Adaptive Differential Evolution Variants Research Articles

Differential Evolution and Engineering Problems

In this paper, the performance of the Differential Evolution algorithm is evaluated when solving real-world problems. A Set of 13 engineering optimisation problems was selected from the fields of mechanics and industry to illustrate the usability of the Differential Evolution algorithm. Twelve variants of the standard Differential Evolution with various settings of the control parameters are compared with 19 state-of-the-art adaptive variants of this algorithm. The results are analysed statistically to achieve significant differences. Three variants of adaptive Differential Evolution provided better results compared to other algorithms. Some adaptive variants of Differential Evolution perform significantly worse than the original Differential Evolution with the fixed setting of the control parameters.

Differential Evolution with Autonomous Selection of Mutation Strategies and Control Parameters and Its Application

The existing numerous adaptive variants of differential evolution (DE) have been improved the search ability of classic DE to certain extent. Nevertheless, those variants of DE do not obtain the promising performance in solving black box problems with unknown features, which is mainly because the adaptive rules of those variants are designed according to their designers’ cognition on the problem features. To enhance the optimization ability of DE in optimizing black box problems with unknown features, a differential evolution with autonomous selection of mutation strategies and control parameters (ASDE) is proposed in this paper, inspired by autonomous decision‐making mechanism of reinforcement learning. In ASDE, a historical experience archive with population features is utilized to preserve accumulated historical experience of the combination of mutation strategies and control parameters. Furthermore, the accumulated historical experience can be autonomously mapped into rules repository, and the individuals can choose the combination of mutation strategies and control parameters according to those rules. Additionally, an updating and utilization mechanism of the historical experience is designed to assure that the historical experience can be effectively accumulated and utilized efficiently. Compared with some state‐of‐the‐art intelligence algorithms on 15 functions of CEC2015, 28 functions of CEC2017, and parameter extraction problems of the photovoltaic model, ASDE has the advantages of solution accuracy, convergence speed, and robustness in solving black box problems with unknown features.

Honey Badger Algorithm: New metaheuristic algorithm for solving optimization problems

Recently, the numerical optimization field has attracted the research community to propose and develop various metaheuristic optimization algorithms. This paper presents a new metaheuristic optimization algorithm called Honey Badger Algorithm (HBA). The proposed algorithm is inspired from the intelligent foraging behavior of honey badger, to mathematically develop an efficient search strategy for solving optimization problems. The dynamic search behavior of honey badger with digging and honey finding approaches are formulated into exploration and exploitation phases in HBA. Moreover, with controlled randomization techniques, HBA maintains ample population diversity even towards the end of the search process. To assess the efficiency of HBA, 24 standard benchmark functions, CEC’17 test-suite, and four engineering design problems are solved. The solutions obtained using the HBA have been compared with ten well-known metaheuristic algorithms including Simulated annealing (SA), Particle Swarm Optimization (PSO), Covariance Matrix Adaptation Evolution Strategy (CMA-ES), Success-History based Adaptive Differential Evolution variants with linear population size reduction (L-SHADE), Moth-flame Optimization (MFO), Elephant Herding Optimization (EHO), Whale Optimization Algorithm (WOA), Grasshopper Optimization Algorithm (GOA), Thermal Exchange Optimization (TEO) and Harris hawks optimization (HHO). The experimental results, along with statistical analysis, reveal the effectiveness of HBA for solving optimization problems with complex search-space, as well as, its superiority in terms of convergence speed and exploration–exploitation balance, as compared to other methods used in this study. The source code of HBA is currently available for public at https://www.mathworks.com/matlabcentral/fileexchange/98204-honey-badger-algorithm.

2D multi-area coverage path planning using L-SHADE in simulated ocean survey

Ocean environmental surveys typically involve multi-area coverage path planning tasks. The most important problem is improving the coverage efficiency of the task. A new path planning method based on Successful History-Based Adaptive Differential Evolution variants with Linear population size reduction(L-SHADE) is presented to solve this problem. The method comprises two parts: the part of sub area coverage path planning and the part of finding the optimized sequence of sub area start points. The key idea is establishing the relationship between the starting point of each sub area and the optimized multi-area path. We implement the method through numbering the possible starting point of sub area path and proposing a computing formula. In addition, the results of L-SHADE mutation process are optimized which make L-SHADE possible to apply in multi-area coverage path planning. This method avoids area discretization and exponential growth of computational quantities, and it is suitable for complex areas as well as multi-area. The simulation results with MATLAB showed the improvement of coverage path planning task execution efficiency. Compared with the method thinking of the sub area as the center of it, our method reduced the multi-area coverage path length by 4%–7%. From the simulations and analysis, we concluded that the method is able to improve the efficiency and stability of multi-area coverage path planning.

Adaptive Distributed Differential Evolution.

Due to the increasing complexity of optimization problems, distributed differential evolution (DDE) has become a promising approach for global optimization. However, similar to the centralized algorithms, DDE also faces the difficulty of strategies' selection and parameters' setting. To deal with such problems effectively, this article proposes an adaptive DDE (ADDE) to relieve the sensitivity of strategies and parameters. In ADDE, three populations called exploration population, exploitation population, and balance population are co-evolved concurrently by using the master-slave multipopulation distributed framework. Different populations will adaptively choose their suitable mutation strategies based on the evolutionary state estimation to make full use of the feedback information from both individuals and the whole corresponding population. Besides, the historical successful experience and best solution improvement are collected and used to adaptively update the individual parameters (amplification factor F and crossover rate CR) and population parameter (population size N), respectively. The performance of ADDE is evaluated on all 30 widely used benchmark functions from the CEC 2014 test suite and all 22 widely used real-world application problems from the CEC 2011 test suite. The experimental results show that ADDE has great superiority compared with the other state-of-the-art DDE and adaptive differential evolution variants.

Comparison of nature-inspired population-based algorithms on continuous optimisation problems

Eleven swarm-intelligence-based (SI) and bio-inspired (BI) algorithms are compared with four advanced adaptive differential evolution (DE) variants, the classic DE and the blind random search on two benchmark sets. One of the benchmark sets is the CEC 2011 collection of 22 real-world optimisation problems, the latter is the suite of 30 artificial optimisation problems defined for the competition of the algorithms within CEC 2014. The results of the experiments demonstrate the superiority of the adaptive DE variants both on real-world problems and the artificial CEC 2014 test suite at all the levels of dimension (10, 30, and 50). Some of the SI and BI algorithms perform even worse than the blind random search. The efficiency of the classic DE is comparable with the better performing SI and BI methods. The results entitle to form a recommendation for practitioners: Do not propose a pseudo-new algorithm but select from the optimisation algorithms supported by thorough research and good ranking at international competitions of optimisation algorithms.

Optimized PID Controller Using Adaptive Differential Evolution with Meanof-pbest Mutation Strategy

On the basis of JADE (adaptive differential evolution with optional external archive) and the modified differential evolution with <i>p</i>-best crossover (MDE_<i>p</i>BX), this study attempts to propose a modified mutation strategy termed "DE/(<i>p</i>best)/1" for the differential evolution (DE) algorithm, where “(<i>p</i>best)” represents the mean of p top-best vectors. Two modified parameter adaptation mechanisms are also proposed to update the crossover rate and the scale factor, respectively, in an adaptive manner. The DE variant with the proposed mutation strategy and two modified adaptation mechanisms is termed adaptive differential evolution with mean-of-<i>p</i>best mutation strategy, denoted by ADE_<i>p</i>BM is comparable to or better than the four state-of-the-art adaptive DE variants in terms of accuracy, reliability and efficiency.

The contour fitting property of differential mutation

State-of-the-art global optimization techniques adapt the search range and direction to the objective function. Differential Evolution algorithms perform this adaptation implicitly, leading to a contour fitting property which has been empirically observed, but lacks theoretical grounding. In this paper, we formalize the contour fitting notion and derive an analytical model that links the differential mutation operator with the adaptation of the range and direction of search. Our analysis uses the Differential Mutation Evolutionary Algorithm (DMEA), which optimizes the multidimensional Gaussian objective function. Through our analysis, we are able to make several observations. Firstly, a normally distributed population remains normal in consecutive iterations. Moreover, parameters of the population distribution can be updated with explicit algebraic formulas. Furthermore, for a scaling factor below a critical value, the population reaches a stable state. Finally, the covariance matrix of a population in a stable state is proportional to the covariance matrix of the Gaussian objective function. The analytical results explaining the contour fitting property are confirmed with a simulation study. Although this work focuses on theoretical analyses, the proposed DE/prop/1 mutation and DMEA algorithm maintain population diversity and therefore, can lead to optimization by means of saddle-crossing and can become a basis for adaptive Markov Chain Monte Carlo sampling schemes or an element of strategy adaptive differential evolution variants. The latter approach was tested on the CEC 2017 benchmark and found to significantly improve the performance of the SaDE algorithm.

Algorithmic design issues in adaptive differential evolution schemes: Review and taxonomy

Abstract The performance of most metaheuristic algorithms depends on parameters whose settings essentially serve as a key function in determining the quality of the solution and the efficiency of the search. A trend that has emerged recently is to make the algorithm parameters automatically adapt to different problems during optimization, thereby liberating the user from the tedious and time-consuming task of manual setting. These fine-tuning techniques continue to be the object of ongoing research. Differential evolution (DE) is a simple yet powerful population-based metaheuristic. It has demonstrated good convergence, and its principles are easy to understand. DE is very sensitive to its parameter settings and mutation strategy; thus, this study aims to investigate these settings with the diverse versions of adaptive DE algorithms. This study has two main objectives: (1) to present an extension for the original taxonomy of evolutionary algorithms (EAs) parameter settings that has been overlooked by prior research and therefore minimize any confusion that might arise from the former taxonomy and (2) to investigate the various algorithmic design schemes that have been used in the different variants of adaptive DE and convey them in a new classification style. In other words, this study describes in depth the structural analysis and working principle that underlie the promising and recent work in this field, to analyze their advantages and disadvantages and to gain future insights that can further improve these algorithms. Finally, the interpretation of the literature and the comparative analysis of the algorithmic schemes offer several guidelines for designing and implementing adaptive DE algorithms. The proposed design framework provides readers with the main steps required to integrate any proposed meta-algorithm into parameter and/or strategy adaptation schemes.

Nature-Inspired Algorithms in Real-World Optimization Problems

Eight popular nature inspired algorithms are compared with the blind random search and three advanced adaptive variants of differential evolution (DE) on real-world problems benchmark collected for CEC 2011 algorithms competition. The results show the good performance of the adaptive DE variants and their superiority over the other algorithms in the test problems. Some of the nature-inspired algorithms perform even worse that the blind random search in some problems. This is a strong argument for recommendation for application, where well-verified algorithm successful in competitions should be preferred instead of developing some new algorithms.

Levy distributed parameter control in differential evolution for numerical optimization

Differential evolution (DE) algorithm is a population based stochastic search technique widely applied in scientific and engineering fields for global optimization over real parameter space. The performance of DE algorithm highly depends on the selection of values of the associated control parameters. Therefore, finding suitable values of control parameters is a challenging task and researchers have already proposed several adaptive and self-adaptive variants of DE. In the paper control parameters are adapted by levy distribution, named as Levy distributed DE (LdDE) which efficiently handles exploration and exploitation dilemma in the search space. In order to assure a fair comparison with existing parameter controlled DE algorithms, we apply the proposed method on number of well-known unimodal, basic and expanded multimodal and hybrid composite benchmark optimization functions having different dimensions. The empirical study shows that the proposed LdDE algorithm exhibits an overall better performance in terms of accuracy and convergence speed compared to five prominent adaptive DE algorithms.

System identification and control of robot manipulator based on fuzzy adaptive differential evolution algorithm

A requirement for new robotic manipulators is the ability to detect and manipulate objects in their environments. Robotic manipulators are highly nonlinear systems, and an accurate mathematical model is difficult to obtain using conventional techniques. Therefore, an efficient technique is required to deal with these types of complex and dynamic systems. Differential Evolution (DE) algorithm is a very powerful optimization technique and has become popular in many fields. Arguably, it is now one of the most predominant stochastic algorithms for real-parameter optimization. However, DE is very sensitive to its control parameters of the mutation operation (F) and crossover operation (CR) in such a way that their fine tuning greatly affect DE performance. Fuzzy Adaptive DE (FADE) algorithm is one of the well known adaptive DE variants that show superiority and reliability in solving different types of optimization problems. The objective of this article is to develop a new dynamic parameter identification framework to estimate the barycentric parameters of the CRS A456 robot manipulator based on FADE. The simulation results presented in this paper show the effectiveness of the FADE method over other conventional techniques, transcending the limits of the existing state-of-the-art algorithms in solving the problem of robot.

RDEL: Restart Differential Evolution algorithm with Local Search Mutation for global numerical optimization

In this paper, a novel version of Differential Evolution (DE) algorithm based on a couple of local search mutation and a restart mechanism for solving global numerical optimization problems over continuous space is presented. The proposed algorithm is named as Restart Differential Evolution algorithm with Local Search Mutation (RDEL). In RDEL, inspired by Particle Swarm Optimization (PSO), a novel local mutation rule based on the position of the best and the worst individuals among the entire population of a particular generation is introduced. The novel local mutation scheme is joined with the basic mutation rule through a linear decreasing function. The proposed local mutation scheme is proven to enhance local search tendency of the basic DE and speed up the convergence. Furthermore, a restart mechanism based on random mutation scheme and a modified Breeder Genetic Algorithm (BGA) mutation scheme is combined to avoid stagnation and/or premature convergence. Additionally, an exponent increased crossover probability rule and a uniform scaling factors of DE are introduced to promote the diversity of the population and to improve the search process, respectively. The performance of RDEL is investigated and compared with basic differential evolution, and state-of-the-art parameter adaptive differential evolution variants. It is discovered that the proposed modifications significantly improve the performance of DE in terms of quality of solution, efficiency and robustness.

A new self-adaptation scheme for differential evolution

The performance of Differential Evolution (DE) largely depends on the choice of trial vector generation strategy and the values of its control parameters. In the past years, quite a few DE variants have been developed to adaptively adjust the strategy and control parameters during the search process. However, these variants may not perform satisfactorily when coping with computationally expensive problems (CEPs) for which a satisfying solution needs to be obtained with very limited fitness evaluations (FEs). In this paper, we demonstrate that not only can surrogate models be used to approximate the fitness function, they can also provide a good alternative method to adapt the strategy and control parameters of DE, and thus propose a framework called DE with Surrogate-assisted Self-Adaptation (DESSA). DESSA generates multiple trial vectors using different trial vector generation strategies and parameter settings, and then employs a surrogate model to identify the potentially best trial vector to undergo real fitness evaluation. As each trial vector corresponds to a unique combination of strategy and parameter setting, the surrogate model acts like a strategy/parameter setting selector that aims to identify the most suitable strategy and parameter setting for each target vector. Since DESSA can be easily combined with different DE variants, three concrete DE variants, namely DESSA-CoDE, DESSA-SaDE, and DESSA-CoDE*, are proposed. Comprehensive empirical studies demonstrate that DESSA can lead to superior performance over the compared adaptive DE variants. More importantly, it is shown that DESSA has the potential of accommodating more search strategies, which may lead to novel DE variants with even more competitive performance.

Repairing the crossover rate in adaptive differential evolution

Differential evolution (DE) is a simple yet powerful evolutionary algorithm (EA) for global numerical optimization. However, its performance is significantly influenced by its parameters. Parameter adaptation has been proven to be an efficient way for the enhancement of the performance of the DE algorithm. Based on the analysis of the behavior of the crossover in DE, we find that the trial vector is directly related to its binary string, but not directly related to the crossover rate. Based on this inspiration, in this paper, we propose a crossover rate repair technique for the adaptive DE algorithms that are based on successful parameters. The crossover rate in DE is repaired by its corresponding binary string, i.e. by using the average number of components taken from the mutant. The average value of the binary string is used to replace the original crossover rate. To verify the effectiveness of the proposed technique, it is combined with an adaptive DE variant, JADE, which is a highly competitive DE variant. Experiments have been conducted on 25 functions presented in CEC-2005 competition. The results indicate that our proposed crossover rate technique is able to enhance the performance of JADE. In addition, compared with other DE variants and state-of-the-art EAs, the improved JADE method obtains better, or at least comparable, results in terms of the quality of final solutions and the convergence rate.

Real parameter optimization by an effective differential evolution algorithm

This paper introduces an Effective Differential Evolution (EDE) algorithm for solving real parameter optimization problems over continuous domain. The proposed algorithm proposes a new mutation rule based on the best and the worst individuals among the entire population of a particular generation. The mutation rule is combined with the basic mutation strategy through a linear decreasing probability rule. The proposed mutation rule is shown to promote local search capability of the basic DE and to make it faster. Furthermore, a random mutation scheme and a modified Breeder Genetic Algorithm (BGA) mutation scheme are merged to avoid stagnation and/or premature convergence. Additionally, the scaling factor and crossover of DE are introduced as uniform random numbers to enrich the search behavior and to enhance the diversity of the population. The effectiveness and benefits of the proposed modifications used in EDE has been experimentally investigated. Numerical experiments on a set of bound-constrained problems have shown that the new approach is efficient, effective and robust. The comparison results between the EDE and several classical differential evolution methods and state-of-the-art parameter adaptive differential evolution variants indicate that the proposed EDE algorithm is competitive with , and in some cases superior to, other algorithms in terms of final solution quality, efficiency, convergence rate, and robustness.

SYNCHRONOUS AND ASYNCHRONOUS MIGRATION IN ADAPTIVE DIFFERENTIAL EVOLUTION ALGORITHMS

The influence of synchronous and asynchronous migration on the per- formance of adaptive differential evolution algorithms is investigated. Six adaptive differential evolution variants are employed by the parallel migration model with a star topology. Synchronous and asynchronous migration models with various parameters settings were experimentally compared with non-parallel adaptive al- gorithms in six shifted benchmark problems of dimension D = 30. Three different ways of exchanging individuals are applied in a synchronous island model with a fixed number of islands. Three different numbers of sub-populations are set up in an asynchronous island model. The parallel synchronous and asynchronous migration models increase performance in most problems.

A COMBINED APPROACH TO ADAPTIVE DIFFERENTIAL EVOLUTION

The paper deals with the adaptive mechanisms in differential evolution (DE) algorithm. DE is a simple and effective stochastic algorithm frequently used in solving the real-world global optimization problems. The efficiency of the algo- rithm is sensitive to setting its control parameters. Several adaptive approaches have appeared recently in order to avoid control-parameter tuning. A new adaptive variant of differential evolution is proposed in this study. It is based on a combina- tion of two adaptive approaches published before. The new algorithm was tested on the well-known set of benchmark problems developed for the special session of CEC2005 at four levels of population size and its performance was compared with the adaptive variants that were applied in the design of the new algorithm. The new adaptive DE variant outperformed the others in several test problems but its efficiency on average was not better.

Towards Improving Self-adaptive Differential Evolution for Numerical Optimization: A Progress Note

Differential evolution (DE) is a popular, simple, fast, efficient and stochastic optimization technique which shows a solid performance for diverse continuous optimization problems. However, the control parameters used in DE are fixed. This fact motivated many researchers in past few years to present improved variants of DE. It has been done by (1) modifying the self structure of DE, (2) integrating additional components within the structure of DE. For each category, several algorithms have been reported in the literature. Among of them, in this article, we have been selected four self structural modified adaptive variants of DE, called DE/best/1, DE with random scale factor, DE with time varying scale factor, modified differential evolution, after studying their working principles. Performance comparisons of all these algorithms are provided against the classical DE for ten numerical benchmark functions with the following performance measures: solution quality, number of generations required to find the optimal solution and frequency of finding the optimal solution. From the simulation results, it has been observed that the convergence speed of the recently proposed modified differential evolution is significantly better than others. Also statistical significance test has been carried out to establish the statistical significance of the results.

Modified differential evolution approach for optimization of planar parallel manipulators force capabilities

The global optimization problem is not easy to solve and is still an open challenge for researchers since an analytical optimal solution is difficult to obtain even for relatively simple application problems. Conventional deterministic numerical algorithms tend to stop the search in local minimum nearest to the input starting point, mainly when the optimization problem presents nonlinear, non-convex and non-differential functions, multimodal and nonlinear. Nowadays, 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. The primary advantage of EAs over other numerical methods is that they just require the objective function values, while properties such as differentiability and continuity are not necessary. In this context, the differential evolution (DE), a paradigm of the evolutionary computation, has been widely used for solving numerical global optimization problems in continuous search space. DE is a powerful population-based stochastic direct search method. DE simulates natural evolution combined with a mechanism to generate multiple search directions based on the distribution of solutions in the current population. Among DE advantages are its simple structure, ease of use, speed, and robustness, which allows its application on several continuous nonlinear optimization problems. However, the performance of DE greatly depends on its control parameters, such as crossover rate, mutation factor, and population size and it often suffers from being trapped in local optima. Conventionally, users have to determine the parameters for problem at hand empirically. Recently, several adaptive variants of DE have been proposed. In this paper, a modified differential evolution (MDE) approach using generation-varying control parameters (mutation factor and crossover rate) is proposed and evaluated. The proposed MDE presents an efficient strategy to improve the search performance in preventing of premature convergence to local minima. The efficiency and feasibility of the proposed MDE approach is demonstrated on a force optimization problem in Robotics, where the force capabilities of a planar 3-RRR parallel manipulator are evaluated considering actuation limits and different assembly modes. Furthermore, some comparison results of MDE approach with classical DE to the mentioned force optimization problem are presented and discussed.