Composite Differential Evolution Research Articles

A novel solution to optimal power flow problems using composite differential evolution integrating effective constrained handling techniques

Optimal power flow is a complex and highly non-linear problem in which steady-state parameters are needed to find a network’s efficient and economical operation. In addition, the difficulty of the Optimal power flow problem becomes enlarged when new constraints are added, and it is also a challenging task for the power system operator to solve the constrained Optimal power flow problems efficiently. Therefore, this paper presents a constrained composite differential evolution optimization algorithm to search for the optimum solution to Optimal power flow problems. In the last few decades, numerous evolutionary algorithm implementations have emerged due to their superiority in solving Optimal power flow problems while considering various objectives such as cost, emission, power loss, etc. evolutionary algorithms effectively explore the solution space unconstrainedly, often employing the static penalty function approach to address the constraints and find solutions for constrained Optimal power flow problems. It is a drawback that combining evolutionary algorithms and the penalty function approach requires several penalty parameters to search the feasible space and discard the infeasible solutions. The proposed a constrained composite differential evolution algorithm combines two effective constraint handling techniques, such as feasibility rule and ɛ constraint methods, to search in the feasible space. The proposed approaches are recognized on IEEE 30, 57, and 118-bus standard test systems considering 16 study events of single and multi-objective optimization functions. Ultimately, simulation results are examined and compared with the many recently published techniques of Optimal power flow solutions owing to show the usefulness and performance of the proposed a constrained composite differential evolution algorithm.

Improving effort-aware defect prediction by directly learning to rank software modules

Effort-Aware Defect Prediction (EADP) ranks software modules according to the defect density of software modules, which allows testers to find more bugs while reviewing a certain amount of Lines Of Code (LOC). Most existing methods regard the EADP task as a regression or classification problem. Optimizing the regression loss or classification accuracy might result in poor effort-aware performance. Therefore, we propose a method called EALTR to improve the EADP performance by directly maximizing the Proportion of the found Bugs ([email protected]%) value when inspecting the top 20% LOC. EALTR uses the linear regression model to build the EADP model, and then employs the composite differential evolution algorithm to generate a set of coefficient vectors for the linear regression model. Finally, EALTR selects the coefficient vector that achieves the highest [email protected]% value on the training dataset to construct the EADP model. To further reduce the Initial False Alarms (IFA) value of EALTR, we propose a re-ranking strategy in the prediction phase. Our experimental results on eleven project datasets with 41 releases show that EALTR can find 15.97%–54.47% more bugs than the baseline methods whose IFA values are less than 10 and the re-ranking strategy significantly reduces the IFA value by 21.24%. Our study verifies the effectiveness of directly optimizing the effort-aware metric (i.e., [email protected]%) to build the EADP model. EALTR is recommended as an effective EADP method, since it can help software testers find more bugs.

A Hybrid Composite Differential Evolution and Multiobjective Particle Swarm Optimization Evolutionary Algorithm and Its Application

A Hybrid Composite Differential Evolution and Multiobjective Particle Swarm Optimization Evolutionary Algorithm and Its Application

Flexible resource dynamic aggregation regulation method of virtual power plant to ensure more renewable energy generation

The development of large-scale sustainable energy has affected the security of electricity systems. Virtual power plant (VPP) realize multi-energy synergistic complementation and efficient operation mainly with electricity. The paper proposed a flexible resource dynamic aggregation regulation method of VPP to ensure more renewable energy generation, which enables the efficient operation of multiple energy sources with electricity as the main source through collaborative and complementary measures. Firstly, the operating mode of VPP under market mechanisms is proposed, and the operating mechanism for VPP's participation in the market is established. Secondly, the types of flexible resources are identified, a cooperative game relationship between multiple autonomous agents within the power grid and VPP is formed to support an intelligent control method for VPP considering the complementarity of multiple energy sources and carbon emissions. Finally, a novel inverse cotangent compound differential evolution (NICCDE) algorithm is proposed by combining the innovative composite differential evolution algorithm with the tangent function, which realizes the flexible synergistic utilization of multiple energy sources. and reduces the training cost of the algorithm. Case studies from the conducted case study demonstrate the significant cost reduction achieved by the proposed method in comparison to conventional approaches when applied to VPP. Moreover, the utilization of this method enhances the precision and comprehensiveness of the search outcomes, thereby augmenting the overall effectiveness of the VPP system.

An adaptive tradeoff evolutionary algorithm with composite differential evolution for constrained multi-objective optimization

Convergence, diversity, and feasibility are crucial factors in solving constrained multi-objective optimization problems (CMOPs). Their imbalance can result in the algorithm failing to converge well to the Pareto front, especially when dealing with complex CMOPs. To address this issue, we propose an adaptive tradeoff evolutionary algorithm (ATEA), which can adjust the environment selection strategy based on the characteristics of problem, aiming to achieve a balance between convergence and diversity while ensuring feasibility of the population. The ATEA divides the search process into three phases: In the extended exploration phase, a global search is conducted using a guided constraint relaxation technique to enable the population to quickly traverse the infeasible region and approach the feasible region. In the tradeoff exploration phase, constraints are further detected and estimated to retain more feasible individuals and competing infeasible individuals, allowing the population to accurately identify all possible feasible regions and gradually expand towards the feasible boundary. The exploitation phase explores under-explored regions in the earlier phases with the aim of accelerating the convergence of the population and escaping from the local optima. Extensive experiments conducted on four benchmark test suites demonstrate that ATEA exhibits superior performance in three benchmark test suites compared with six other state-of-the-art algorithms.

Reinforcement learning-based composite differential evolution for integrated demand response scheme in industrial microgrids

The fourth industrial revolution is being propelled by the “Energy Internet,” which aims to encourage the integration of industrial multi-energy microgrids (MEMG) and renewable energy sources. The conventional demand response (DR) schemes only utilize a single energy source, which limits the industrial users (IUs) and prevents them from making full use of the demand side's communication capabilities. However, smart industrial multi-energy microgrids (MEMGs) give IUs additional options for meeting their energy needs by integrating diverse energy sources, including electricity, natural gas, and thermal power. This new approach to DR programs is known as “Integrated Demand Response” (IDR). This research work proposes a smart IDR program for a novel grid-connected industrial MEMG framework consisting of exhaust air wind turbines, concentrated photovoltaic-thermal panels, an electrical energy storage system (EES), a thermal energy storage (TES), a diesel generator, an indirect customer-to-customer energy trading platform, and typical electrical and thermal industrial loads. The proposed smart IDR considers the uncertainties of both wind and solar power generation and the buying and selling costs of electrical and thermal energy to automatically reduce the industry's total power consumption and battery EES degradation costs. A novel State-Action-Reward-State-Action (SARSA)-based composite different evolution (DE) method is proposed to solve a complex scenario-based non-convex optimization problem. It uses two selection strategies, three mutation strategies, and a positive feedback mechanism to change the states of the individuals. The strategies are coupled in pairs, resulting in a total of six distinct actions that may be performed by the SARSA agents. This allows an individual to not get stuck at a local optimum and adaptively benefit from all the mutation and parameter selection methods. Moreover, SARSA has introduced two more factors, the discount factor and the learning rate, which further improve the optimization performance. The proposed method is also compared with five other state-of-the-art methods to prove its effectiveness in minimizing industrial energy bills and battery degradation costs. The simulated results confirmed that the proposed SARSA-based composite DE algorithm has achieved the lowest total energy cost and battery degradation costs when compared with other state-of-the-art algorithms.

Synthesis of Low Sidelobe Pattern with Enhanced Axial Radiation for Sparse Conformal Arrays Based on MCDE Algorithm

A hybrid optimization method for the synthesis of a sparse conformal array with the verification of a truncated cone antenna array is proposed in this manuscript. This array synthesis is studied aiming at enhancing axial radiation and reducing the peak sidelobe level (PSLL) by figuring out the optimal antenna element arrangement and corresponding feeding scheme. A multi-agent composite differential evolution (MCDE) algorithm is established by integrating a multi-agent system (MAS) with a differential evolution (DE) algorithm. In addition, a hybrid strategy method and a time-varying weighting factor are added to the mutation operator to accelerate convergence. Two examples of 64-element and 900-element truncated cone antenna arrays were synthesized. After forming a sparse antenna array out of the original full array, the number of antennas was decreased to 80% and 56.8%, respectively. The results show that the main beam of the sparse conformal antenna array is accurately fixed to the axial direction with the PSLL less than −20 dB at both the φ = 0° and φ = 90° planes, which proves the effectiveness of this method in conformal sparse array synthesis.

Speeding up Composite Differential Evolution for structural optimization using neural networks

ABSTRACT Composite Differential Evolution (CoDE) is categorized as a (µ + λ)-Evolutionary Algorithm where each parent produces three trials. Thanks to that, the CoDE algorithm has a strong search capacity. However, the production of many offspring increases the computation cost of fitness evaluation. To overcome this problem, neural networks, a powerful machine learning algorithm, are used as surrogate models for rapidly evaluating the fitness of candidates, thereby speeding up the CoDE algorithm. More specifically, in the first phase, the CoDE algorithm is implemented as usual, but the fitnesses of produced candidates are saved to the database. Once a sufficient amount of data has been collected, a neural network is developed to predict the constraint violation degree of candidates. Offspring produced later will be evaluated using the trained neural network and only the best among them is compared with its parent by exact fitness evaluation. In this way, the number of exact fitness evaluations is significantly reduced. The proposed method is applied for three benchmark problems of 10-bar truss, 25-bar truss, and 72-bar truss. The results show that the proposed method reduces the computation cost by approximately 60%.

Adaptive Range Composite Differential Evolution for Fast Optimal Reactive Power Dispatch

This paper proposes a novel adaptive range composite differential evolution (ARCoDE) algorithm to efficiently and accurately solve optimal reactive power dispatch (ORPD) problem. Because of a novel adaptive range strategy for control parameters, the proposed ARCoDE possesses superior exploration and exploitation capabilities that can efficiently handle the ORPD problem involving complicated constraints and discrete and continuous variables. This has been demonstrated in case studies using the IEEE optimal power flow testbeds considering complex wind and demand scenarios. The superior performance of ARCoDE has been further validated through comparisons with several award-winning algorithms in 2014 IEEE Competition on “Application of Modern Heuristic Optimization Algorithms for Solving Optimal Power Flow Problems”, given limited iterations of in evolutionary optimization process.

Solution to economic load dispatch using quasi-oppositional based CoDE by considering transmission line losses

The main objective of economic dispatch problem is to optimally allocate the load demand among the generating stations such that there is decrease in production cost of the power generation. In the present paper, a quasi-oppositional based composite differential evolution (QOCoDE) technique is proposed to economic load dispatch (ELD) problem. The suggested method provides optimal solutions by combining various strategies in generating trial vector with suitable control parameter settings. The proposed technique is applied on various generating units by considering fixed boundary conditions and transmission losses. The obtained results are compared with various evolutionary algorithms. The results demonstrate the capability of QOCoDE to provide optimal solutions when compared to other evolutionary techniques.

Nickel Foam Surface Defect Identification Based on Improved Probability Extreme Learning Machine

Background: In the nickel foam production process, the detection and identification of surface defects relies heavily upon the operators’ experiences. However, the manual observation is of high labor intensity, low efficiency, strong subjectivity and high error rate. Objective: Therefore, this paper proposes a new method for the nickel foam surface defect detection and identification, based on an improved probability extreme learning machine. Methods: At first, a machine vision system for nickel foam is established, and gray level cooccurrence matrix is used to calculate defect features, which are inputted into extreme learning machine to train the defect classifier. Then a composite differential evolution algorithm is used to optimize the input weights and hidden layer thresholds. Finally, an integrated probabilistic ELM is proposed to avoid misjudgments when multiple probabilities values are almost identical. Conclusion: Experiments show that the proposed method can achieve a defect-identifying accuracy, which meets an enterprise’s needs.

Constrained Composite Differential Evolution Search for Optimal Site and Size of Distributed Generation Along with Reconfiguration in Radial Distribution Network

This paper proposed a novel method to find the Optimal Feeder Reconfiguration (OFR) of radial distribution network along with optimal site and size of Distributed Generation (DG) with an objective of power loss reduction. OFR and DG allocation problems are highly non-linear and complex optimization problems, complexity of problem is further increased with the addition of distribution operation constraints. In the last two decades, Evolutionary Algorithms (EAs) have been implemented successfully to find the OFR and DG allocation considering different objective functions. However, search space adopted by EAs are unconstrained, therefore numerous methodologies are adapted to discard infeasible solutions. The penalty approach is most widely used in the literature, it requires appropriate selection of penalty parameters using a tedious trial and error method. In this paper, a new EA Constrained Composite Differential Evolution (C2oDE) is proposed find optimal capacity and site of DG along with reconfiguration problem. In the proposed algorithms three trial vectors are generated to strike balance among exploration and exploitation. Furthermore, to find the feasible solutions in the decision space two most widely used constraint handling techniques that include feasibility rule and ɛ-constrained method are added to select the trail vector and individuals respectively for the next generation. Proposed C2oDE method has been validated by considering IEEE 33-bus, 69-bus and 119-bus distribution networks at five different cases. Simulation results obtained shows better performance of proposed method against the most recent literature to find both OFR and DG allocation

A method for axis straightness error evaluation based on improved differential evolution algorithm

This paper proposes an improved differential evolution algorithm (IoCoDE) for the accurate evaluation of minimum zone axis straightness error. In the proposed algorithm, the good point set method is adopted to initialize the population, which can effectively improve the population diversity. Additionally, in order to balance the global and local search capabilities and speed up the convergence of the proposed algorithm, an opposition-based learning strategy is introduced. The nonlinear optimal target model for straightness error evaluation is put forward in detail. Four typical benchmark functions are utilized to test the performance of the improved algorithm. According to the practical examples, the results indicate that the evaluation accuracy of IoCoDE is better than linking both ends, least square method (LSM), composite differential evolution algorithm (CoDE), and other common evaluation algorithms. In addition, due to the simplicity and efficiency of the proposed algorithm, it is suitable for other forms and position error evaluation.

A Comparative Study of Differential Evolution Variants in Constrained Structural Optimization

Differential evolution (DE) is a population-based metaheuristic algorithm that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. Such algorithms make few or no assumptions about the problem being optimized and can search very large spaces of candidate solutions. DE is arguably one of the most versatile and stable population-based search algorithms that exhibits robustness to multi-modal problems. In the field of structural engineering, most real-world optimization problems are associated with one or several constraints. Constrained optimization problems are often challenging to solve due to their complexity and high nonlinearity. In this work we examine the performance of several DE variants, namely the traditional DE, the composite DE (CODE), the adaptive DE with optional external archive (JADE) and the self-adaptive DE (JDE and SADE), for handling constrained structural optimization problems associated with truss structures. The performance of each DE variant is evaluated by using five well-known benchmark structures in 2D and 3D. The evaluation is done on the basis of final optimum result and the rate of convergence. Valuable conclusions are obtained from the statistical analysis which can help a structural engineer in practice to choose the suitable algorithm for these kind of problems.

A novel design method for dual-passband IIR digital filters

With the rapid development of wireless communication technology, digital filters are now key components in many modern digital systems. Dual-passband digital filter is an important module of digital filter and has attracted wide attention. This paper proposes a novel evolutionary method to design diversified structure digital filters. Our proposed method using an adaptive multiple-elites- guide composite differential evolution algorithm, coupled with a shift mechanism (AMECoDEs) doesn’t need to use known circuit structures. Structures and parameters are evolved by crossover, mutation, and selection. Thus, our proposed method can directly design the diversified dual-passband digital filter structure and can effectively balance exploration and exploitation to prevent individuals from premature convergence. In our experiment, the connection probability, the subsystem number of the filter structure, as well as the scale factor and the crossover rate of AMECoDEs are explored to determine the optimal configuration. Compared with exiting state-of-the-art evolutionary algorithms for the design of the symmetrical and asymmetrical dual-bandpass filters, our proposed method has the smallest average passband ripple and stopband attenuation with the fastest convergence.

On the Performance of Differential Evolution Variants in Constrained Structural Optimization

Constrained optimization is a highly important field of engineering as most real-world optimization problems are associated with one or several constraints. Such problems are often challenging to solve due to their complexity and high nonlinearity. Differential evolution (DE) is arguably one of the most versatile and stable population-based search algorithms that exhibits robustness to multi-modal problems and has shown to be very efficient when solving constrained global optimization problems. In this paper we investigate the performance of several DE variants existing in the literature such as the traditional DE, the composite DE (CoDE), the adaptive DE with optional external archive (JADE) and the self-adaptive DE (jDE and SaDE), for handling constrained structural optimization problems. The performance of each DE variant is quantified by using three well-known benchmark structures in 2D and 3D. It is shown that JADE, which updates control parameters in an adaptive way, truly exhibits superior performance and outperforms the other DE variants in all the cases examined.

On the Cooperation Between Evolutionary Algorithms and Constraint Handling Techniques: A Further Empirical Study

Cooperation between Evolutionary Algorithms (EAs) and Constraint Handling Techniques (CHTs) plays an important role in Constrained Optimization Evolutionary Algorithms (COEAs). A constrained composite differential evolution (C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> oDE) sets a good example on the cooperation. This paper tries to further study the inner mechanism, i.e., the effect of different methods on generating and selecting solutions. In the solution generating part, a new method, which adopts stochastic ranking in selecting the best individual in the DE mutation operators, is proposed. In the solution selecting part, a new constraint handling technique combination is added. The experiments on benchmark functions from IEEE CEC2006 verify the effect. During the experiment, it is found that a new cooperation manner performs better than C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> oDE, which reflects the importance of cooperation.

A structure evolution-based design for stable IIR digital filters using AMECoDEs algorithm

This paper proposes a subsystem-based structure evolution algorithm for stable IIR digital filter design. The method designs the IIR digital filter through optimizing the filter structure. A filter structure is defined as the connection of the subsystems. A subsystem is a 2-order IIR digital structure with uncertain parameters. Subsystems are randomly connected with the constraints of no feedback branches between subsystems. The subsystem’s parameters and the connections between subsystems are optimized by evolutionary algorithms. An adaptive multiple-elites-guided composite differential evolution algorithm (AMECoDEs) is used to optimize this problem. Four classic types of filters, lowpass, highpass, bandpass and bandstop filters are designed. Five state-of-the-art evolutionary algorithms are compared. The simulation results show that AMECoDEs holds the first place on comprehensive performance and convergence rate. At the same time, the poles of filters all reside within the unit circle, which validates the stability of the IIR digital filters.

Composite Differential Evolution for Constrained Evolutionary Optimization

When solving constrained optimization problems (COPs) by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution (DE) for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite DE, the feasibility rule and the $\boldsymbol {\varepsilon }$ constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated COPs. By assembling the above techniques together, a constrained composite DE is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods.

Optimal Control of DFIG Wind Energy System in Multi-machine Power System using Advanced Differential Evolution

The Vector controlled doubly fed induction generator (DFIG) wind energy system in a multi-machine power system is very sensitive to faults on transmission lines and thus affects the stability of the system. The performance of vector controlled DFIG highly depends on PI controller parameters. The objective of this paper is to optimize the performance of vector controlled DFIG in multi-machine power systems under faulty conditions by tuning the parameters using advanced differential evolution algorithm. An objective function is formulated, which drives the system with good voltage profile, reduced power oscillations under faulty conditions. The parameters of PI controller are tuned using Composite Differential Evolution algorithm. Simulations are performed on a two area benchmark problem in Matlab/Simulink. The simulation results of the optimized DFIG wind energy system are compared with the actual existed system. The simulation results show that the overall performance and stability of the optimized system are enhanced.