Standard Differential Evolution Algorithm Research Articles

Constraint Consensus Mutation-Based Differential Evolution for Constrained Optimization

Until now, numerous mutation strategies have been introduced as search operators within the differential evolution (DE) algorithm. These operators are designed mainly to improve fitness value while also maintaining diversity in the population, but they do not directly act to reduce constraint violations of constrained problems. Interestingly, the so-called constraint handling techniques, used with most evolutionary algorithms, are not a part of the actual search process. Instead, the constraint violations are only considered in the ranking and selection of individuals for participation in the search process. This paper introduces a new DE mutation operator that incorporates a mechanism, based on constraint consensus, that can directly help to reduce the constraint violations during the evolutionary search process. The proposed DE algorithm has been tested on a set of well-known constrained benchmark problems. The experimental results show that the proposed algorithm is able to obtain better solutions, compared to the standard DE algorithm, with significantly reduced computational effort. The algorithm also outperforms state-of-the-art algorithms.

Multiple Gravity Assist Spacecraft Trajectories Design Based on BFS and EP_DE Algorithm

The paper deals with the multiple gravity assist trajectories design. In order to improve the performance of the heuristic algorithms, such as differential evolution algorithm, in multiple gravity assist trajectories design optimization, a method combining BFS (breadth-first search) and EP_DE (differential evolution algorithm based on search space exploring and principal component analysis) is proposed. In this method, firstly find the possible multiple gravity assist planet sequences with pruning based BFS and use standard differential evolution algorithm to judge the possibility of all the possible trajectories. Then select the better ones from all the possible solutions. Finally, use EP_DE which will be introduced in this paper to find an optimal decision vector of spacecraft transfer time schedule (launch window and transfer duration) for each selected planet sequence. In this paper, several cases are presented to prove the efficiency of the method proposed.

A novel 3-layer mixed cultural evolutionary optimization framework for optimal operation of syngas production in a Texaco coal-water slurry gasifier

Optimizing operational parameters for syngas production of Texaco coal-water slurry gasifier studied in this paper is a complicated nonlinear constrained problem concerning 3 BP (Error Back Propagation) neural networks. To solve this model, a new 3-layer cultural evolving algorithm framework which has a population space, a medium space and a belief space is firstly conceived. Standard differential evolution algorithm (DE), genetic algorithm (GA), and particle swarm optimization algorithm (PSO) are embedded in this framework to build 3-layer mixed cultural DE/GA/PSO (3LM-CDE, 3LM-CGA, and 3LM-CPSO) algorithms. The accuracy and efficiency of the proposed hybrid algorithms are firstly tested in 20 benchmark nonlinear constrained functions. Then, the operational optimization model for syngas production in a Texaco coal-water slurry gasifier of a real-world chemical plant is solved effectively. The simulation results are encouraging that the 3-layer cultural algorithm evolving framework suggests ways in which the performance of DE, GA, PSO and other population-based evolutionary algorithms (EAs) can be improved, and the optimal operational parameters based on 3LM-CDE algorithm of the syngas production in the Texaco coal-water slurry gasifier shows outstanding computing results than actual industry use and other algorithms.

Optimum design of frame structures using the Eagle Strategy with Differential Evolution

Modern metaheuristic algorithms are in general suited for global optimization. This paper combines the recently developed eagle strategy algorithm with differential evolution. The new algorithm, denoted as the ES–DE, is implemented by interfacing SAP2000 structural analysis code and MATLAB mathematical software. The performance of the ES–DE is evaluated by solving four benchmark problems where the objective is to minimize the weight of steel frames. The optimized designs obtained by the proposed algorithm are better than those found by the standard differential evolution algorithm and also very competitive with literature. The overall convergence behavior is significantly enhanced by the hybrid optimization strategy.

Differential evolution to solve the lot size problem in stochastic supply chain management systems

An advanced resource planning model is presented to support optimal lot size decisions for overall performance improvement of real-life supply chain management systems in terms of either total delivery time or total setup costs. Based on a queueing network, a model is developed for a mix of products, which follow a sequence of operations taking place at multiple interdependent supply chain members. At the same time, various sources of uncertainty, both in demand and process characteristics, are taken into account. In addition, the model includes the impact of parallel servers for multiple resources with period dependent time schedules. The corrupting influence of variabilities from rework and breakdown is also explicitly modeled. This integer non-linear problem is solved by standard differential evolution algorithms. They are able to find each product’s lot size that minimizes its total supply chain lead time. We show that this solution approach outperforms the steepest descent method, an approach commonly used in the search for optimal lot sizes. For problems of realistic size, we propose appropriate control parameters for an efficient differential evolutionary search process. Based on these results, we add a major conclusion on the debate concerning the convexity between lot size and lead time in a complex supply chain environment.

The Algorithm for Algorithms: An Evolutionary Algorithm Based on Automatic Designing of Genetic Operators

At present there is a wide range of evolutionary algorithms available to researchers and practitioners. Despite the great diversity of these algorithms, virtually all of the algorithms share one feature: they have been manually designed. A fundamental question is “are there any algorithms that can design evolutionary algorithms automatically?” A more complete definition of the question is “can computer construct an algorithm which will generate algorithms according to the requirement of a problem?” In this paper, a novel evolutionary algorithm based on automatic designing of genetic operators is presented to address these questions. The resulting algorithm not only explores solutions in the problem space like most traditional evolutionary algorithms do, but also automatically generates genetic operators in the operator space. In order to verify the performance of the proposed algorithm, comprehensive experiments on 23 well-known benchmark optimization problems are conducted. The results show that the proposed algorithm can outperform standard differential evolution algorithm in terms of convergence speed and solution accuracy which shows that the algorithm designed automatically by computers can compete with the algorithms designed by human beings.

Modified differential evolution with self-adaptive parameters method

The differential evolution algorithm (DE) is a simple and effective global optimization algorithm. It has been successfully applied to solve a wide range of real-world optimization problem. In this paper, the proposed algorithm uses two mutation rules based on the rand and best individuals among the entire population. In order to balance the exploitation and exploration of the algorithm, two new rules are combined through a probability rule. Then, self-adaptive parameter setting is introduced as uniformly random numbers to enhance the diversity of the population based on the relative success number of the proposed two new parameters in a previous period. In other aspects, our algorithm has a very simple structure and thus it is easy to implement. To verify the performance of MDE, 16 benchmark functions chosen from literature are employed. The results show that the proposed MDE algorithm clearly outperforms the standard differential evolution algorithm with six different parameter settings. Compared with some evolution algorithms (ODE, OXDE, SaDE, JADE, jDE, CoDE, CLPSO, CMA-ES, GL-25, AFEP, MSAEP and ENAEP) from literature, experimental results indicate that the proposed algorithm performs better than, or at least comparable to state-of-the-art approaches from literature when considering the quality of the solution obtained.

A new modified differential evolution algorithm scheme-based linear frequency modulation radar signal de-noising

The main intention of this study was to investigate the development of a new optimization technique based on the differential evolution (DE) algorithm, for the purpose of linear frequency modulation radar signal de-noising. As the standard DE algorithm is a fixed length optimizer, it is not suitable for solving signal de-noising problems that call for variability. A modified crossover scheme called rand-length crossover was designed to fit the proposed variable-length DE, and the new DE algorithm is referred to as the random variable-length crossover differential evolution (rvlx-DE) algorithm. The measurement results demonstrate a highly efficient capability for target detection in terms of frequency response and peak forming that was isolated from noise distortion. The modified method showed significant improvements in performance over traditional de-noising techniques.

Pigeon-inspired optimization: a new swarm intelligence optimizer for air robot path planning

Purpose – The purpose of this paper is to present a novel swarm intelligence optimizer — pigeon-inspired optimization (PIO) — and describe how this algorithm was applied to solve air robot path planning problems. Design/methodology/approach – The formulation of threat resources and objective function in air robot path planning is given. The mathematical model and detailed implementation process of PIO is presented. Comparative experiments with standard differential evolution (DE) algorithm are also conducted. Findings – The feasibility, effectiveness and robustness of the proposed PIO algorithm are shown by a series of comparative experiments with standard DE algorithm. The computational results also show that the proposed PIO algorithm can effectively improve the convergence speed, and the superiority of global search is also verified in various cases. Originality/value – In this paper, the authors first presented a PIO algorithm. In this newly presented algorithm, map and compass operator model is presented based on magnetic field and sun, while landmark operator model is designed based on landmarks. The authors also applied this newly proposed PIO algorithm for solving air robot path planning problems.

Differential evolution methods based on local searches

In this paper we analyze the behavior of a quite standard Differential Evolution (DE) algorithm applied to the objective function transformed by means of local searches. First some surprising results are presented which concern the application of this method to standard test functions.Later we introduce an application to disk- and to sphere-packing problems, two well known and particularly hard global optimization problems. For these problems some more refined variations of the basic method are necessary in order to take at least partially into considerations the many symmetries those problems possess. Coupling these techniques with DE and local optimization resulted in a new method which, when tested on moderately sized packing problems, was capable of confirming known putative optima for the problem of packing disks, and of discovering quite a significant number of new putative optima for the problem of packing spheres.

An Adaptive Cauchy Differential Evolution Algorithm for Global Numerical Optimization

Adaptation of control parameters, such as scaling factor (F), crossover rate (CR), and population size (NP), appropriately is one of the major problems of Differential Evolution (DE) literature. Well-designed adaptive or self-adaptive parameter control method can highly improve the performance of DE. Although there are many suggestions for adapting the control parameters, it is still a challenging task to properly adapt the control parameters for problem. In this paper, we present an adaptive parameter control DE algorithm. In the proposed algorithm, each individual has its own control parameters. The control parameters of each individual are adapted based on the average parameter value of successfully evolved individuals' parameter values by using the Cauchy distribution. Through this, the control parameters of each individual are assigned either near the average parameter value or far from that of the average parameter value which might be better parameter value for next generation. The experimental results show that the proposed algorithm is more robust than the standard DE algorithm and several state-of-the-art adaptive DE algorithms in solving various unimodal and multimodal problems.

Nested DE based parameter estimation for multiple vortex ring microburst model

Modelling of microburst is significant for flight simulations. The most widely used model of microburst is the one based on the principle of multiple vortex ring. The characteristics of the microburst are directly determined by the parameters of the model. The conventional method to fix the parameters of multiple vortex ring microburst model is using experiential formula, which is not flexible enough. In this paper, we treat the parameters estimation of multiple vortex ring model as an optimization problem, and introduce the differential evolution algorithm to solve it. In the process of estimating the parameters by the maximum wind velocity, there are two interrelated optimization processes. Therefore, we improved the standard differential evolution algorithm in this paper. A nested differential evolution algorithm is proposed to accomplish the two optimization process, intermediate optimization and objective optimization. The numerical experiments show that this method can flexibly generate microburst with any maximum wind velocity, and the error meet the requirement set by the user.

Computational Approach Based on a Differential Evolution with Self-Adaptive Concept for Microwave Imaging of Two-Dimensional Inverse Scattering Problem

The application of four techniques for the shape reconstruction of a metallic cylinder by measured scattered fields is studied in this article. These approaches are applied to two-dimensional configurations. Finite-difference time-domain is employed for the analysis of the forward scattering part, while the inverse scattering problems are transformed into optimization problems. Different differential evolutionary algorithms are applied to reconstruct the location and shape of the two-dimensional metallic cylinder. These techniques have been tested in the case of simulated measurements contaminated by additive white Gaussian noise. The reconstructed results by algorithm with self-adaptive control parameter settings are better than these obtained by the standard differential evolution algorithm and dynamic differential evolution algorithm.

A Cluster-Based Differential Evolution Algorithm With External Archive for Optimization in Dynamic Environments

This paper presents a Cluster-based Dynamic Differential Evolution with external Archive (CDDE_Ar) for global optimization in dynamic fitness landscape. The algorithm uses a multipopulation method where the entire population is partitioned into several clusters according to the spatial locations of the trial solutions. The clusters are evolved separately using a standard differential evolution algorithm. The number of clusters is an adaptive parameter, and its value is updated after a certain number of iterations. Accordingly, the total population is redistributed into a new number of clusters. In this way, a certain sharing of information occurs periodically during the optimization process. The performance of CDDE_Ar is compared with six state-of-the-art dynamic optimizers over the moving peaks benchmark problems and dynamic optimization problem (DOP) benchmarks generated with the generalized-dynamic-benchmark-generator system for the competition and special session on dynamic optimization held under the 2009 IEEE Congress on Evolutionary Computation. Experimental results indicate that CDDE_Ar can enjoy a statistically superior performance on a wide range of DOPs in comparison to some of the best known dynamic evolutionary optimizers.

A differential evolution algorithm with intersect mutation operator

This paper proposes a novel differential evolution (DE) algorithm with intersect mutation operation called intersect mutation differential evolution (IMDE) algorithm. Instead of focusing on setting proper parameters, in IMDE algorithm, all individuals are divided into the better part and the worse part according to their fitness. And then, the novel mutation and crossover operations have been developed to generate the new individuals. Finally, a set of famous benchmark functions have been used to test and evaluate the performance of the proposed IMDE. The experimental results show that the proposed algorithm is better than, or at least comparable to the self-adaptive DE (JDE), which is proven to be better than the standard DE algorithm. In further study, the IMDE algorithm has also been compared with several improved Particle Swarm Optimization (PSO) algorithms, Artificial Bee Colony (ABC) algorithm and Bee Swarm Optimization (BSO) algorithm. And the IMDE algorithm outperforms these algorithms.

A computationally efficient hybrid approach for engineering optimization problems

This article proposes a computationally efficient hybrid search approach for solution of constrained engineering problems by hybridizing differential evolution, a very robust evolutionary algorithm, with sequential quadratic programming, a nonlinear programming technique. Moreover, constraint handling method of standard differential evolution was also modified by embedding a pareto based ranking scheme in the standard differential evolution algorithm. The performance of proposed hybrid algorithm was evaluated based on a set of well-known mathematical and engineering benchmark problems. The comparison of results with those of other evolutionary algorithms demonstrates that the proposed method is highly competitive in terms of solution quality and that the proposed algorithm is computationally efficient as it requires much lower number of function evaluations to achieve the same performance.

Dynamic economic dispatch for wind-thermal power system using a novel bi-population chaotic differential evolution algorithm

Based on in-depth analysis of the stochastic nature of wind power output, the Weibull distribution parameters of regional wind speed for different time intervals are obtained respectively, and then the probability density functions of wind power output for different time intervals are achieved. These functions can be used to calculate output-overestimate and output-underestimate probabilities in each interval, so possible extra costs for maintaining the power system stability caused by incorporating unstable wind power can be calculated. Taking into account the possible costs, a stochastic optimization model for dynamic economic dispatch of wind-thermal power system is established to minimize the comprehensive operation expected cost. Moreover, a new algorithm, bi-population chaotic differential evolution (BPCDE) algorithm is proposed to solve this complicated model. The algorithm introduces bi-population evolution strategy, chaotic map update mechanism and Metropolis rule to improve the standard differential evolution algorithm. These improvements can overcome the premature problem caused by lacking of the individual diversity in the later stage of differential evolution and strengthen the global search ability of the algorithm. The validity and superiority are demonstrated by simulation results on a power system integrated with large scale wind farms.

Remote Sensing Image Subpixel Mapping Based on Adaptive Differential Evolution

In this paper, a novel subpixel mapping algorithm based on an adaptive differential evolution (DE) algorithm, namely, adaptive-DE subpixel mapping (ADESM), is developed to perform the subpixel mapping task for remote sensing images. Subpixel mapping may provide a fine-resolution map of class labels from coarser spectral unmixing fraction images, with the assumption of spatial dependence. In ADESM, to utilize DE, the subpixel mapping problem is transformed into an optimization problem by maximizing the spatial dependence index. The traditional DE algorithm is an efficient and powerful population-based stochastic global optimizer in continuous optimization problems, but it cannot be applied to the subpixel mapping problem in a discrete search space. In addition, it is not an easy task to properly set control parameters in DE. To avoid these problems, this paper utilizes an adaptive strategy without user-defined parameters, and a reversible-conversion strategy between continuous space and discrete space, to improve the classical DE algorithm. During the process of evolution, they are further improved by enhanced evolution operators, e.g., mutation, crossover, repair, exchange, insertion, and an effective local search to generate new candidate solutions. Experimental results using different types of remote images show that the ADESM algorithm consistently outperforms the previous subpixel mapping algorithms in all the experiments. Based on sensitivity analysis, ADESM, with its self-adaptive control parameter setting, is better than, or at least comparable to, the standard DE algorithm, when considering the accuracy of subpixel mapping, and hence provides an effective new approach to subpixel mapping for remote sensing imagery.

A Chaotic Approach of Differential Evolution Optimization Applied to Loudspeaker Design Problem

Over the past few years, the field of global optimization has been very active, producing different kinds of deterministic and stochastic algorithms for optimization in the continuous domain. These days, the use of evolutionary algorithms (EAs) to solve optimization problems is a common practice due to their competitive performance on complex search spaces. EAs are well known for their ability to deal with nonlinear and complex optimization problems. Differential evolution (DE) algorithms are a family of evolutionary optimization techniques that use a rather greedy and less stochastic approach to problem solving, when compared to classical evolutionary algorithms. The main idea is to construct, at each generation, for each element of the population a mutant vector, which is constructed through a specific mutation operation based on adding differences between randomly selected elements of the population to another element. Due to its simple implementation, minimum mathematical processing and good optimization capability, DE has attracted attention. This paper proposes a new approach to solve electromagnetic design problems that combines the DE algorithm with a generator of chaos sequences. This approach is tested on the design of a loudspeaker model with 17 degrees of freedom, for showing its applicability to electromagnetic problems. The results show that the DE algorithm with chaotic sequences presents better, or at least similar, results when compared to the standard DE algorithm and other evolutionary algorithms available in the literature.

Improved Differential Evolution Based on Stochastic Ranking for Robust Layout Synthesis of MEMS Components

This paper introduces an improved differential evolution (DE) algorithm for robust layout synthesis of microelectromechanical system components subject to inherent geometric uncertainties. A case study of the layout synthesis of a comb-driven microresonator shows that the approach proposed in this paper can lead to design results that meet the target performance and are less sensitive to geometric uncertainties than the typical designs. It is also demonstrated that the algorithm proposed in this paper cannot only obtain better results than the standard DE algorithm but also outperform some other state-of-the-art algorithms in constrained optimization.