Multi-objective Optimization Based Differential Evolution Constrained Optimization Algorithm

In recent years, Differential Evolution (DE) algorithm that is one of the most important delegate of the evolutionary algorithms have been successfully used for solving different optimization problems with its both serial and parallel variants. In this study, the performance of DE algorithm powered with cooperative emigrant creation strategy was investigated over the different types of numerical problems and obtained results were compared with the results of the serial DE and parallel DE algorithm supported with conventional emigrant creation strategy. Experimental studies showed that the convergence speed of the parallel DE algorithm is significantly improved with the cooperative emigrant creation strategy and the proposed parallel DE algorithm produces better results compared to the serial DE algorithm and parallel DE algorithm with the conventional emigrant creation strategy.

Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem

This paper proposes two improved algorithms, the DE-PSO algorithm, which combines differential evolution and phased strategy, and the hybrid particle swarm optimization algorithm integrating whale algorithm (WOAPSO), which combines the whale optimization mechanism. Compared to traditional calibration methods (such as the Newmark three- and two-parameter methods), which rely on empirical simplified models, adapting them to the complex seismic nonstationarity and multipeak characteristics is difficult. However, although intelligent optimization algorithms, such as particle swarm optimization (PSO) and differential evolution (DE) have improved calibration accuracy in recent years, insufficient convergence stability and low computational efficiency, among other problems, persist. Therefore, based on experiments, the performances of these algorithms were compared with those of standard PSO, traditional DE, and other algorithms. The results demonstrate the significant superiority of DE-PSO and WOAPSO. In 50 repeated experiments, the fitness standard deviation (STD) was significantly reduced, and the algorithms achieved rapid convergence by the mid-iteration stage, which effectively resolves the issues of premature convergence and local oscillation tendencies inherent in the standard Particle Swarm Optimization algorithm. Regarding the key parameters (Tg, βmax, γ) of the standard, the STD of the improved algorithm approached zero, verifying its strong adaptability to multimodal optimization problems. Furthermore, the DE-PSO algorithm had the best performance in balancing computational efficiency and stability, with a convergence speed that is three times faster than that of standard DE algorithm while maintaining the lowest parameter volatility. This study provides an efficient algorithmic tool for the rapid analysis of strong motion records and the efficient calibration of design response spectra, which has implications for the seismic optimization design of complex structures and can be guided by regulations, contributing to engineering seismic practice.

A self-competitive mutation strategy for Differential Evolution algorithms with applications to Proportional–Integral–Derivative controllers and Automatic Voltage Regulator systems

The Differential Evolution (DE) algorithm, under the family of Evolutionary Algorithms (EAs), is one of the powerful algorithms used for solving continuous parameter optimization challenges. The simplistic nature and robustness of the classical DE algorithm have drawn researchers' attention towards its progressive enhancement. This work reports on an investigation of the behavioral changes of the classical DE algorithm, evoked when its mutation and crossover components are fine tuned for enhancement of DE's performance. The scope of this study covers the implementation of a mutation level enhancement and a crossover level enhancement, followed by their integration. The mutation and the crossover components are augmented by incorporation of Centroid DE and Superior-Superior & Superior-Inferior DE logics, respectively. The algorithms appraised in this inquiry were classical DE, Centroid based DE(cDE), Superior-Superior based DE (ssDE), Superior-Inferior DE (siDE), Centroid Superior-Superior DE (cssDE) and Centroid Superior-Inferior DE (csiDE). These algorithms were evaluated by comparison of the values of their mean objective function (MOV), and their speed, at solving the global optimization problems in a simple benchmarking function suite with 4 functions of different categories. The study concludes that the DE algorithm shows enhancement performance with modified mutation and crossover components. However, with a trend for inconsistency for varying values of its control parameters and benchmarking problems.

Differential Evolution (DE) is a simple and fast population based Nature Inspired Algorithm (NIA). When it is experimented for benchmark problems as well as real world problems it outperformed other population based NIAs and other search metaheuristics in terms of rate of convergence. But it is not an exception in class of population based algorithms, it also show premature convergence and stagnates at suboptimal points. Therefore this paper tries to sustain a better convergence speed and keep away from stagnation by introducing levy flight random search process along with opposition based learning strategy in original DE algorithm. The proposed algorithm named as Opposition Based Levy Flight Search in DE (OLFDE) Algorithm. The newly proposed algorithm OLFDE tested over fourteen benchmark problems and three real world problems (Pressure Vessel Design, Parameter estimation for frequency modulated sound wave and Compression Spring problem) in order to prove its efficiency over some recent variants of DE.

Regulation-based formulas and improved Differential Evolution(DE) algorithm is used to optimize PID parameters. In order to improve the global search ability and the convergence rate of the common DE algorithm, self-adaptive method is introduced to obtain DE parameters. On the other hand, initial population quality of DE algorithm has important influence on convergence of the algorithm. So the regulation-based formulas are used to guide the production of initial population, which is good to improve the convergence rate and realize obtaining of PID parameters completely adaptive without any personal experience. The simulation is developed on steam temperature system of cycle fluidized bed boiler with serious parameter uncertainties and many disturbance and long-time delay. The results show that the improved DE algorithm has higher optimal speed, small amount of calculation and effective optimization of parameters. The proposed method has better control quality and system robustness.

In this work, a method to control the parameters of Differential Evolution (DE) algorithm is proposed. Here the control parameters of DE are co-evolved by Particle Swarm Optimization (PSO) algorithm. The classical DE algorithm has two main control parameters: Scale Factor (F) and Cross-over Rate (CR). These are selected on trial-and-error basis for solving optimization problems. Several optimization problems lead to optimal or sub-optimal solution by proper selection of control parameters of the DE algorithm. In this proposed method, PSO algorithm is used to tune the scale factor and cross-over rate in DE algorithm. Basically PSO algorithm is used as a meta-optimizer for DE algorithm. The proposed method is termed as mPSO-DE in this paper. The mPSO-DE algorithm is applied on 12 benchmark unconstrained optimization problems. The obtained results are compared with that of classical DE algorithm. From the experimental studies, it has been found that the proposed mPSO-DE algorithm performed better than DE algorithm.

In modern aviation power systems, the dynamic stability of power generation systems has become a major challenge. To tackle issues such as slow response, poor voltage stability, and voltage oscillations in aircraft synchronous generators under sudden load changes, a Proportional-Integral-Derivative (PID) voltage regulator modified using the Differential Evolution (DE) algorithm has been developed. Additionally, the DE algorithm’s convergence speed and robustness are enhanced through the incorporation of directional search strategies and adaptive control parameters. Simulation results demonstrate that the optimized regulator delivers rapid response and minimal overshoot, thereby improving the accuracy and dynamic performance of the voltage regulator. The modified DE algorithm notably accelerates convergence compared to the traditional DE algorithm.

Thiswork proposes a Differential Evolution (DE) algorithm based energy management system (EMS) to optimize the performance of a microgrid in the presence of renewable energy sources. Various types of distributed generators (DGs), namely Micro Turbine (MT), Phosphoric Acid Fuel Cell (PAFC), Wind Turbine (WT), Photo-voltaic (PV) and battery (batt) are present in the micro-grid. Out of these DGs, WT and PV have a randomized natural behavior. To optimize the micro-grid operation and cover the uncertainty in power generation from the renewable resources, the incentive based demand response programs are incorporated in the EMS. The performance of EMS is optimized by minimizing the operating cost of the micro-grid and by minimizing its pollutant emissions using DE algorithm. The results obtained using DE algorithm are compared with the Particle Swarm Optimization (PSO) based reported results. On comparison the proposed DE algorithm is found to be superior in terms of solution quality and convergence speed.

The paper considers dimensional synthesis of a path generator four-bar linkage by applying the modified Differential Evolution (DE) algorithm. During the search of the space, the DE algorithm may skip the right solution and lead to premature convergence. If the step is reduced, the search space is reduced as well, so that convergence becomes slower. Search efficiency may be achieved by including Lévy Flight in the DE algorithm. Namely, when the DE algorithm identifies the space of best solution, then a Levý Flight step is used for local search in that region, which significantly increases the exploitation capability and allows obtaining a very efficient solution of the optimization problem. The algorithm was tested with three examples of dimensional synthesis of a path generator four-bar linkage. The proposed algorithm can be very efficiently applied to solving very complex optimization problems.

The Differential Evolution (DE) algorithm was initially proposed for continuous numerical optimization, but it has been applied with success in many combinatorial optimization problems, particularly permutation-based integer combinatorial problems. In this paper, a new and general approach for combinatorial optimization is proposed using the Differential Evolution algorithm. The proposed approach aims at preserving its interesting search mechanism for discrete domains, by defining the difference between two candidate solutions as a differential list of movements in the search space. Thus, a more meaningful and general differential mutation operator for the context of combinatorial optimization problems can be produced. We discuss three alternatives for using the differential list of movements within the differential mutation operation. We present results on instances of the Traveling Salesman Problem (TSP) and the N-Queen Problem (NQP) to illustrate the adequacy of the proposed approach for combinatorial optimization.

Many practical engineering problems can be transformed into constrained optimization problems (COPs) , scholars prefer to use evolutionary algorithms (EA) to deal with COPS. Differential evolution (DE) algorithm has strong global search and convergence ability than other EA, however, when dealing with COPs, the search ability of DE algorithm is affected by parameter setting and constraint handling technology (CHT) is needed. In this paper, an improved differential evolution algorithm with a new hybrid CHT (IDE-HCHT) is used to deal with COPs, at the same time, the hybrid CHT replaces the selection step of the DE algorithm, and improves the processing efficiency of the algorithm. To verify its superiority, CEC2017 benchmark function is tested by the novel IDE-HCHT, and two other start-of-the-art algorithms, LSHADE44, UDE. The results show that the proposed method shows better competitive performance against the two algorithms.

Throughout the past few decades, a variant of differential evolution (DE) algorithms have been introduced with a competitive performance on complex optimization problems. However, the DE superiority is highly dependent on its control parameters and the search operators (i.e., mutation and crossover schemes). Therefore, to obtain the optimal performance, tuning the parameters is essential. In this paper, the DE algorithm is proposed that uses a new designed mutation scaling factor to dynamically adapt the movement of the individuals in the search space toward the optimal value during the evolutionary process. The numerical experiments are conducted on thirty CEC 2014 benchmark functions on four different dimensions; 10, 30, 50, and 100. The obtained results demonstrate that the proposed algorithm is highly competitive and shows better performance than the classical DE algorithm.

In this paper we present a boundary search based ACO algorithm for solving nonlinear constrained optimization problems. The aim of this work is twofold. Firstly, we present a modified search engine which implements a boundary search approach based on a recently proposed ACO metaheuristic for continues problems. Secondly, we propose the incorporation of the stochastic ranking technique to deal with feasible and infeasible solutions during the search which focuses on the boundary region. In our experimental study we compare the overall performance of the proposed ACO algorithm by including two different complementary constraint-handling techniques: a penalty function and stochastic ranking. In addition, we include in our comparison of results the stochastic ranking algorithm, which was originally implemented using an evolution strategy as its search engine.