The input layer, hidden layer, and output layer are three models of the neural processors that make up feedforward neural networks (FNNs). Evolutionary algorithms have been extensively employed in training FNNs, which can correctly actualize any finite training sample set. In this paper, an enhanced marine predators algorithm (MPA) based on the ranking-based mutation operator (EMPA) was presented to train FNNs, and the objective was to attain the minimum classification, prediction, and approximation errors by modifying the connection weight and deviation value. The ranking-based mutation operator not only determines the best search agent and elevates the exploitation ability, but it also delays premature convergence and accelerates the optimization process. The EMPA integrates exploration and exploitation to mitigate search stagnation, and it has sufficient stability and flexibility to acquire the finest solution. To assess the significance and stability of the EMPA, a series of experiments on seventeen distinct datasets from the machine learning repository of the University of California Irvine (UCI) were utilized. The experimental results demonstrated that the EMPA has a quicker convergence speed, greater calculation accuracy, higher classification rate, strong stability and robustness, which is productive and reliable for training FNNs.

Nature-inspired approach: An enhanced whale optimization algorithm for global optimization

The whale optimization algorithm is based on the bubble-net attacking behavior of humpback whales and simulates encircling prey, bubble-net attacking and searching for prey to obtain the global optimal solution. However, the basic whale optimization algorithm has the disadvantage of search stagnation, easily falls into a local optimum, has slow convergence speed and has low calculation accuracy. The Lévy flight strategy is beneficial for expanding the search range and prevents the algorithm from falling into a local optimum, which enhances the global search ability. The ranking-based mutation operator can increase the selection probability and accelerate the convergence speed to enhance the local search ability. To overcome these shortcomings and avoid premature convergence, the Lévy flight strategy and the ranking-based mutation operator are added to the whale optimization algorithm. In this paper, an enhanced whale optimization algorithm is proposed, which realizes complementary advantages to balance exploration and exploitation. Eighteen benchmark test functions and five structural engineering design problems are used to verify the robustness and overall optimization performance of the enhanced whale optimization algorithm. The experimental results show that the enhanced whale optimization algorithm is an effective and feasible method that has a fast convergence speed, high calculation accuracy, strong robustness and stability.

Differential evolution algorithm with fitness and diversity ranking-based mutation operator

Abstract Differential evolution (DE) is a simple and efficient global optimization algorithm. Benefitting from its concise structure and strong search ability, DE has been widely used in various fields. Generally, the convergence performance of DE largely depends on its mutation operation. Meanwhile, individuals’ positions, which are selected as base vectors or making up difference vectors, are very important in mutation strategy. In this paper, we propose a differential evolution algorithm with both fitness and diversity ranking-based mutation operator (FDDE). Different from methods that use fitness as the only index to measure the quality of individuals, FDDE aims to assign suitable position for each individual in the mutation strategy by together considering both individuals’ fitness and their diversity contribution. Firstly, a new method of estimating the individual diversity by fitness values has been proposed. Then, each individual's fitness ranking and diversity contribution are considered together to calculate a newly defined individual's final ranking. Finally, the final ranking are used in the mutation strategy. The newly improved mutation operator could be integrated with any classical or advanced DE variants with little additional time or space complexity. The proposed FDDE is compared with some DE variants based on numerical experiments over the CEC (Congress on Evolutionary Computation) 2005 benchmark sets, CEC 2013 benchmark sets and CEC 2014 benchmark sets. Experimental results clearly indicate that FDDE performs better on most test functions and improves the convergence performance of its competitors of jDE, rank-jDE, advanced SHADE, rank-SHADE and L -SHADE in both low and high dimensional problems.

Modified water wave optimization algorithm for underwater multilevel thresholding image segmentation

Multilevel thresholding is a simple and important method for image segmentation in various applications that has drawn widespread attention in recent years. However, the computational complexity increases correspondingly when the threshold levels increase. To overcome this drawback, a modified water wave optimization (MWWO) algorithm with the elite opposition-based learning strategy and the ranking-based mutation operator for underwater image segmentation is proposed in this paper. The elite opposition-based learning strategy increases the diversity of the population and prevents the search from stagnating to improve the calculation accuracy. The ranking-based mutation operator increases the selection probability. MWWO can effectively balance exploration and exploitation to obtain the optimal solution in the search space. To objectively evaluate the overall performance of the proposed algorithm, MWWO is compared with six state-of-the-art meta-heuristic algorithms by maximizing the fitness value of Kapur’s entropy method to obtain the optimal threshold through experiments on ten test images. The fitness value, the best threshold values, the execution time, the peak signal to noise ratio (PSNR), the structure similarity index (SSIM), and the Wilcoxon’s rank-sum test are used as important metrics to evaluate the segmentation effect of underwater images. The experimental results show that MWWO has a better segmentation effect and stronger robustness compared with other algorithms and an effective and feasible method for solving underwater multilevel thresholding image segmentation.

Multi-Objective Optimization Design of a Modular Linear Permanent-Magnet Vernier Machine by Combined Approximation Models and Differential Evolution

In this article, a modular linear permanent-magnet (PM) vernier machine is presented and optimized for high-precision and safety-critical direct-drive applications. The novelty of this article is to not only propose a multi-objective optimization method, but also present a modular linear PM vernier machine. The presented machine has the merit of desired fault-tolerant capability and improved force performances by mainly adopting the modular mover structure. And, the design principle of modular mover structure is introduced in detail in this article. To realize low detent force, high thrust force, low force ripple, and good fault tolerance, modular mover structure, PM array with flux-intensifying effect and six-phase structure are adopted in machine design. Furthermore, a new multi-objective optimization method is proposed to obtain a set of tradeoff solutions among multiple optimization objectives in machine optimization. First, to decompose the high dimension design space, the design variables are stratified into nonsensitive and sensitive levels by utilizing a comprehensive sensitivity analysis. Second, combined approximation models are implemented to decrease the large amount of computations. Then, to enhance the efficiencies of two multi-objective optimization processes, multi-objective differential evolution algorithm with ranking-based mutation operator is employed. After the optimization by the proposed multi-objective optimization method, the desired comprehensive performances with high optimization efficiency and accuracy can be obtained. Finally, to verify the results of theoretical analysis, a prototype machine is fabricated.

Modified Whale Optimization Algorithm for Infinitive Impulse Response System Identification

System identification based on infinite impulse response (IIR) models has received much attention because it is used in a variety of real-world applications. However, an IIR model might have a multimodal error surface. To attain an ideal identification, an efficient and robust method is necessary. In this study, a modified whale optimization algorithm (WOA) with a ranking-based mutation operator, called the RWOA, is presented to solve the IIR system identification problem. The RWOA integrates a ranking-based mutation operator into the basic WOA to enhance performance by speeding up the convergence rate and then enhances the exploitation capability. The experimental results of actual and reduced-order identification for a standard system using our proposed RWOA were superior to those of five state-of-the-art algorithms (including the basic WOA), in terms of improving the quality and stability of the results, in most cases, and significantly speeding up convergence.

Multiobjective Optimization of a Double-Side Linear Vernier PM Motor Using Response Surface Method and Differential Evolution

This paper designs a double-side linear vernier permanent-magnet motor, which incorporates the merits of high thrust force capability, high power factor, and high efficiency. Since the parameters of the motor are very sensitive and the high thrust force capability comes along with the high force ripple, a framework of multiobjective optimization is proposed to improve the overall motor performances. The sensitivity analysis is used to select significant variables and the multiobjective differential evolution with ranking-based mutation operator is conducted with the response surface models to generate the Pareto solution set. The electromagnetic performances of the optimal motor are compared with the initial motor by simulating step by step based on finite-element analysis. Finally, a prototype motor is manufactured and the experimental results validate the improved motor performances.

Dynamic Optimization of the Tandem Acetylene Hydrogenation Process

In ethylene production units, the acetylene side product is converted into additional C2H4 over a palladium–carbon fixed bed reactor, in which the catalyst activity is affected by the formation of green oil impurities. We determined the optimal dynamic operating conditions for two reactors in series undergoing catalyst deactivation while maintaining the selectivity and conversion rate. The optimal switching periods for the reactors were investigated with dynamic optimization of the hydrogen input and inlet temperature with the incremental feature. Control vector parametrization was used to transform this dynamic problem into a finite-dimensional nonlinear programming problem. An incremental-encoding differential evolution with constraint ranking-based mutation operator (IEDE-CRMO) was proposed based on the reaction selectivity and catalyst activity variation to meet certain requirements of the control variables and to solve a complex industrial process. The IEDE-CRMO method was applied in an industrial C2...

Solving chemical dynamic optimization problems with ranking-based differential evolution algorithms

Dynamic optimization problems (DOPs) described by differential equations are often encountered in chemical engineering. Deterministic techniques based on mathematic programming become invalid when the models are non-differentiable or explicit mathematical descriptions do not exist. Recently, evolutionary algorithms are gaining popularity for DOPs as they can be used as robust alternatives when the deterministic techniques are invalid. In this article, a technology named ranking-based mutation operator (RMO) is presented to enhance the previous differential evolution (DE) algorithms to solve DOPs using control vector parameterization. In the RMO, better individuals have higher probabilities to produce offspring, which is helpful for the performance enhancement of DE algorithms. Three DE-RMO algorithms are designed by incorporating the RMO. The three DE-RMO algorithms and their three original DE algorithms are applied to solve four constrained DOPs from the literature. Our simulation results indicate that DE-RMO algorithms exhibit better performance than previous non-ranking DE algorithms and other four evolutionary algorithms.

Multi-objective differential evolution with ranking-based mutation operator and its application in chemical process optimization

Dynamic optimization problems in chemical processes are often quite challenging because these problems often involve multiple and conflicting objectives. To solve the multi-objective dynamic optimization problems (MDOPs), in this paper, we propose a new multi-objective differential evolution (MODE) variant, named MODE-RMO for short, inspired by the phenomenon that good individuals which contain good information often have more chance to be utilized to guide other individuals. In MODE-RMO, the ranking-based mutation operator is integrated into the MODE algorithm to accelerate the convergence speed, and thus enhance the performance. The performance of our proposed algorithm is firstly evaluated in ten test functions and compared with other MOEAs. The results demonstrate that MODE-RMO can generate Pareto optimal fronts with satisfactory convergence and diversity. Finally, MODE-RMO is applied to solve three MDOPs taken from literature using control vector parameterization. The obtained results indicate that MODE-RMO is an effective and efficient approach for MDOPs.

Engineering optimization by means of an improved constrained differential evolution

To efficiently optimize the constrained engineering problems, in this paper, an improved constrained differential evolution (DE) method is proposed, where two improvements are presented. Firstly, to make the DE algorithm converge faster, a ranking-based mutation operator that is suitable to the constrained optimization problems is presented. Secondly, an improved dynamic diversity mechanism is proposed to maintain either infeasible or feasible solutions in the population. Combining the two improvements with the DE algorithm, the proposal is referred to as rank-iMDDE, for short. To evaluate the performance of rank-iMDDE, 24 benchmark functions presented in CEC’2006 are selected as the test suite. Moreover, five widely used constrained engineering benchmark problems and four constrained mechanical design problems from the literature are chosen to test the capability of rank-iMDDE for the engineering problems. Experimental results indicate that rank-iMDDE is able to improve the performance of DE in terms of the quality of the final solutions, the convergence rate, and the successful rate. Additionally, it can provide fairly-competitive results compared with other state-of-the-art evolutionary algorithms in both benchmark functions and engineering problems.

Accelerating parameter identification of proton exchange membrane fuel cell model with ranking-based differential evolution

Parameter identification of PEM (proton exchange membrane) fuel cell model is a very active area of research. Generally, it can be treated as a numerical optimization problem with complex nonlinear and multi-variable features. DE (differential evolution), which has been successfully used in various fields, is a simple yet efficient evolutionary algorithm for global numerical optimization. In this paper, with the objective of accelerating the process of parameter identification of PEM fuel cell models and reducing the necessary computational efforts, we firstly present a generic and simple ranking-based mutation operator for the DE algorithm. Then, the ranking-based mutation operator is incorporated into five highly-competitive DE variants to solve the PEM fuel cell model parameter identification problems. The main contributions of this work are the proposed ranking-based DE variants and their application to the parameter identification problems of PEM fuel cell models. Experiments have been conducted by using both the simulated voltage–current data and the data obtained from the literature to validate the performance of our approach. The results indicate that the ranking-based DE methods provide better results with respect to the solution quality, the convergence rate, and the success rate compared with their corresponding original DE methods. In addition, the voltage–current characteristics obtained by our approach are in good agreement with the original voltage–current curves in all cases.