Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization

The performance of an optimization tool is largely determined by the efficiency of the search algorithm used in the process. The fundamental nature of a search algorithm will essentially determine its search efficiency and thus the types of problems it can solve. Modern metaheuristic algorithms are generally more suitable for global optimization. This paper carries out extensive global optimization of unconstrained and constrained problems using the recently developed eagle strategy by Yang and Deb in combination with the efficient differential evolution. After a detailed formulation and explanation of its implementation, the proposed algorithm is first verified using twenty unconstrained optimization problems or benchmarks. For the validation against constrained problems, this algorithm is subsequently applied to thirteen classical benchmarks and three benchmark engineering problems reported in the engineering literature. The performance of the proposed algorithm is further compared with various, state-of-the-art algorithms in the area. The optimal solutions obtained in this study are better than the best solutions obtained by the existing methods. The unique search features used in the proposed algorithm are analyzed, and their implications for future research are also discussed in detail.     

一种引入Nelder-Mead算子的改进狼群搜索算法*

为了克服狼群搜索算法(WSA)存在的不足,提出一种新的混合优化算法,称之为引入Nelder-Mead算子的改进狼群搜索算法。该算法使每只狼在搜索中可利用群体信息和个体记忆来指导其搜索猎物,以提高算法的全局搜索能力;让每只狼在搜索中可使用Nelder-Mead方法,以弥补WSA算法在局部搜索能力上的不足。针对12个基准测试实例的实验结果表明, 该算法能够寻得更优的最优解,且鲁棒性更强。     

自适应动态邻域布谷鸟混合算法求解TSP问题

针对离散布谷鸟算法求解旅行商问题时邻域搜索效率低和易陷入局部最优解等问题,提出了一种自适应动态邻域布谷鸟混合算法（Adaptive Dynamic Neighborhood Hybrid Cuckoo Search algorithm,ADNHCS）。为了提升邻域搜索效率,设计了一种圆限定突变的动态邻域结构来降低经典算法的随机性;此外,提出了可根据迭代过程进行自适应参数调整的策略,并结合禁忌搜索算法来提升全局寻优的能力。使用MATLAB和标准TSPLIB数据库中的若干经典算例对算法性能进行了实验仿真,结果表明与其他基于布谷鸟算法、经典和新型群智能优化算法相比,ADNHCS算法在全局寻优能力以及稳定性方面表现更优。     

The improvement of glowworm swarm optimization for continuous optimization problems

Glowworm swarm optimization (GSO) algorithm is the one of the newest nature inspired heuristics for optimization problems. In order to enhances accuracy and convergence rate of the GSO, two strategies about the movement phase of GSO are proposed. One is the greedy acceptance criteria for the glowworms update their position one-dimension by one-dimension. The other is the new movement formulas which are inspired by artificial bee colony algorithm (ABC) and particle swarm optimization (PSO). To compare and analyze the performance of our proposed improvement GSO, a number of experiments are carried out on a set of well-known benchmark global optimization problems. The effects of the parameters about the improvement algorithms are discussed by uniform design experiment. Numerical results reveal that the proposed algorithms can find better solutions when compared to classical GSO and other heuristic algorithms and are powerful search algorithms for various global optimization problems.     

一种新型非线性收敛因子的灰狼优化算法*

针对标准灰狼优化算法在求解复杂工程优化问题时存在求解精度不高和易陷入局部最优的缺点,提出一种新型灰狼优化算法用于求解无约束连续函数优化问题。该算法首先利用反向学习策略产生初始种群个体,为算法全局搜索奠定基础;受粒子群优化算法的启发,提出一种非线性递减收敛因子更新公式,其动态调整以平衡算法的全局搜索能力和局部搜索能力;为避免算法陷入局部最优,对当前最优灰狼个体进行变异操作。对10个测试函数进行仿真实验,结果表明,与标准灰狼优化算法相比,改进灰狼优化算法具有更好的求解精度和更快的收敛速度。     

具有混合群智能行为的萤火虫群优化算法研究

萤火虫群优化算法是一种新型的群智能优化算法,基本的萤火虫群优化算法存在收敛精度低等问题。为了提高算法的性能,借鉴蜂群和鸟群的群体智能行为,改进萤火虫群优化算法的移动策略。运用均匀设计调整改进算法的参数取值。若干经典测试问题的实验仿真结果表明,引入混合智能行为大幅提升了算法的优化性能。     

一种基于教与学的混合灰狼优化算法

针对灰狼优化算法(GWO)存在收敛精度不高、易陷入局部最优的不足,提出一种基于教与学的混合灰狼优化算法(HGWO).首先,采用佳点集理论进行种群初始化,提高初始种群的遍历性;其次,提出一种非线性控制参数策略,在迭代前期增加全局搜索能力,避免算法陷入局部最优,在迭代后期增加局部开发能力,提高收敛精度;最后,结合教与学算法(TLBO)和粒子群优化算法,修改原位置更新公式以优化算法搜索方式,从而提升算法的收敛性能.为验证HGWO算法的有效性,选取9种标准测试函数,将HGWO算法、GWO算法以及其他群体智能优化算法和其他改进GWO算法进行仿真实验.实验结果表明,所提出的HGWO算法性能优于GWO算法和其他群体智能优化算法,且在改进算法中具有一定优势.     

A genetic algorithm and a particle swarm optimizer hybridized with Nelder–Mead simplex search

This paper integrates Nelder–Mead simplex search method (NM) with genetic algorithm (GA) and particle swarm optimization (PSO), respectively, in an attempt to locate the global optimal solutions for the nonlinear continuous variable functions mainly focusing on response surface methodology (RSM). Both the hybrid NM–GA and NM–PSO algorithms incorporate concepts from the NM, GA or PSO, which are readily to implement in practice and the computation of functional derivatives is not necessary. The hybrid methods were first illustrated through four test functions from the RSM literature and were compared with original NM, GA and PSO algorithms. In each test scheme, the effectiveness, efficiency and robustness of these methods were evaluated via associated performance statistics, and the proposed hybrid approaches prove to be very suitable for solving the optimization problems of RSM-type. The hybrid methods were then tested by ten difficult nonlinear continuous functions and were compared with the best known heuristics in the literature. The results show that both hybrid algorithms were able to reach the global optimum in all runs within a comparably computational expense.     

文化基因算法在多约束背包问题中的应用

文化基因算法是一种启发式算法,与一些经典数学方法相比,更适于求解多约束背包问题.文化基因算法是一种基于种群的全局搜索和基于个体的局部启发式搜索的结合体,针对多约束问题,提出采用贪婪策略通过违反度排序的方法处理多约束条件,全局搜索采用遗传算法,局部搜索采用模拟退火策略,解决具有多约束条件的0-1背包问题.通过对几个实例的求解,表明文化基因算法与标准遗传算法相比,具有更优的搜索性能.     

Explosion gravitation field algorithm with dust sampling for unconstrained optimization

Gravitation Field Algorithm (GFA) is a novel optimization algorithm derived from the Solar Nebular Disk Model (SNDM) in astronomy and inspired by the formation process of planets. Although it has achieved good performance when solving many unconstrained optimization problems, which demonstrated its promising application potential in many real-world problems, GFA still has much room for improvement, especially when it comes to the accuracy and efficiency of the algorithm.In this research, an improved GFA algorithm called Explosion Gravitation Field Algorithm (EGFA) is proposed for unconstrained optimization problems, with the introduction of two strategies: Dust Sampling (DS) and Explosion Operation. The task of DS is to locate the space that contains the optimal solution(s) by initializing the dust population randomly in the search space; while the Explosion Operator is to improve the accuracy of solutions and decrease the probability of the algorithm falling into local optima by generating the new population around the center dust to replace the original population.A comparison of experimental results on six classical unconstrained benchmark problems with different dimensions demonstrates that the proposed EGFA outperforms the original GFA and several classical metaheuristic optimization algorithms, such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), in terms of accuracy and efficiency in lower dimensions. Additionally, the comparison of results on three real datasets indicate that EGFA performs better than the original GFA and k-means for solving clustering problems.     

A hybrid cuckoo search and genetic algorithm for reliability–redundancy allocation problems

Solving reliability and redundancy allocation problems via meta-heuristic algorithms has attracted increasing attention in recent years. In this study, a recently developed meta-heuristic optimization algorithm cuckoo search (CS) is hybridized with well-known genetic algorithm (GA) called CS–GA is proposed to solve the reliability and redundancy allocation problem. By embedding the genetic operators in standard CS, the balance between the exploration and exploitation ability further improved and more search space are observed during the algorithms’ performance. The computational results carried out on four classical reliability–redundancy allocation problems taken from the literature confirm the validity of the proposed algorithm. Experimental results are presented and compared with the best known solutions. The comparison results with other evolutionary optimization methods demonstrate that the proposed CS–GA algorithm proves to be extremely effective and efficient at locating optimal solutions.     

Memetic algorithm with Preferential Local Search using adaptive weights for multi-objective optimization problems

Evolutionary multi-objective optimization algorithms are generally employed to generate Pareto optimal solutions by exploring the search space. To enhance the performance, exploration by global search can be complemented with exploitation by combining it with local search. In this paper, we address the issues in integrating local search with global search such as: how to select individuals for local search; how deep the local search is performed; how to combine multiple objectives into single objective for local search. We introduce a Preferential Local Search mechanism to fine tune the global optimal solutions further and an adaptive weight mechanism for combining multi-objectives together. These ideas have been integrated into NSGA-II to arrive at a new memetic algorithm for solving multi-objective optimization problems. The proposed algorithm has been applied on a set of constrained and unconstrained multi-objective benchmark test suite. The performance was analyzed by computing different metrics such as Generational distance, Spread, Max spread, and HyperVolume Ratio for the test suite functions. Statistical test applied on the results obtained suggests that the proposed algorithm outperforms the state-of-art multi-objective algorithms like NSGA-II and SPEA2. To study the performance of our algorithm on a real-world application, Economic Emission Load Dispatch was also taken up for validation. The performance was studied with the help of measures such as Hypervolume and Set Coverage Metrics. Experimental results substantiate that our algorithm has the capability to solve real-world problems like Economic Emission Load Dispatch and is able to produce better solutions, when compared with NSGA-II, SPEA2, and traditional memetic algorithms with fixed local search steps.     

Two effective hybrid metaheuristic algorithms for minimization of multimodal functions

Global optimization problems naturally arise from many applications. We propose two hybrid metaheuristic algorithms for finding a global optimum of a continuous function. Our proposed algorithms are hybridizations of genetic algorithm (GA) and variable neighbourhood search (VNS). To increase the efficiency of our algorithms, for smooth functions we present an effective locally improving line search procedure, and for non-smooth functions, we use the simplex method proposed by Nelder and Mead. By use of the recently adopted non-parametric statistical tests of Kruskal–Wallis and Mann–Whitney for analysing the behaviour of evolutionary algorithms, we compare both the efficiency and the effectiveness of our proposed algorithms with efficiently representative metaheuristic algorithms such as the multiagent GA proposed by Liang et al., the ant colony algorithm proposed by Toksari, and the VNS of Toksari and Güner on a variety of standard test functions. Computational experiments demonstrate that our proposed algorithms are efficiently effective.     

差分型复杂过程全局进化方法

复杂过程全局进化算法是一种具有类似分散搜索的通用框架结构,能够高效完成全局搜索的新型进化算法。在该算法的基础上,提出了差分型复杂过程全局进化算法。差分型算法采用拉丁超立方体抽样生成多样性种群,并应用“最小欧几里德距离的最大值法”产生参考集Refset2,以保证参考集的多样性。采用差分变异和交叉策略替代原算法的线性合并,兼顾算法的收敛速度和种群的多样性。应用Nelder-Mead直接搜索法进行局部搜索,防止搜索过程在局部最优点附近反复。仿真结果表明差分型复杂过程全局进化算法,具有较高的搜索效率。     

一种改进的求解TSP混合粒子群优化算法

为解决粒子群算法在求解组合优化问题中存在的早熟性收敛和收敛速度慢等问题,将粒子群算法与局部搜索优化算法结合,可抑制粒子群算法早熟收敛问题,提高粒子群算法的收敛速度。通过建立有效的局部搜索优化算法所需借助的参照优化边集,提高了局部搜索优化算法的求解质量和求解效率。新的混合粒子群算法高效收敛于中小规模旅行商问题的全局最优解,实验表明改进的混合粒子群算法是有效的。     

求解优化问题的混合PSO-Solver算法

融合了粒子群算法(PSO) 和Solver 加载宏,形成混合PSO-Solver算法进行优化问题的求解。PSO作为全局搜索算法首先给出问题的全局可行解,Solver则是基于梯度信息的局部搜索工具,对粒子群算法得出的解再进行改进,二者互相结合,既加快了全局搜索的速度,又有效地避免了陷入局部最优。算法用VBA语言进行编程,简单且易于实现。通过对无约束优化问题和约束优化问题的求解,以及和标准PSO、其他一些混合算法的比较表明,PSO-Solver算法能够有效地提高求解过程的收敛速度和解的精确性。     

HSWOA: An ensemble of hunger games search and whale optimization algorithm for global optimization

The search for food stimulated by hunger is a common phenomenon in the animal world. Mimicking the concept, recently, an optimization algorithm Hunger Games Search (HGS) has been proposed for global optimization. On the other side, the Whale Optimization Algorithm (WOA) is a commonly utilized nature-inspired algorithm portrayed by a straightforward construction with easy parameters imitating the hunting behavior of humpback whales. However, due to minimum exploration of the search space, WOA has a high chance of trapping into local solutions, and more exploitation leads it towards premature convergence. The concept of hunger from HGS is merged with the food searching techniques of the whale to lessen the inherent drawbacks of WOA. Two weights of HGS are adaptively designed for every whale using the respective hunger level for balancing search strategies. Performance verification of the proposed hunger search-based whale optimization algorithm (HSWOA) is done by comparing it with 10 state-of-the-art algorithms, including three very recently developed algorithms on 30 classical benchmark functions. Comparison with some basic algorithms, recently modified algorithms, and WOA variants is performed using IEEE CEC 2019 function set. Statistical performance of the proposed algorithm is verified with Friedman's test, boxplot analysis, and Nemenyi multiple comparison test. The operating speed of the algorithm is determined and tested with complexity analysis and convergence analysis. Finally, seven real-world engineering problems are solved and compared with a list of metaheuristic algorithms. Numerical and statistical performance comparison with state-of-the-art algorithms confirms the efficacy of the newly designed algorithm.     

An adaptive balance optimization algorithm and its engineering application

The policy of balance between exploration capability and exploitation capability directly affects the solution performance of the meta-heuristic algorithm in a limited time. In order to better balance the exploration and exploitation capabilities of the algorithm and meet the solution requirements of complex real-world problems, the adaptive balance optimization algorithm (ABOA) is proposed in this paper. The algorithm consists of a global search phase (GSP) and a local search phase (LSP) and is controlled by a fixed parameter. ABOA not only considers the balance of exploration and exploitation capabilities of the algorithm throughout the whole iterative process but also focuses on the balance of exploration and exploitation in both GSP and LSP. The search in both phases is focused around the respective search centers from outside to inside. ABOA balances the exploration and exploitation capabilities of the algorithm throughout the search process by two adaptive policies: changing the search area and changing the search center. Fifty-two unconstrained benchmark test functions were employed to evaluate the performance of ABOA. The results of ABOA were compared with nine excellent optimization algorithms available in the literature. The statistical results and Friedman test showed that ABOA was significantly competitive. Finally, the results of the examined engineering design problems showed that ABOA can solve the constrained optimization problem better compared to other methods.     

一种新型的混沌步长果蝇优化算法

针对果蝇优化算法存在算法易早熟、收敛不足的问题,将Hénon混沌映射引用为步长因子,提出了一种混沌步长果蝇优化算法。利用Hénon映射所产生的混沌现象具有良好的遍历性、多样性的特点来改进果蝇算法的固定步长,并增加放大系数以提高算法的全局和局部搜索能力以及跳出局部最优解的能力。对10个经典测试函数进行测试,并与多个算法进行了对比分析,研究结果表明,该算法具有较高的全局搜索和跳出局部最优解的能力。     

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.