Memory based Hybrid Dragonfly Algorithm for numerical optimization problems

Dragonfly algorithm (DA) is a recently proposed optimization algorithm based on the static and dynamic swarming behaviour of dragonflies. Due to its simplicity and efficiency, DA has received interest of researchers from different fields. However, it lacks internal memory which may lead to its premature convergence to local optima. To overcome this drawback, we propose a novel Memory based Hybrid Dragonfly Algorithm (MHDA) for solving numerical optimization problems. The pbestand gbest concept of Particle Swarm optimization (PSO) is added to conventional DA to guide the search process for potential candidate solutions and PSO is then initialized with pbest of DA to further exploit the search space. The proposed method combines the exploration capability of DA and exploitation capability of PSO to achieve global optimal solutions. The efficiency of the MHDA is validated by testing on basic unconstrained benchmark functions and CEC 2014 test functions. A comparative performance analysis between MHDA and other powerful optimization algorithms have been carried out and significance of the results is proved by statistical methods. The results show that MHDA gives better performance than conventional DA and PSO. Moreover, it gives competitive results in terms of convergence, accuracy and search-ability when compared with the state-of-the-art algorithms. The efficacy of MHDA in solving real world problems is also explained with three engineering design problems.     

采用双变异策略的自适应差分进化算法及应用

为了克服差分进化算法早熟收敛和寻优精度低的缺点,提出一种采用双变异策略的自适应差分进化算法（Adaptive Differential Evolution Algorithm using Double mutation strategies,DADE）。DADE引入基于种群相似度和中心解的双变异策略,有效平衡了算法的全局搜索和局部搜索;自适应交叉概率使种群个体向更新成功的个体学习,有利于后续种群的进化。在7个测试函数和3个电力系统动态经济调度（Dynamic Economic Dispatch,DED）问题上的优化结果表明,DADE算法与其他4种DE算法相比具有更强的全局寻优能力,且对电力系统动态经济调度问题的优化结果优于文献中所报道的结果。     

A DE and PSO based hybrid algorithm for dynamic optimization problems

Many real world optimization problems are dynamic in which the fitness landscape is time dependent and the optima change over time. Such problems challenge traditional optimization algorithms. For such problems, optimization algorithms not only have to find the global optimum but also need to closely track its trajectory. In this paper, a new hybrid algorithm integrating a differential evolution (DE) and a particle swarm optimization (PSO) is proposed for dynamic optimization problems. Multi-population strategy is adopted to enhance the diversity and try to keep each subpopulation on a different peak in the fitness landscape. A hybrid operator combining DE and PSO is designed, in which each individual is sequentially carried out DE and PSO operations. An exclusion scheme is proposed that integrates the distance based exclusion scheme with the hill-valley function to track the adjacent peaks. The algorithm is applied to the set of benchmark functions used in CEC 2009 competition for dynamic environment. Experimental results show that it is more effective in terms of overall performance than other comparative algorithms.     

求解约束优化问题的复合人工蜂群算法

针对约束优化问题,提出一种复合人工蜂群算法.该算法引入多维随机变异操作和最优引导变异操作平衡算法的探索能力和开发能力.将ε约束和可行性规则相结合平衡目标函数与约束,加快算法的收敛.通过对CEC 2006中20个测试函数和CEC 2010中18个测试函数及3个实际工程优化问题的实验结果分析表明,该算法对约束优化问题可行有...     

A novel differential evolution algorithm for solving constrained engineering optimization problems

This paper introduces a novel differential evolution (DE) algorithm for solving constrained engineering optimization problems called (NDE). The key idea of the proposed NDE is the use of new triangular mutation rule. It is based on the convex combination vector of the triplet defined by the three randomly chosen vectors and the difference vectors between the best, better and the worst individuals among the three randomly selected vectors. The main purpose of the new approach to triangular mutation operator is the search for better balance between the global exploration ability and the local exploitation tendency as well as enhancing the convergence rate of the algorithm through the optimization process. In order to evaluate and analyze the performance of NDE, numerical experiments on three sets of test problems with different features, including a comparison with thirty state-of-the-art evolutionary algorithms, are executed where 24 well-known benchmark test functions presented in CEC’2006, five widely used constrained engineering design problems and five constrained mechanical design problems from the literature are utilized. The results show that the proposed algorithm is competitive with, and in some cases superior to, the compared ones in terms of the quality, efficiency and robustness of the obtained final solutions.     

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.     

Improving the performance of differential evolution algorithm using Cauchy mutation

Differential evolution (DE) is a powerful yet simple evolutionary algorithm for optimization of real-valued, multimodal functions. DE is generally considered as a reliable, accurate and robust optimization technique. However, the algorithm suffers from premature convergence and/or slow convergence rate resulting in poor solution quality and/or larger number of function evaluation resulting in large CPU time for optimizing the computationally expensive objective functions. Therefore, an attempt to speed up DE is considered necessary. This research introduces a modified differential evolution (MDE) that enhances the convergence rate without compromising with the solution quality. The proposed MDE algorithm maintains a failure_counter (FC) to keep a tab on the performance of the algorithm by scanning or monitoring the individuals. Finally, the individuals that fail to show any improvement in the function value for a successive number of generations are subject to Cauchy mutation with the hope of pulling them out of a local attractor which may be the cause of their deteriorating performance. The performance of proposed MDE is investigated on a comprehensive set of 15 standard benchmark problems with varying degrees of complexities and 7 nontraditional problems suggested in the special session of CEC2008. Numerical results and statistical analysis show that the proposed modifications help in locating the global optimal solution in lesser numbers of function evaluation in comparison with basic DE and several other contemporary optimization algorithms.     

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.     

An improved electromagnetism-like mechanism algorithm for constrained optimization

Many problems in scientific research and engineering applications can be decomposed into the constrained optimization problems. Most of them are the nonlinear programming problems which are very hard to be solved by the traditional methods. In this paper, an electromagnetism-like mechanism (EM) algorithm, which is a meta-heuristic algorithm, has been improved for these problems. Firstly, some modifications are made for improving the performance of EM algorithm. The process of calculating the total force is simplified and an improved total force formula is adopted to accelerate the searching for optimal solution. In order to improve the accuracy of EM algorithm, a parameter called as move probability is introduced into the move formula where an elitist strategy is also adopted. And then, to handle the constraints, the feasibility and dominance rules are introduced and the corresponding charge formula is used for biasing feasible solutions over infeasible ones. Finally, 13 classical functions, three engineering design problems and 22 benchmark functions in CEC’06 are tested to illustrate the performance of proposed algorithm. Numerical results show that, compared with other versions of EM algorithm and other state-of-art algorithms, the improved EM algorithm has the advantage of higher accuracy and efficiency for constrained optimization problems.     

An adaptive surrogate assisted differential evolutionary algorithm for high dimensional constrained problems

Differential evolution (DE) is a competitive algorithm for constrained optimization problems (COPs). In this study, in order to improve the efficiency and accuracy of the DE for high dimensional problems, an adaptive surrogate assisted DE algorithm, called ASA-DE is suggested. In the ASA, several kinds of surrogate modeling techniques are integrated. Furthermore, to avoid violate the constraints and obtain better solution simultaneously, adaptive strategies for population size and mutation are also suggested in this study. The suggested adaptive population strategy which controls the exploring and exploiting states according to whether algorithm find enough feasible solution is similar to a state switch. The mutation strategy is used to enhance the effect of state switch based on adaptive population size. Finally, the suggested ASA-DE is evaluated on the benchmark problems from congress on evolutionary computation (CEC) 2017 constrained real parameter optimization. The experimental results show the proposed algorithm is a competitive one compared to other state-of-the-art algorithms.     

基于简化群优化算法和协方差矩阵学习的差分进化算法

把SSO算法的交叉策略、协方差矩阵学习策略与传统的DE算法结合,提出一个新的DE算法的变种,我们把它称作SCDE算法。正如我们所知,DE算法的变异策略在DE算法中占据了非常重要的位置,然而,传统的DE算法的变异策略都是用相对位置来产生候选解,本文尝试利用个体历史最优解来诱导变异产生候选解,这将大大提高种群跳出局部最优的能力。此外,将算法的变异和交叉操作放在由种群的协方差矩阵的所有特征向量组成的坐标系中执行,这将使算法的交叉和变异操作具有旋转不变性。实验结果表明,本文提出的新的交叉和变异策略可以大大提高DE算法在CEC 2013中28个测试函数的全局寻优能力。     

多策略融合算术优化算法及其工程优化

针对算术优化算法(AOA)在搜索过程中容易陷入局部极值点、收敛速度慢以及求解精度低等缺陷,提出一种多策略集成的算术优化算法(MFAOA)。首先,采用Sobol序列初始化AOA种群,增加初始个体的多样性,为算法全局寻优奠定基础;然后,重构数学优化器加速函数(MOA),权衡全局搜索与局部开发过程的比重;最后,利用混沌精英突变策略,改善算法过于依赖当前最优解的问题,增强算法跳出局部极值的能力。选用12个基准函数和部分CEC2014测试函数进行实验仿真,结果表明MFAOA在求解精度和收敛速度上均有明显的提升;另外,通过对两个工程实例进行优化,验证了MFAOA在工程优化问题上的可行性。     

Artificial algae algorithm (AAA) for nonlinear global optimization

In this study, a novel bio-inspired metaheuristic optimization algorithm called artificial algae algorithm (AAA) inspired by the living behaviors of microalgae, photosynthetic species, is introduced. The algorithm is based on evolutionary process, adaptation process and the movement of microalgae. The performance of the algorithm has been verified on various benchmark functions and a real-world design optimization problem. The CEC’05 function set was employed as benchmark functions and the test results were compared with the algorithms of Artificial Bee Colony (ABC), Bee Algorithm (BA), Differential Evolution (DE), Ant Colony Optimization for continuous domain (ACO_R) and Harmony Search (HS_POP). The pressure vessel design optimization problem, which is one of the widely used optimization problems, was used as a sample real-world design optimization problem to test the algorithm. In order to compare the results on the mentioned problem, the methods including ABC and Standard PSO (SPSO2011) were used. Mean, best, standard deviation values and convergence curves were employed for the analyses of performance. Furthermore, mean square error (MSE), root mean square error (RMSE) and mean absolute percentage error (MAPE), which are computed as a result of using the errors of algorithms on functions, were used for the general performance comparison. AAA produced successful and balanced results over different dimensions of the benchmark functions. It is a consistent algorithm having balanced search qualifications. Because of the contribution of adaptation and evolutionary process, semi-random selection employed while choosing the source of light in order to avoid local minima, and balancing of helical movement methods each other. Moreover, in tested real-world application AAA produced consistent results and it is a stable algorithm.     

Constrained differential evolution using generalized opposition-based learning

Differential evolution (DE) is a well-known optimization approach to deal with nonlinear and complex optimization problems. However, many real-world optimization problems are constrained problems that involve equality and inequality constraints. DE with constraint handling techniques, named constrained differential evolution (CDE), can be used to solve constrained optimization problems. In this paper, we propose a new CDE framework that uses generalized opposition-based learning (GOBL), named GOBL-CDE. In GOBL-CDE, firstly, the transformed population is generated using general opposition-based learning in the population initialization. Secondly, the transformed population and the initial population are merged and only half of the best individuals are selected to compose the new initial population to proceed mutation, crossover, and selection. Lastly, based on a jumping probability, the transformed population is calculated again after generating new populations, and the fittest individuals are selected to compose new population from the union of the current population and the transformed population. The GOBL-CDE framework can be applied to most CDE variants. As examples, in this study, the framework is applied to two popular representative CDE variants, i.e., rank-iMDDE and \(\varepsilon \)DEag. Experiment results on 24 benchmark functions from CEC’2006 and 18 benchmark functions from CEC’2010 show that the proposed framework is an effective approach to enhance the performance of CDE algorithms.     

Accelerated biogeography-based optimization with neighborhood search for optimization

Biogeography-based optimization (BBO) inherently lacks exploration capability that leads to slow convergence. To address this limitation, authors present a memetic algorithm (MA) named as aBBOmDE, which is a new variant of BBO. In aBBOmDE, the performance of BBO is accelerated with the help of a modified mutation and clear duplicate operators. Then modified DE (mDE) is embedded as a neighborhood search operator to improve the fitness from a predefined threshold. mDE is used with mutation operator DE/best/1/bin to explore the search near the best solution. The length of local search is a choice that balances between the search capability and the computational cost. In aBBOmDE, migration mechanism is kept same as that of BBO in order to maintain its exploitation ability. Modified operators are utilized to enhance the exploration ability while a neighborhood search operator further enhances the search capability of the algorithm. This combination significantly improves the convergence characteristics of the original algorithm. Extensive experiments have been carried out on forty benchmark functions to show the effectiveness of the proposed algorithm. The results have been compared with original BBO, DE, CMAES, other MA and DE/BBO, a hybrid version of DE and BBO. aBBOmDE is also applied to compute patch dimensions of rectangular microstrip patch antennas (MSAs) with various substrate thicknesses so as to be used a CAD formula for antenna design.     

Performance assessment of foraging algorithms vs. evolutionary algorithms

The class of foraging algorithms is a relatively new field based on mimicking the foraging behavior of animals, insects, birds or fish in order to develop efficient optimization algorithms. The artificial bee colony (ABC), the bees algorithm (BA), ant colony optimization (ACO), and bacterial foraging optimization algorithms (BFOA) are examples of this class to name a few. This work provides a complete performance assessment of the four mentioned algorithms in comparison to the widely known differential evolution (DE), genetic algorithms (GAs), harmony search (HS), and particle swarm optimization (PSO) algorithms when applied to the problem of unconstrained nonlinear continuous function optimization. To the best of our knowledge, most of the work conducted so far using foraging algorithms has been tested on classical functions. This work provides the comparison using the well-known CEC05 benchmark functions based on the solution reached, the success rate, and the performance rate.     

Constrained differential evolution with multiobjective sorting mutation operators for constrained optimization

Differential evolution (DE) is a simple and powerful evolutionary algorithm for global optimization. DE with constraint handling techniques, named constrained differential evolution (CDE), can be used to solve constrained optimization problems (COPs). In existing CDEs, the parents are randomly selected from the current population to produce trial vectors. However, individuals with fitness and diversity information should have more chances to be selected. This study proposes a new CDE framework that uses nondominated sorting mutation operator based on fitness and diversity information, named MS-CDE. In MS-CDE, firstly, the fitness of each individual in the population is calculated according to the current population situation. Secondly, individuals in the current population are ranked according to their fitness and diversity contribution. Lastly, parents in the mutation operators are selected in proportion to their rankings based on fitness and diversity. Thus, promising individuals with better fitness and diversity are more likely to be selected as parents. The MS-CDE framework can be applied to most CDE variants. In this study, the framework is applied to two popular representative CDE variants, (μ + λ)-CDE and ECHT-DE. Experiment results on 24 benchmark functions from CEC’2006 and 18 benchmark functions from CEC’2010 show that the proposed framework is an effective approach to enhance the performance of CDE algorithms.     

A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems

In the real-world applications, most optimization problems are subject to different types of constraints. These problems are known as constrained optimization problems (COPs). Solving COPs is a very important area in the optimization field. In this paper, a hybrid multi-swarm particle swarm optimization (HMPSO) is proposed to deal with COPs. This method adopts a parallel search operator in which the current swarm is partitioned into several subswarms and particle swarm optimization (PSO) is severed as the search engine for each sub-swarm. Moreover, in order to explore more promising regions of the search space, differential evolution (DE) is incorporated to improve the personal best of each particle. First, the method is tested on 13 benchmark test functions and compared with three stateof-the-art approaches. The simulation results indicate that the proposed HMPSO is highly competitive in solving the 13 benchmark test functions. Afterward, the effectiveness of some mechanisms proposed in this paper and the effect of the parameter setting were validated by various experiments. Finally, HMPSO is further applied to solve 24 benchmark test functions collected in the 2006 IEEE Congress on Evolutionary Computation (CEC2006) and the experimental results indicate that HMPSO is able to deal with 22 test functions.     

CCSA: Conscious Neighborhood-based Crow Search Algorithm for Solving Global Optimization Problems

In this paper, a conscious neighborhood-based crow search algorithm (CCSA) is proposed for solving global optimization and engineering design problems. It is a successful improvement to tackle the imbalance search strategy and premature convergence problems of the crow search algorithm. CCSA introduces three new search strategies called neighborhood-based local search (NLS), non-neighborhood based global search (NGS) and wandering around based search (WAS) in order to improve the movement of crows in different search spaces. Moreover, a neighborhood concept is defined to select the movement strategy between NLS and NGS consciously, which enhances the balance between local and global search. The proposed CCSA is evaluated on several benchmark functions and four applied problems of engineering design. In all experiments, CCSA is compared by other state-of-the-art swarm intelligence algorithms: CSA, BA, CLPSO, GWO, EEGWO, WOA, KH, ABC, GABC, and Best-so-far ABC. The experimental and statistical results show that CCSA is very competitive especially for large-scale optimization problems, and it is significantly superior to the compared algorithms. Furthermore, the proposed algorithm also finds the best optimal solution for the applied problems of engineering design.     

一种基于粒子群算法求解约束优化问题的混合算法

通过将粒子群算法(PSO)与差别进化算法(DE)相结合，提出一种混合算法PSODE，用于求解约束优化问题．PSODE是在PSO算法中适当引入不可行解，将粒子群拉向约束边界，加强对约束边界的搜索，同时与DE算法结合以加强搜索能力．基于典型高维复杂函数的仿真表明，该算法简单高效，鲁棒性强．