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。     

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.     

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.     

求解带约束优化问题的混合式多策略萤火虫算法

目前多目标优化算法主要针对如何处理多个目标之间的冲突,对于如何处理约束考虑较少,鉴于此,提出一种求解带约束优化问题的混合式多策略萤火虫算法(HMSFA-PC).首先,提出一种改进的动态罚函数策略对约束优化问题进行预处理,将其转换为非约束优化问题;其次,对萤火虫算法本身进行改进,采用Lévy flights搜索机制有效地增大搜索范围;接着,引入随机扩张因子改进算法吸引模型,使种群突破束缚,有效避免早熟收敛,提出自适应维度重组机制,根据不同迭代时期选择差异性较大的个体进行信息交互、相互学习.为检验算法处理无约束优化问题的性能,将其在基准测试函数上与部分典型算法进行比较;为检验算法处理约束优化问题的性能,将其在实际约束测试问题中与一些顶尖约束求解算法进行比较.结果表明,HMSFA-PC在处理无约束优化问题时具有收敛速度快、收敛精度高等优势,并且在动态罚函数的协作下求解实际约束优化问题时仍具有良好的优化性能.     

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.     

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.     

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。     

Simplex filter: A novel heuristic filter for nonlinear systems state estimation

This paper introduces a new filter for nonlinear systems state estimation. The new filter formulates the state estimation problem as a stochastic dynamic optimization problem and utilizes a new stochastic method based on simplex technique to find and track the best estimation. The vertices of the simplex search the state space dynamically in a similar scheme to the optimization algorithm, known as Nelder-Mead simplex. The parameters of the proposed filter are tuned, using an information visualization technique to identify the optimal region of the parameters space. The visualization is performed using the concept of parallel coordinates. The proposed filter is applied to estimate the state of some nonlinear dynamic systems with noisy measurement and its performance is compared with other filters.     

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。     

一种基于冷链低碳物流路径的混合优化算法

冷链物流运输路径优化问题是国内外学者近几年研究的一个热点问题.首先分析了冷链物流运输的特点和需求,并且提出了考虑综合代价、带硬时间窗和容量约束的单物流中心车辆路径优化模型,其中综合代价包括固定代价、车辆运输代价、货损代价、制冷代价、时间惩罚代价和碳排放代价.车辆路径规划问题是一个NP问题,需要使用智能优化算法对解空间进...     

A hybrid cuckoo search-genetic algorithm for hole-making sequence optimization

Biologically-inspired algorithms are stochastic search methods that emulate the behavior of natural biological evolution to produce better solutions and have been widely used to solve engineering optimization problems. In this paper, a new hybrid algorithm is proposed based on the breeding behavior of cuckoos and evolutionary strategies of genetic algorithm by combining the advantages of genetic algorithm into the cuckoo search algorithm. The proposed hybrid cuckoo search-genetic algorithm (CSGA) is used for the optimization of hole-making operations in which a hole may require various tools to machine its final size. The main objective considered here is to minimize the total non-cutting time of the machining process, including the tool positioning time and the tool switching time. The performance of CSGA is verified through solving a set of benchmark problems taken from the literature. The amount of improvement obtained for different problem sizes are reported and compared with those by ant colony optimization, particle swarm optimization, immune based algorithm and cuckoo search algorithm. The results of the tests show that CSGA is superior to the compared algorithms.     

一种快速收敛的混合遗传算法

利用遗传算法早熟的特点 ,构造出一种快速收敛的混合算法来求解优化问题 ,并分析了它的收敛性。它是使用遗传算法来生成搜索方向 ,从而保证了算法的收敛性。该算法利用遗传算法的全局搜索能力 ,并采用 Nelder- Mead单纯形法来加强算法的局部搜索能力 ,加快了算法的收敛速率。模拟实验表明 ,该方法具有高效性和鲁棒性     

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。     

Integrating Conjugate Gradients Into Evolutionary Algorithms for Large-Scale Continuous Multi-Objective Optimization

Large-scale multi-objective optimization problems (LSMOPs) pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces. While evolutionary algorithms are good at solving small-scale multi-objective optimization problems, they are criticized for low efficiency in converging to the optimums of LSMOPs. By contrast, mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems, but they have difficulties in finding diverse solutions for LSMOPs. Currently, how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored. In this paper, a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method. On the one hand, conjugate gradients and differential evolution are used to update different decision variables of a set of solutions, where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front. On the other hand, objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions, and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent. In comparison with state-of-the-art evolutionary algorithms, mathematical programming methods, and hybrid algorithms, the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.      

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。     

一种基于单纯形搜索的粒子群优化算法

为了改善粒子群优化算法的求解性能,提出了一种基于单纯形搜索和粒子群优化的混合算法。该算法一方面自适应地确定惯性权重、认知以及社会参数来达到免参数目的,另一方面利用单纯形搜索来引导部分粒子的搜索方向,从而加速算法收敛。数值实验结果表明,与传统的粒子群算法和其他基于单纯形的粒子群算法相比,提出算法在评估次数、求解精度方面表现良好。     

A Fully Distributed Hybrid Control Framework For Non-Differentiable Multi-Agent Optimization

This paper develops a fully distributed hybrid control framework for distributed constrained optimization problems. The individual cost functions are non-differentiable and convex. Based on hybrid dynamical systems, we present a distributed state-dependent hybrid design to improve the transient performance of distributed primal-dual first-order optimization methods. The proposed framework consists of a distributed constrained continuous-time mapping in the form of a differential inclusion and a distributed discrete-time mapping triggered by the satisfaction of local jump set. With the semistability theory of hybrid dynamical systems, the paper proves that the hybrid control algorithm converges to one optimal solution instead of oscillating among different solutions. Numerical simulations illustrate better transient performance of the proposed hybrid algorithm compared with the results of the existing continuous-time algorithms.