Scalability of generalized adaptive differential evolution for large-scale continuous optimization

Differential evolution (DE) has become a very powerful tool for global continuous optimization problems. Parameter adaptations are the most commonly used techniques to improve its performance. The adoption of these techniques has assisted the success of many adaptive DE variants. However, most studies on these adaptive DEs are limited to some small-scale problems, e.g. with less than 100 decision variables, which may be quite small comparing to the requirements of real-world applications. The scalability performance of adaptive DE is still unclear. In this paper, based on the analyses of similarities and drawbacks of existing parameter adaptation schemes in DE, we propose a generalized parameter adaptation scheme. Applying the scheme to DE results in a new generalized adaptive DE (GaDE) algorithm. The scalability performance of GaDE is evaluated on 19 benchmark functions with problem scale from 50 to 1,000 decision variables. Based on the comparison with three other algorithms, GaDE is very competitive in both the performance and scalability aspects.     

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.     

Multi-population differential evolution with balanced ensemble of mutation strategies for large-scale global optimization

Differential evolution (DE) is a simple, yet very effective, population-based search technique. However, it is challenging to maintain a balance between exploration and exploitation behaviors of the DE algorithm. In this paper, we boost the population diversity while preserving simplicity by introducing a multi-population DE to solve large-scale global optimization problems. In the proposed algorithm, called mDE-bES, the population is divided into independent subgroups, each with different mutation and update strategies. A novel mutation strategy that uses information from either the best individual or a randomly selected one is used to produce quality solutions to balance exploration and exploitation. Selection of individuals for some of the tested mutation strategies utilizes fitness-based ranks of these individuals. Function evaluations are divided into epochs. At the end of each epoch, individuals between the subgroups are exchanged to facilitate information exchange at a slow pace. The performance of the algorithm is evaluated on a set of 19 large-scale continuous optimization problems. A comparative study is carried out with other state-of-the-art optimization techniques. The results show that mDE-bES has a competitive performance and scalability behavior compared to the contestant algorithms.     

Two-stage update biogeography-based optimization using differential evolution algorithm (DBBO)

The present paper proposes a new stochastic optimization algorithm as a hybridization of a relatively recent stochastic optimization algorithm, called biogeography-based optimization (BBO) with the differential evolution (DE) algorithm. This combination incorporates DE algorithm into the optimization procedure of BBO with an attempt to incorporate diversity to overcome stagnation at local optima. We also propose to implement an additional selection procedure for BBO, which preserves fitter habitats for subsequent generations. The proposed variation of BBO, named DBBO, is tested for several benchmark function optimization problems. The results show that DBBO can significantly outperform the basic BBO algorithm and can mostly emerge as the best solution providing algorithm among competing BBO and DE algorithms.     

多目标混沌差分进化算法

将差分进化算法用于多目标优化问题,提出了多目标混沌差分进化算法(CDEMO).该算法利用混沌序列初始化种群,并用混沌备用种群进行替换操作.该操作不仅起到了维持非劣最优解集均匀性的作用,而且增强了算法的搜索功能.对CDEMO的性能进行研究,数值实验结果表明了CDEMO的有效性.     

Learning-enhanced differential evolution for numerical optimization

Differential evolution (DE) is a simple and powerful population-based search algorithm, successfully used in various scientific and engineering fields. However, DE is not free from the problems of stagnation and premature convergence. Hence, designing more effective search strategies to enhance the performance of DE is one of the most salient and active topics. This paper proposes a new method, called learning-enhanced DE (LeDE) that promotes individuals to exchange information systematically. Distinct from the existing DE variants, LeDE adopts a novel learning strategy, namely clustering-based learning strategy (CLS). In CLS, there are two levels of learning strategies, intra-cluster learning strategy and inter-cluster learning strategy. They are adopted for exchanging information within the same cluster and between different clusters, respectively. Experimental studies over 23 benchmark functions show that LeDE significantly outperforms the conventional DE. Compared with other clustering-based DE algorithms, LeDE can obtain better solutions. In addition, LeDE is also shown to be significantly better than or at least comparable to several state-of-art DE variants as well as some other evolutionary algorithms.     

一种改进的约束优化差分进化算法

提出一种改进的差分进化算法用于求解约束优化问题.该算法在处理约束时不引入惩罚因子,使约束处理问题简单化.利用佳点集方法初始化个体以维持种群的多样性.结合差分进化算法两种不同变异策略的特点,对可行个体与不可行个体分别采用DE/best/1变异策略和DE/rand/1策略,以提高算法的全局收敛性能和收敛速率.用几个标准的Benchmark问题进行了测试,实验结果表明该算法是一种求解约束优化问题的有效方法.     

A 2-Opt based differential evolution for global optimization

Differential evolution (DE) is a simple and effective global optimization algorithm. It has been successfully applied to solve a wide range of real-world optimization problems. However, DE has shown some weaknesses, especially the long computational times because of its stochastic nature. This drawback sometimes limits its application to optimization problems. Therefore we propose the 2-Opt based DE (2-Opt DE) which is inspired by 2-Opt algorithms to accelerate DE. The novel mutation schemes of 2-Opt DE, DE/2-Opt/1 and DE/2-Opt/2 are substituted for mutation schemes of the original DE namely DE/rand/1 and DE/rand/2. We also provide a comparison of 2-Opt DE to DE. A comprehensive set of 19 benchmark functions is employed for experimental verification. The experimental results confirm that 2-Opt DE outperforms the original DE in terms of solution accuracy and convergence speed.     

Adaptive direction information in differential evolution for numerical optimization

Differential evolution (DE) is a powerful evolutionary algorithm (EA) for numerical optimization. It has been successfully used in various scientific and engineering fields. In most of the DE algorithms, the neighborhood and direction information are not fully and simultaneously exploited to guide the search. Most recently, to make full use of these information, a DE framework with neighborhood and direction information (NDi-DE) was proposed. It was experimentally demonstrated that NDi-DE was effective for most of the DE algorithms. However, the performance of NDi-DE heavily depends on the selection of direction information. To alleviate this drawback and improve the performance of NDi-DE, the adaptive operator selection (AOS) mechanism is introduced into NDi-DE to adaptively select the direction information for the specific DE mutation strategy. Therefore, a new DE framework, adaptive direction information based NDi-DE (aNDi-DE), is proposed in this study. With AOS, the good balance between exploration and exploitation of aNDi-DE can be dynamically achieved. In order to evaluate the effectiveness of aNDi-DE, the proposed framework is applied to the original DE algorithms, as well as several advanced DE variants. Experimental results show that aNDi-DE is able to adaptively select the most suitable type of direction information for the specific DE mutation strategy during the evolutionary process. The efficiency and robustness of aNDi-DE are also confirmed by comparing with NDi-DE.     

A self-adaptive differential evolution algorithm for continuous optimization problems

This paper proposes a new self-adaptive differential evolution algorithm (DE) for continuous optimization problems. The proposed self-adaptive differential evolution algorithm extends the concept of the DE/current-to-best/1 mutation strategy to allow the adaptation of the mutation parameters. The control parameters in the mutation operation are gradually self-adapted according to the feedback from the evolutionary search. Moreover, the proposed differential evolution algorithm also consists of a new local search based on the krill herd algorithm. In this study, the proposed algorithm has been evaluated and compared with the traditional DE algorithm and two other adaptive DE algorithms. The experimental results on 21 benchmark problems show that the proposed algorithm is very effective in solving complex optimization problems.     

An improved adaptive differential evolution algorithm for continuous optimization

1. Download : Download full-size image

     

Two hybrid differential evolution algorithms for engineering design optimization

This paper presents two hybrid differential evolution algorithms for optimizing engineering design problems. One hybrid algorithm enhances a basic differential evolution algorithm with a local search operator, i.e., random walk with direction exploitation, to strengthen the exploitation ability, while the other adding a second metaheuristic, i.e., harmony search, to cooperate with the differential evolution algorithm so as to produce the desirable synergetic effect. For comparison, the differential evolution algorithm that the two hybrids are based on is also implemented. All algorithms incorporate a generalized method to handle discrete variables and Deb's parameterless penalty method for handling constraints. Fourteen engineering design problems selected from different engineering fields are used for testing. The test results show that: (i) both hybrid algorithms overall outperform the differential evolution algorithms; (ii) among the two hybrid algorithms, the cooperative hybrid overall outperforms the other hybrid with local search; and (iii) the performance of proposed hybrid algorithms can be further improved with some effort of tuning the relevant parameters.     

An improved decomposition method for large-scale global optimization: bidirectional-detection differential grouping

Applied Intelligence - Differential grouping (DG) is an efficient decomposition method that is used to solve large-scale global optimization (LSGO) problems. To further reduce the computational...     

一种改进的多目标约束优化差分进化算法

提出一种新的多目标优化差分进化算法用于求解约束优化问题.该算法利用佳点集方法初始化个体以维持种群的多样性.将约束优化问题转化为两个目标的多目标优化问题.基于Pareto支配关系,将种群分为Pareto子集和Non-Pareto子集,结合差分进化算法两种不同变异策略的特点,对Non-Pareto子集和Pareto子集分别采用DE/best/1变异策略和DE/rand/1变异策略.数值实验结果表明该算法具有较好的寻优效果.     

Circle detection using discrete differential evolution optimization

This paper introduces a circle detection method based on differential evolution (DE) optimization. Just as circle detection has been lately considered as a fundamental component for many computer vision algorithms, DE has evolved as a successful heuristic method for solving complex optimization problems, still keeping a simple structure and an easy implementation. It has also shown advantageous convergence properties and remarkable robustness. The detection process is considered similar to a combinational optimization problem. The algorithm uses the combination of three edge points as parameters to determine circle candidates in the scene yielding a reduction of the search space. The objective function determines if some circle candidates are actually present in the image. This paper focuses particularly on one DE-based algorithm known as the discrete differential evolution (DDE), which eventually has shown better results than the original DE in particular for solving combinatorial problems. In the DDE, suitable conversion routines are incorporated into the DE, aiming to operate from integer values to real values and then getting integer values back, following the crossover operation. The final algorithm is a fast circle detector that locates circles with sub-pixel accuracy even considering complicated conditions and noisy images. Experimental results on several synthetic and natural images with varying range of complexity validate the efficiency of the proposed technique considering accuracy, speed, and robustness.     

Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization

We propose a novel hybrid algorithm named PSO-DE, which integrates particle swarm optimization (PSO) with differential evolution (DE) to solve constrained numerical and engineering optimization problems. Traditional PSO is easy to fall into stagnation when no particle discovers a position that is better than its previous best position for several generations. DE is incorporated into update the previous best positions of particles to force PSO jump out of stagnation, because of its strong searching ability. The hybrid algorithm speeds up the convergence and improves the algorithm’s performance. We test the presented method on 11 well-known benchmark test functions and five engineering optimization functions. Comparisons show that PSO-DE outperforms or performs similarly to seven state-of-the-art approaches in terms of the quality of the resulting solutions.     

Global replacement-based differential evolution with neighbor-based memory for dynamic optimization

Dynamic optimization problems challenge the evolutionary algorithms, owing to the diversity loss or the low search efficiency of the algorithms, especially when the problems change frequently. This paper presents a novel differential evolution algorithm to address the dynamic optimization problems. Unlike the most used “DE/rand/1” mutation operator, in this paper, the “DE/best/1” mutation is employed to generate a mutant individual. In order to enhance the search efficiency of differential evolution, the classical differential evolution algorithm is modified by a novel replacement operator, in which the worst individual in the whole population is replaced by the newly generated trial vector as a “steady-state” manner. During optimizing, some newly generated solutions are stored into a memory set, in which these stored solutions are located around the current best solution. When the environmental change is detected, the stored solutions are expected to guide the reinitialized solutions to track the new location of global optimum as soon as possible. The performance of the proposed algorithm is compared with six state-of-the-art dynamic evolutionary algorithms over some benchmark problems. The experimental results show that the proposed algorithm clearly outperforms the competitors.     

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.     

Three modified versions of differential evolution algorithm for continuous optimization

Differential evolution (DE) is one simple and effective evolutionary algorithm (EA) for global optimization. In this paper, three modified versions of the DE to improve its performance, to repair its defect in accurate converging to individual optimal point and to compensate the limited amount of search moves of original DE are proposed. In the first modified version called bidirectional differential evolution (BDE), to generate a new trial point, is used from the bidirectional optimization concept, and in the second modified version called shuffled differential evolution (SDE), population such as shuffled frog leaping (SFL) algorithm is divided in to several memeplexes and each memeplex is improved by the DE algorithm. Finally, in the third modified version of DE called shuffled bidirectional differential evolution (SBDE) to improve each memeplex is used from the proposed BDE algorithm. Three proposed modified versions are applied on two types of DE and six obtained algorithms are compared with original DE and SFL algorithms. Experiments on continuous benchmark functions and non-parametric analysis of obtained results demonstrate that applying bidirectional concept only improves one type of the DE. But the SDE and the SBDE have a better success rate and higher solution precision than original DE and SFL, whereas those are more time consuming on some functions. In a later part of the comparative experiments, a comparison of the proposed algorithms with some modern DE and the other EAs reported in the literature confirms a better or at least comparable performance of our proposed algorithms.     

A novel modified differential evolution algorithm for constrained optimization problems

A novel modified differential evolution algorithm (NMDE) is proposed to solve constrained optimization problems in this paper. The NMDE algorithm modifies scale factor and crossover rate using an adaptive strategy. For any solution, if it is at a standstill, its own scale factor and crossover rate will be adjusted in terms of the information of all successful solutions. We can obtain satisfactory feasible solutions for constrained optimization problems by combining the NMDE algorithm and a common penalty function method. Experimental results show that the proposed algorithm can yield better solutions than those reported in the literature for most problems, and it can be an efficient alternative to solving constrained optimization problems.