Differential Evolution Operator Research Articles

Two-stage differential evolution with dynamic population assignment for constrained multi-objective optimization

Using infeasible information to balance objective optimization and constraint satisfaction is a very promising research direction to address constrained multi-objective problems (CMOPs) via evolutionary algorithms (EAs). The existing constrained multi-objective evolutionary algorithms (CMOEAs) still face the issue of striking a good balance when solving CMOPs with diverse characteristics. To alleviate this issue, in this paper we develop a two-stage different evolution with a dynamic population assignment strategy for CMOPs. In this approach, two cooperative populations are used to provide feasible driving forces and infeasible guiding knowledge. To adequately utilize the infeasibility information, a dynamic population assignment model is employed to determine the primary population, which is used as the parents to generate offspring. The entire search process is divided into two stages, in which the two populations work in weak and strong cooperative ways, respectively. Furthermore, multistrategy-based differential evolution operators are adopted to create aggressive offspring. The superior exploration and exploitation ability of the proposed algorithm is validated via some state-of-the-art CMOEAs over artificial benchmarks and real-world problems. The experimental results show that our proposed algorithm gained a better, or more competitive, performance than the other competitors, and it is an effective approach to balancing objective optimization and constraint satisfaction.

A hybrid estimation of distribution algorithm for solving assembly flexible job shop scheduling in a distributed environment

This paper proposes a novel distributed assembly flexible job shop scheduling problem (DAFJSP), which involves three stages: production stage, assembly stage, and delivery stage. The production stage is accomplished in a few flexible job shops, the assembly stage is accomplished in a few single-machine factories, and the delivery stage is to deliver the obtained products to the corresponding customers. To address the problem, a hybrid estimation of distribution algorithm based on differential evolution operator and variable neighborhood search (HEDA-DEV) is proposed with the goal of minimizing the total cost and tardiness. Firstly, a new multidimensional coding method is designed based on the features of the DAFJSP. Secondly, two mutation operators and the similarity coefficient based on the probability matrix are put forward to implement the dynamic mutation. Thirdly, five types of neighborhood structures satisfying cooperative search strategies are employed to adequately improve the local exploitation ability. Finally, the comparison experiment results suggest that the proposed HEDA-DEV has competitive performance compared to the selected efficient algorithms. Moreover, a real case study is used to demonstrate that HEDA-DEV is an effective method for solving DAFJSP.

Simple and General Unitarity Conserving Numerical Real-Time Propagators of the Time-Dependent Schrödinger Equation Based on Magnus Expansion.

Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. We use this property and explicit integration of Lagrange interpolation formulas for the time-dependent Hamiltonian within each time interval and derive approximations that preserve unitarity for the differential time evolution operators of general time-dependent Hamiltonians. The resulting second-order approximation is the same as using the average of Hamiltonians for two end points of time. We identify three fourth-order approximations involving commutators of Hamiltonians at different times and also derive a sixth-order expression. A test of these approximations along with other available expressions for a two-state time-dependent Hamiltonian with sinusoidal time dependences provides information on the relative performance of these approximations and suggests that the derived expressions can serve as useful numerical tools for time evolution in time-resolved spectroscopy, quantum control, quantum sensing, real-time ab initio quantum dynamics, and open system quantum dynamics.

Surrogate-assisted differential evolution using manifold learning-based sampling for high- dimensional expensive constrained optimization problems

To address the challenges of high-dimensional constrained optimization problems with expensive simulation models, a Surrogate-Assisted Differential Evolution using Manifold Learning-based Sampling (SADE-MLS) is proposed. In SADE-MLS, differential evolution operators are executed to generate numerous high-dimensional candidate points. To alleviate the curse of dimensionality, a Manifold Learning-based Sampling (MLS) mechanism is developed to explore the high-dimensional design space effectively. In MLS, the intrinsic dimensionality of the candidate points is determined by a maximum likelihood estimator. Then, the candidate points are mapped into a low-dimensional space using the dimensionality reduction technique, which can avoid significant information loss during dimensionality reduction. Thus, Kriging surrogates are constructed in the low-dimensional space to predict the responses of the mapped candidate points. The candidate points with high constrained expected improvement values are selected for global exploration. Moreover, the local search process assisted by radial basis function and differential evolution is performed to exploit the design space efficiently. Several numerical benchmarks are tested to compare SADE-MLS with other algorithms. Finally, SADE-MLS is successfully applied to a solid rocket motor multidisciplinary optimization problem and a re-entry vehicle aerodynamic optimization problem, with the total impulse and lift to drag ratio being increased by 32.7% and 35.5%, respectively. The optimization results demonstrate the practicality and effectiveness of the proposed method in real engineering practices.

Multi-objective optimization design of anti-roll torsion bar using improved beluga whale optimization algorithm

PurposeThis study aims to reduce the redundant weight of the anti-roll torsion bar brought by the traditional empirical design and improving its strength and stiffness.Design/methodology/approachBased on the finite element approach coupled with the improved beluga whale optimization (IBWO) algorithm, a collaborative optimization method is suggested to optimize the design of the anti-roll torsion bar structure and weight. The dimensions and material properties of the torsion bar were defined as random variables, and the torsion bar's mass and strength were investigated using finite elements. Then, chaotic mapping and differential evolution (DE) operators are introduced to improve the beluga whale optimization (BWO) algorithm and run case studies.FindingsThe findings demonstrate that the IBWO has superior solution set distribution uniformity, convergence speed, solution correctness and stability than the BWO. The IBWO algorithm is used to optimize the anti-roll torsion bar design. The error between the optimization and finite element simulation results was less than 1%. The weight of the optimized anti-roll torsion bar was lessened by 4%, the maximum stress was reduced by 35% and the stiffness was increased by 1.9%.Originality/valueThe study provides a methodological reference for the simulation optimization process of the lateral anti-roll torsion bar.

A New Hyper-Heuristic Multi-Objective Optimisation Approach Based on MOEA/D Framework.

A multi-objective evolutionary algorithm based on decomposition (MOEA/D) serves as a robust framework for addressing multi-objective optimization problems (MOPs). However, it is widely recognized that the applicability of a fixed offspring-generating strategy in MOEA/D can be limited, despite its foundation in the MOEA/D methodology. Consequently, hybrid algorithms have gained popularity in recent years. This study proposes a novel hyper-heuristic approach that integrates the estimation of distribution (ED) and crossover (CX) strategies into the MOEA/D framework based on the view of successful replacement rate (SSR) and attempts to explain the potential reasons for the advantages of hybrid algorithms. The proposed approach dynamically switches from the differential evolution (DE) operator to the covariance matrix adaptation evolution strategy (CMA-ES) operator. Simultaneously, certain subproblems in the neighbourhood denoted as B(i) employ the Improved Differential Evolution (IDE) operator to generate new individuals for balancing the high evaluation costs associated with CMA-ES. Numerical experiments unequivocally demonstrate that the suggested approach offers distinct advantages when applied to a three-objective test suite. These experiments also validate a significant enhancement in the efficiency (SRR) of the DE operator within this context. The perspectives and experimental findings, with a focus on the Success Rate Ratio (SRR), have the potential to provide valuable insights and inspire further research in related domains.

A non-dominated discrete differential evolution for fuel loading pattern optimization of a nuclear research reactor

Abstract This paper presents a detailed description of a new variant of differential evolution for nuclear reactor refueling optimization problem. This variant combines the elitism strategy with a discrete differential evolution. The elitism strategy allows non-dominated solutions found during the search and stored in the archive to participate in the differential evolution operation. The population size is the same as the archive size, and the number of non-dominated solutions participating in the search at a particular generation is controlled by a specific probability. The proposed method is successfully applied to a nuclear research reactor for its first refueling time to search for optimal loading patterns that both maximize the effective multiplication k eff and minimize the power peaking factor PPF of the reactor. The optimal loading patterns can significantly improve the operational time and safety of the reactor compared to the loading pattern used in practice.

An adaptive grey wolf optimization with differential evolution operator for solving the discount {0–1} knapsack problem

An adaptive grey wolf optimization with differential evolution operator for solving the discount {0–1} knapsack problem

Space division and adaptive selection strategy based differential evolution algorithm for multi-objective satellite range scheduling problem

Satellite range scheduling always plays a crucial role in tracking, telemetry, and control of the spacecraft. With the significant increase in the number and type of satellites in orbit, the demands of users for satellite range scheduling are becoming more and more diverse. However, existing studies for the satellite range scheduling problem (SRSP) rarely consider multiple optimization objectives, which is quite significant in practice. Hence, this paper investigates a multi-objective satellite range scheduling problem (MO-SRSP) that optimizes three objectives simultaneously: the overall profits of tasks, load-balance of antennas, and completion timeliness of tasks. To address MO-SRSP, this paper establishes a mathematical model on the basis of analysis of MO-SRSP and proposes a multi-objective evolutionary algorithm, which is called multi-objective differential evolution algorithm based on space division and adaptive selection strategy (MODE-SDAS). The space division strategy will uniformly divide the objective space into a set of subspaces and preserve a set of non-dominated solutions in each subspace during the environmental selection even if some of these solutions are dominated by other solutions in other subspaces, so as to maintain the diversity of the algorithm. The adaptive selection strategy will adaptively allocate computational resources to different subspaces to improve the convergence of the population. Besides, problem-specific designs such as coding and encoding methods, the discrete differential evolution operator, as well as objective-specific individual variation operators are incorporated into the algorithm to enhance the search capability. Finally, extensive experiments based on simulation test cases are carried out to verify the effectiveness and efficiency of MODE-SDAS. The comparison results show that MODE-SDAS significantly outperforms its competitors in terms of three metrics. Meanwhile, knee point analysis, sensitivity analysis, and application insights are presented.

Enhanced SparseEA for large-scale multi-objective feature selection problems

Large-scale multi-objective feature selection problems are widely existing in the fields of text classification, image processing, and biological omics. Numerous features usually mean more correlation and redundancy between features, so effective features are usually sparse. SparseEA is an evolutionary algorithm for solving Large-scale Sparse Multi-objective Optimization Problems (i.e., most decision variables of the optimal solutions are zero). It determines feature Scores by calculating the fitness of individual features, which does not reflect the correlation between features well. In this manuscript, ReliefF was used to calculate the weights of features, with unimportant features being removed first. Then combine the weights calculated by ReliefF with Scores of SparseEA to guide the evolution process. Moreover, the Scores of features remain constant throughout all runs in SparseEA. Therefore, the fitness values of excellent and poor individuals in each iteration are used to update the Scores. In addition, difference operators of Differential Evolution are introduced into SparseEA to increase the diversity of solutions and help the algorithm jump out of the local optimal solution. Comparative experiments are performed on large-scale datasets selected from scikit-feature repository. The results show that the proposed algorithm is superior to the original SparseEA and the state-of-the-art algorithms.

Multiobjective optimization algorithm with dynamic operator selection for feature selection in high-dimensional classification

Feature selection (FS) is an important technique in data preprocessing that aims to reduce the number of features for training while maintaining a high accuracy for classification. In recent studies, FS has been extended to optimize multiple objectives simultaneously in classification. To better solve this problem, this paper proposes a new multiobjective optimization algorithm with dynamic operator selection for feature selection in high-dimensional classification, called FS-DOS. First, two complementary search operators with different characteristics are designed, where the first operator is a quick search (QS) operator aiming to accelerate the convergence speed, and the other operator is a modified binary differential evolution (BDE) operator that can prevent the algorithm from falling into a local optimum. In addition, a dynamic selection strategy based on the idea of resource allocation is also designed to dynamically select the most suitable operator for each solution according to its corresponding performance improvement on aggregated objective values. The simulation results on fifteen different real-world high-dimensional FS datasets show that FS-DOS can obtain a feature subset with higher quality than several state-of-the-art FS algorithms. Importantly, in terms of error rate, FS-DOS wins 55 out of 75 comparisons. In terms of dimensionality reduction, the number of features selected by FS-DOS is between one hundredth and one thousandth of the original dataset.

Realizing the Improvement of the Reliability and Efficiency of Intelligent Electricity Inspection: IAOA-BP Algorithm for Anomaly Detection

Anomaly detection can improve the service level of the grid, effectively save human resources and reduce the operating cost of a power company. In this study, an improved arithmetic optimization-backpropagation (IAOA-BP) neural algorithm for an anomaly detection model was proposed for electricity inspection. The dynamic boundary strategy of the cosine control factor and the differential evolution operator are introduced into the arithmetic optimization algorithm (AOA) to obtain the improved arithmetic optimization algorithm (IAOA). The algorithm performance test proves that the IAOA has better solving ability and stability compared with the AOA, WOA, SCA, SOA and SSA. The IAOA was subsequently used to obtain the optimal weights and thresholds for BP. In the experimental phase, the proposed model is validated with electricity data provided by a power company. The results reveal that the overall determination accuracy using the IAOA-BP algorithm remains above 96%, and compared with other algorithms, the IAOA-BP has a higher accuracy and can meet the requirements grid supervision. The power load data anomaly detection model proposed in this study has some implications that might suggest how power companies can promote grid business model transformation, improve economic efficiency, enhance management and improve service quality.

Cooperative Global Path Planning for Multiple Unmanned Aerial Vehicles Based on Improved Fireworks Algorithm Using Differential Evolution Operation

Cooperative Global Path Planning for Multiple Unmanned Aerial Vehicles Based on Improved Fireworks Algorithm Using Differential Evolution Operation

Performance Analysis of Multi-Objective Simulated Annealing Based on Decomposition

Simulated annealing is a metaheuristic that balances exploration and exploitation to solve global optimization problems. However, to deal with multi- and many-objective optimization problems, this balance needs to be improved due to diverse factors such as the number of objectives. To deal with this issue, this work proposes MOSA/D, a hybrid framework for multi-objective simulated annealing based on decomposition and evolutionary perturbation functions. According to the literature, the decomposition strategy allows diversity in a population while evolutionary perturbations add convergence toward the Pareto front; however, a question should be asked: What is the effect of such components when included as part of a multi-objective simulated annealing design? Hence, this work studies the performance of the MOSA/D framework considering in its implementation two widely used perturbation operators: classical genetic operators and differential evolution. The proposed algorithms are MOSA/D-CGO, based on classical genetic operators, and MOSA/D-DE, based on differential evolution operators. The main contribution of this work is the performance analysis of MOSA/D using both perturbation operators and identifying the one most suitable for the framework. The approaches were tested using DTLZ on two and three objectives and CEC2009 benchmarks on two, three, five, and ten objectives; the performance analysis considered diversity and convergence measured through the hypervolume (HV) and inverted generational distance (IGD) indicators. The results pointed out that there is a promising improvement in performance in favor of MOSA/D-DE.

Adaptive cylinder vector particle swarm optimization with differential evolution for UAV path planning

Particle swarm optimization (PSO) algorithm has a potential to solve route planning problem for unmanned aerial vehicle (UAV). However, the traditional PSO algorithm is easy to fall into local optimum under the complicated environments with multiple threats. In order to improve the performance in different complicated environments, a novel and effective PSO algorithm with adaptive adjustment of the parameters, cylinder vector and different evolution operator, named ACVDEPSO, is proposed and demonstrated to be effective for route planning problem for UAV. In the proposed ACVDEPSO, the velocity of the particle is converted to its cylinder vector for the convenience of the path search. It is worth highlighting that the parameters of ACVDEPSO algorithm are automatically chosen by the time and the fitness values of the particles. Furthermore, a challenger based on differential evolution operator is introduced to reduce the probability of falling into local optimum and accelerate the algorithm convergence speed. The simulation experiments have been conducted in real digital elevation model (DEM) maps to test the performance of the ACVDEPSO. The experiment results validate that the optimization performance of the ACVDEPSO outperforms the other comparison methods, which can efficiently generate a higher quality path for UAV under the complicated 3D environments.

Evolutionary competitive multitasking optimization via improved adaptive differential evolution

Competitive multitasking optimization (CMTO) is a special multitasking optimization paradigm that has been recently proposed. In the CMTO problems, the objective values of all tasks are competitive, and the purpose of CMTO is to find an optimal solution for multiple tasks. However, existing algorithms designed for the CMTO problems perform poorly since their resource allocation strategies are prone to incorrect task selection. To remedy this drawback, this paper proposes an improved multitasking adaptive differential evolution, which can be featured as: (i) a success-history based resource allocation strategy is proposed; (ii) an adaptive random mating probability control strategy is devised to adapt to different task combinations; (iii) an adaptive multitasking differential evolution operator is designed to enhance the searchability. To evaluate the performance of the proposed method, three CMTO benchmark test suites and two real-world optimization problems are chosen. Compared with other related methods, the results show that the proposed method achieved better performance empirically.

An Improved Whale Optimizer with Multiple Strategies for Intelligent Prediction of Talent Stability

Talent resources are a primary resource and an important driving force for economic and social development. At present, researchers have conducted studies on talent introduction, but there is a paucity of research work on the stability of talent introduction. This paper presents the first study on talent stability in higher education, aiming to design an intelligent prediction model for talent stability in higher education using a kernel extreme learning machine (KELM) and proposing a differential evolution crisscross whale optimization algorithm (DECCWOA) for optimizing the model parameters. By introducing the crossover operator, the exchange of information regarding individuals is facilitated and the problem of dimensional lag is improved. Differential evolution operation is performed in a certain period of time to perturb the population by using the differences in individuals to ensure the diversity of the population. Furthermore, 35 benchmark functions of 23 baseline functions and CEC2014 were selected for comparison experiments in order to demonstrate the optimization performance of the DECCWOA. It is shown that the DECCWOA can achieve high accuracy and fast convergence in solving both unimodal and multimodal functions. In addition, the DECCWOA is combined with KELM and feature selection (DECCWOA-KELM-FS) to achieve efficient talent stability intelligence prediction for universities or colleges in Wenzhou. The results show that the performance of the proposed model outperforms other comparative algorithms. This study proposes a DECCWOA optimizer and constructs an intelligent prediction of talent stability system. The designed system can be used as a reliable method of predicting talent mobility in higher education.

Multistrategy Integrated Marine Predator Algorithm Applied to 3D Surface WSN Coverage Optimization

Achieving maximum network coverage with a limited number of sensor nodes is key to node deployment of wireless sensor network (WSN). This paper proposes an improved marine predator algorithm (IMPA) for 3D surface wireless sensor network deployment. A population evolution strategy based on random opposition-based learning and differential evolution operator is proposed to enrich the population diversity and improve the global search capability of the algorithm. The grouping idea of the Shuffled Frog Leaping Algorithm (SFLA) is then introduced. A local search strategy based on the SFLA is proposed to replace the FADs effect of MPA and enhance the ability of the algorithm to escape from the local optimum. A quasireflected opposition-based learning strategy is also presented to improve the optimization accuracy, accelerate the convergence speed of the algorithm, and improve the quality of the solution. Fifteen benchmark functions are selected for testing. The results are compared with seven different algorithms. The results show that the improved algorithm has excellent optimization performances. Finally, the IMPA is applied to optimize WSN coverage on 3D surfaces. The experimental results show that the proposed IMPA has good terrain adaptation and optimal deployment capabilities. It can improve the coverage of the network, reduce the deployment cost, and extend the network life cycle.

Fault feature extraction for planetary bearing of CRF pump in nuclear power plant based on TFDC-QPSO-optimised MOMEDA

To address the issue of weak fault features and difficulty in feature extraction for planetary gearbox bearings of the circulation water pump (CRF pump) unit in the conventional island of a nuclear power plant, a deconvolution method, named the multipoint optimal minimum entropy deconvolution adjusted (MOMEDA), is optimised by a mixing operator improved quantum behaviour particle swarm optimisation (QPSO) algorithm, to extract the periodic fault impulse of planetary gearbox bearings. In the mixing operator, a differential evolution operator is introduced to improve particle swarms’ diversity and enhance the algorithm’s global optimisation capability. Meanwhile, a proposed adaptive CrossOver operator is incorporated into the algorithm to increase its convergence speed. Then, combining these two types of operators can construct a parameter optimisation algorithm displaying both global optimisation capability and high algorithm execution efficiency. Consider capturing the periodic impulsive features relating to bearing faults. A fitness function based on the characteristic information of the deconvolution signal in the time and frequency domain is proposed. This function serves as the objective function to facilitate the parameter optimisation on MOMEDA. Thereby, it enhances the optimisation capability of our feature extraction method. Experiments were conducted by adopting the proposed method on the signals collected from the inner- and outer-race faulty planetary bearing in a test bed, in which favourable feature extraction results are obtained. After the comparative analysis, we observed that both significances of features extracted by this method and the execution efficiency of the algorithm are superior compared to other methods. The on-site feature extraction results of the input shaft bearing in the planetary gearbox of a CRF pump unit in a nuclear power plant also demonstrated the engineering practicability of the method proposed in this work.

An enhanced decomposition-based multi-objective evolutionary algorithm with a self-organizing collaborative scheme

The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multi-objective optimization problem (MOP) into multiple single-objective subproblems using an aggregation function and optimizes them together using a collaborative approach. MOEA/D exhibits extraordinary optimization ability in solving MOPs. However, the algorithm’s performance is hampered by the single evolutionary operator, fixed control parameters, and fixed neighborhood architecture used in primal MOEA/D. To obtain the balance between convergence and diversity, a self-organizing collaborative scheme (SCS) is designed to achieve the best combination of differential evolution (DE) operator, control parameters, and neighborhood size in this paper. The SCS is integrated into MOEA/D to form the MOEA/D-SCS. In MOEA/D-SCS, firstly, the evolutionary process is separated into three stages: early, middle, and late, and different indicators are utilized to screen elite and inferior solutions for the early and late stages. Secondly, different evolutionary strategies are developed for the three stages and the various types of solutions to help boost the algorithm’s efficiency. Then, to enhance convergence and diversity in different evolutionary stages, a neighborhood reconstruction strategy is proposed to assign different neighborhood sizes according to the neighborhood information. Finally, the capability of MOEA/D-SCS was tested using three standard test suites, ZDT, DTLZ, and UF, and a MOP of sewage treatment. The simulation results demonstrate that the proposed MOEA/D-SCS can achieve better optimization results and show stronger optimization ability in most cases compared to state-of-the-art evolutionary algorithms, such as MOEA/D-DE, MOEA/D-STM, MOEA/D-FRRMAB, MOEA/D-DRA, NSGA-II, and dMOPSO, especially in problems with multiple peaks, complex Pareto fronts, and practical engineering optimization problems.