An easy‐to‐implement differential evolution approach for multi‐objective optimizations

There has been considerable research done on multi-chamber mufflers used in the elimination of industrial venting noise. However, most research has been restricted to lower frequencies using the plane wave theory. This has led to underestimating acoustical performances at higher frequencies. Additionally, because of the space-constrained problem in most plants, the need for optimization of a compact muffler seems obvious. Therefore, a muffler composed of multiple rectangular fin-shaped chambers is proposed. Based on the eigenfunction theory, a four-pole matrix used to evaluate the acoustic performance of mufflers will be deduced. A numerical case for eliminating pure tones using a three-fin-chamber muffler will also be examined. To delineate the best acoustical performance of a space-constrained muffler, a numerical assessment using the Differential Evolution (DE) method is adopted. Before the DE operation for pure tone elimination can be carried out, the accuracy of the mathematical model must be checked using experimental data. The results reveal that the broadband noise has been efficiently reduced using the three-fin-chamber muffler. Consequently, a successful approach in eliminating a pure tone using optimally shaped three-fin-chamber mufflers and a differential evolution method within a constrained space has been demonstrated.

An improved differential evolution (DE) method based on the dynamic search strategy (IDEBDSS) is proposed to solve dynamic economic dispatch problem with valve-point effects in this paper. The proposed method combines the DE algorithm with the dynamic search strategy, which improves the performance of the algorithm. DE is the main optimizer in the method proposed. While chaotic sequences are applied to obtain the dynamic parameter settings in DE, dynamic search strategy which consists of two steps, global search strategy and local search strategy, is used to improve algorithm efficiency. To accelerate convergence, a new infeasible solution handing method is adopted in the local search strategy; meanwhile, an orthogonal crossover (OX) operator is added to the global search strategy to enhance the optimization search ability. Finally, the feasibility and effectiveness of the proposed methods are demonstrated by three test systems, and the simulation results reveal that the IDEBDSS method can obtain better solutions with higher efficiency than the standard DE and other methods reported in the recent literature.

This paper focuses on the real-time kinematics solution of an aerial manipulator mounted on an aerial vehicle, the vehicle’s motion isn’t considered in this study. Robot kinematics using Denavit-Hartenberg model was presented. The fundamental scope of this paper is to obtain a global online solution of design configurations with a weighted specific objective function and imposed constraints are fulfilled. Acknowledging the forward kinematics equations of the manipulator; the trajectory planning issue is consequently assigned to on an optimization issue. Several types of computing methods are documented in the literature and are well-known for solving complicated nonlinear functions. Accordingly, this study suggests two kinds of artificial intelligent techniques which are regarded as search methods; they are differential evolution (DE) method and modified shuffled frog-leaping algorithm (MSFLA). These algorithms are constrained metaheuristic and population-based approaches. moreover, they are able to solve the inverse kinematics problem taking into account the mobile platform additionally avoiding singularities since it doesn’t demand the inversion of a Jacobian matrix. Simulation results are carried out for trajectory planning of 6 degree-of-freedom (DOF) kinematically aerial manipulator and confirmed the feasibility and effectiveness of the supposed methods.

With the development of computer science, more and more complex problems rely on the help of computers for solving. When facing the parameter optimization problem of complex models, traditional intelligent optimization algorithms often require multiple iterations on the target problem. It can bring unacceptable costs and resource costs in dealing with these complex problems. In order to solve the parameter optimization of complex problems, in this paper we propose a multi-level surrogate-assisted optimization algorithm (MLSAO). By constructing surrogate models at different levels, the algorithm effectively explores the parameter space, avoiding local optima and enhancing optimization efficiency. The method combines two optimization algorithms, differential evolution (DE) and Downhill simplex method. DE is focused on global level surrogate model optimization. Downhill simplex is concentrated on local level surrogate model update. Random forest and inverse distance weighting (IDW) are constructed for global and local level surrogate model respectively. These methods leverage their respective advantages at different stages of the algorithm. The MLSAO algorithm is evaluated against other state-of-the-art approaches using benchmark functions of varying dimensions. Comprehensive results from the comparisons showcase the superior performance of the MLSAO algorithm in addressing expensive optimization problems. Moreover, we implement the MLSAO algorithm for tuning precipitation parameters in the Community Earth System Model (CESM). The outcomes reveal its effective enhancement of CESM's simulation accuracy for precipitation in the North Indian Ocean and the North Pacific region. These experiments demonstrate that MLSAO can better address parameter optimization problems under complex conditions.

A method for reconstructing dielectric objects buried in a half space is proposed. The approach is based on the inverse scattering formulation. The Green's function for the half space is used as the kernel of the integral equations relating the dielectric properties of the object to the samples of the scattered electric field. The inverse problem is recast as a global optimization problem by constructing a functional to be minimized. A differential evolution method is used to obtain a global minimum of this functional. The paper provides the mathematical formulation of the approach. Moreover, numerical results are reported.

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

To overcome this noise, traditional reactive as well as dissipative mufflers have been used. However, the allowable backpressure and the extra load acting on the cooling tower are limited. So, in order to efficiently reduce the broad noise under a low-pressure drop and a small dead weight, a straight multi-array resonator muffler without sound absorbing wool is required. Multi-array Helmholtz mufflers with complicated Helmholtz resonators were found to be too expensive in manufacturing costs and can be easily accumulated with duct and water. Therefore, a straight multi-array side-branched muffler with an empty chamber is proposed. Here, to efficiently reduce the broadband noise level, eight kinds of mufflers (muffler A–H) with 1–8 raw chambers internally partitioned with concentric perforated plate will also be introduced. To delineate the best acoustical performance of a space-constrained muffler, a numerical assessment using a four-pole matrix method in conjunction with a differential evolution method is adopted. To verify the availability of the differential evolution optimization, a numerical optimization of mufflers A–H at a pure tone (400 Hz) is exemplified. Before the differential evolution operation in broadband noise elimination can be carried out, the accuracy of the mathematical model has been checked using the experimental data. Consequently, a successful approach in eliminating a broadband noise with a low-pressure drop and a dead load using optimally shaped straight multi-array side-branched mufflers and a differential evolution method within a constrained space has been demonstrated.

Researchers can solve Simple optimization problems using various methods. But differential Evolution (DE) is a method(population based) to solve complex optimization problems in some easy steps that is not possible to handle by mathematical optimization methods. For global optimization problems DE is a probabilistic approach. DE when tested over some bench mark functions and real world problems it performed better than some evolutionary algorithms and swarm - intelligence based algorithms. Balancing between Exploration and Exploitation using DE mutation and crossover with control parameters F and CR (fine tunned) is to be done. DE does not complete demand of good convergence and stagnation. DE Explore better but this exploration capability sometimes may skip the true solution and exhibit premature convergence. To improve this we can decrease the step size but this exhibit stagnation. So for Better exploitation, another approach called Memetic algorithm based on levy flight based local search strategy is used with DE. Further to balance exploration and exploitation in local search area in this paper a population or generation based exploitation of local search area in LFDE is proposed that is called PGLFDE. To show better result proposed strategy is tested on some bench mark functions and compare with recent variants of DE.

When designing a well field for efficiently extracting groundwater or petroleum, it is common for designers to rely on computational optimization methods to determine the optimal placement of wells. The goal of these methods is to find a well-field solution that maximizes the value of a defined objective function, and to do so while utilizing the least amount of computational effort. To achieve this, researchers have developed algorithms based on a wide range of heuristics. Within groundwater management, popular methods include particle swarm optimization (PSO) and genetic algorithms such as differential evolution (DE). This study seeks to investigate a recently developed method called Extremal Optimization for Well Placement Problems (EO-WPP), and to compare its performance with established methods like PSO and DE. EO-WPP is an optimization method based on the extremal optimization (EO) algorithm. EO optimizes by iteratively identifying and modifying the least effective components of a solution. By following this heuristic, the EO algorithm has the potential to quickly find optimal solutions while requiring minimal computational effort. To test this, the performance of DE, PSO and EO-WPP was compared on four benchmark problems. Two of these are the Rastrigin and the Rosenbrock benchmark functions. These functions were used because of their quick evaluation and their popularity in optimization literature. The third benchmark is a synthetic groundwater model, built to test the methods under the context of groundwater management. The final benchmark is a field problem using the Aberdeen groundwater model in South Dakota. The results reveal that EO-WPP was able to outperform DE and PSO on all tested benchmarks. EO-WPP is an effective and efficient optimization tool for well placement design in groundwater management.

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.

Fuel cells are complex multiphysical systems characterized by a stratified geometry consisting of thin layers of different materials. Their full characterization involves a number of physical parameters, which are important for quantifying and comparing the performance of the materials. The physical parameters are also used in fuel cell models, which allow the fast exploration of different operating scenarios and can be implemented in optimization procedures aimed at achieving the best structural and operating conditions. The system of equations involved in these models, e.g. the Nernst equation, the Butler-Volmer equation and the diffusion equation, are strongly non-linear; thus, the model itself is extremely sensitive to parameter variations. Careful ex-situ measurements of such parameters can be performed by means of a number of diagnostic techniques, whose results are however not completely consistent with fuel cell operation due to several effects, e.g. variable interactions and boundary effects in the thin layers of the fuel cell. Conversely, “in situ” measurements can provide meaningful operational values, but a very few techniques are available to determine a limited number of parameters.A solution can consist in multiple parameter identification from multiple fundamental measurements, such as polarization curve and electrochemical impedance spectroscopy, performed in different conditions, e.g. at different temperature, pressure, concentration, and humidification.If there is only one unknown parameter, the solution is easy, requiring just a statistical interpolating technique. In the case of multiple unknown parameters, which is the most frequent condition, the problem becomes increasingly difficult as the number of parameters increases as duplicity problem emerges, i.e., several groups of parameters may lead to the same performance (e.g. polarization curve).Recently, a number of numerical tools are under development to face this kind of problems, some based on stochastic mathematical models, each presenting specific features in terms of accuracy, convergence, stability, robustness, and calculation speed [1]. Among the most promising methods, some of which have already been applied to multiple fuel cell parameter identification, are the Ishibashi–Kimura method [2], the Lambert W-function method [3], the Levenberg-Marquardt algorithm (LMA), the Gauss-Newton algorithm (GNA), the hybrid artificial bee colony algorithm [4], the trust region method, the current switching method [5], the simulated annealing method [6], and the particle swarm optimization (PSO) [7], and the differential evolution method [8].The presentation will focus on the application of a particular class of stochastic optimization methods to the problem of multiple parameters identification. These methods have already been widely tested and applied successfully to the simultaneous search of sets of optimal parameters with different physical dimensions, making them ideal tools to cope with the present problem. Their recent relevant literature is vast. They are especially suited for multimodal and noisy functions over large search spaces, which makes them particularly appealing for the problem at hand. The main drawback of such methods is the high number of objective function evaluations needed for convergence; however, thanks to a particular formulation of the PEMFC model, such drawback can be of minor impact, i.e. the overall computational times are on the order of a few tens of seconds.We are going to present the application of two of the most well-known metaheuristic methods, namely Particle Swarm Optimization (PSO) and Differential Evolution (DE), developed in previous work and suitably adapted. It should be noted that PSO has already been applied to parameter identification for FCs, while the application of DE is novel in this context. This is somewhat surprising since, as results will show, DE provides better results and offers higher robustness. We will present the implementation details regarding PSO and DE. The optimization algorithms have not been tuned to the specific problem and algorithm control parameters have been chosen from reasonable values suggested in literature.

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.

Project scheduling is essential to be planned before activities. Standard methods of project scheduling based on precedence constraints scheduling events and the assumption that resources are not unlimited capacity. But in fact the project activity has resource limits. The main objective is to minimize the total duration of the project with precedence constraints and resource constraints for all project activities. Many optimization methods are used to improve the quality of scheduling and speed up the calculation time. This paper proposed the use of Cross Entropy (CE) method to solve resource constraints project scheduling problem, as well as comparing the advantages and disadvantages between the CE methods with Differential Evolution (DE) method. The purpose CE method consist of four critical steps including generating a sample of random solution, calculating the performance according to the specific fitness function, selecting elite sample and finally updating the previous parameters to get a better sample in the next iteration. To speed up the computation time, in this study decrease the number of samples for each iteration in Cross Entropy algorithm. Numerical experiments with several data sets from the Project Scheduling library (PSPLIB) showed that CE can provide the optimal total duration of the project same as the DE with calculation time is faster than DE.

This paper addresses the simultaneous localization problem of multiple magnetic dipole sources distributed at varying heights in space. To overcome the limitations of traditional optimization-based methods, which are time-consuming and prone to local optima, we propose a fast multi-dipole linear localization (MDLL) method. After performing 2D grid measurements, the MDLL method first determines the number of magnetic sources, their initial positions, and magnetic moments by calculating the magnetic gradient tensor and tilt angle. It then filters effective measurement points for each source using the Voronoi diagram and iteratively refines the results through a single-source linear localization scheme to approach the true values. The simulation and experimental results demonstrate that the MDLL method significantly outperforms the benchmark one-step localization (OSL) and differential evolution (DE) methods in both localization accuracy and computational efficiency. In noise-free simulations, the localization error of MDLL is reduced by over 99% compared to OSL and DE, and its computation speed is more than 20,000 times faster than DE in the scenario with 30 magnetic sources, with the advantage becoming more evident as the number of sources increases. In experiment, the average localization error of MDLL are only 4.55% and 36.94% of that of OSL and DE methods, respectively, and its computation time remains significantly shorter than that of the DE method.

The differential evolution (DE) is an improved version of evolution strategies and Nelder-Mead simplex methods. DE has been successfully applied in various fields, such as optimization nonlinear functions, multi sensor fusion, control system, and system identification. The potentialities of DE are its simple structure, easy use, convergency speed and robustness. This paper proposes a new hybrid methodology for solving the economic load dispatch problem with valvepoint effect. The proposed hybrid method combinates the DE and sequential quadratic programming (SQP) technique. The DE is used to produce good potential solutions, and the SQP is used to fine-tune the DE run. The hybrid methodology and its variants are validated for a test system consisting of 40 thermal units whose incremental fuel cost function takes into account the valvepoint loading effects. The proposed hybrid method outperforms other state-of-theart algorithms in solving load dispatch problems with the valve-point effect.Keywordsdifferential evolutioneconomic dispatchoptimizationpower generation operation and control