解决约束优化问题的改进粒子群算法

针对约束优化问题的求解,提出一种改进的粒子群算法（CMPSO）。在CMPSO算法中,为了增加种群多样性,提升种群跳出局部最优解的能力,引入种群多样性阈值,当种群多样性低于给定阈值时,对全局最优粒子位置和粒子自身最优位置进行多项式变异;并根据粒子违背约束条件的程度,提出一种新的粒子间比较准则来比较粒子间的优劣,该准则可以保留一部分性能较优的不可行解;为提升种群向全局最优解飞行的概率,采取一种广义学习策略。对经典测试函数的仿真结果表明,所提出的算法是一种可行的约束优化问题的求解方法。     

基于环境Pareto 支配选择策略的有约束多目标差分进化算法

在处理有约束多目标问题的进化算法中, 目前普遍采用Deb 教授提出的约束占优的直接支配选择策略. 在约束处理中, 优秀不可行解与优秀可行解同样重要, 但在直接支配选择策略中, 不可行解被选择的几率很小. 针对此问题, 设计一种环境Pareto 支配的选择策略, 并基于此提出用于解决有约束多目标问题的差分进化算法. 对经典测试函数进行仿真计算, 结果表明, 与其他算法相比, 所提出的算法具有更高的收敛性和稳定性.

     

An angle based evolutionary algorithm with infeasibility information for constrained many-objective optimization

Recently, angle-based approaches have shown promising for unconstrained many-objective optimization problems (MaOPs), but few of them are extended to solve constrained MaOPs (CMaOPs). Moreover, due to the difficulty in searching for feasible solutions in high-dimensional objective space, the use of infeasible solutions comes to be more important in solving CMaOPs. In this paper, an angle based evolutionary algorithm with infeasibility information is proposed for constrained many-objective optimization, where different kinds of infeasible solutions are utilized in environmental selection and mating selection. To be specific, an angle-based constrained dominance relation is proposed for non-dominated sorting, which gives infeasible solutions with good diversity the same priority to feasible solutions for escaping from the locally feasible regions. As for diversity maintenance, an angle-based density estimation is developed to give the infeasible solutions with good convergence a chance to survive for next generation, which is helpful to get across the large infeasible barrier. In addition, in order to utilize the potential of infeasible solutions in creating high-quality offspring, a modified mating selection is designed by considering the convergence, diversity and feasibility of solutions simultaneously. Experimental results on two constrained many-objective optimization test suites demonstrate the competitiveness of the proposed algorithm in comparison with five existing constrained many-objective evolutionary algorithms for CMaOPs. Moreover, the effectiveness of the proposed algorithm on a real-world problem is showcased.     

基于种群个体可行性的约束优化进化算法

提出一种新的求解约束优化问题的进化算法.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.基于种群中个体的可行性,分别采用3种不同的交叉方式和混合变异机制用于指导算法快速搜索过程.为了求解位于边界附近的全局最优解,引入一种不可行解保存和替换机制,允许一定比例的最好不可行解进入下一代种群.标准测试问题的实验结果表明了该算法的可行性和有效性.     

一种新的约束优化遗传算法及其工程应用

提出一种新的用于求解约束优化问题的遗传算法,该算法利用佳点集方法初始化个体以维持种群的多样性.在进化过程中,通过可行解与不可行解算术交叉对问题的决策空间进行搜索;对可行种群与不可行种群分别采用高斯变异和柯西变异,从而协调算法的勘探和开采能力.几个标准测试问题的实验结果表明该算法的有效性;应用新算法求解两个工程优化设计问题,结果表明该算法的可行性.     

基于文化微粒群算法的丙烯腈收率软测量模型

丙烯腈收率是丙烯腈装置的关键指标,如何得到丙烯腈收率是厂家很关注的研究,将新型优化算法用于丙烯腈收率软测量建模是1种较好的尝试。将新型微粒群优化算法用于同样新型的文化算法种群空间的优化,设计文化微粒群优化算法。它由种群空间和信念空间2部分组成,在种群空间和信念空间分别采用各自算法并行演化,同时,2个空间又根据一定的协议相互联系。分别将该算法和基本微粒群算法用于一些常用测试函数的优化问题;结果表明,与基本微粒群算法相比,文化微粒群算法加强了全局搜索能力,更容易收敛于全局最优解。最后将文化微粒群优化算法用于优化神经网络,构成文化微粒群神经网络,并将其应用于丙烯腈收率软测量建模。结果表明,此模型精度高,应用前景广阔。     

用于函数优化和特征选择的翻筋斗觅食海鸥优化算法

针对基本海鸥优化算法（SOA）在处理复杂优化问题中存在低精度、慢收敛和易陷入局部最优的不足,提出了一种基于翻筋斗觅食策略的SOA算法（SFSOA）。该算法首先采用基于倒S型函数的控制参数A非线性递减策略更新海鸥个体的位置,以改善个体的质量和加快收敛速度;引入一种基于翻筋斗觅食策略的学习机制以增加海鸥个体位置的多样性,避免算法在搜索后期陷入局部最优值。选取八个基准函数优化问题进行数值实验,并与基本SOA、灰狼优化算法和改进SOA进行比较,结果表明,所提算法具有较高的解精度、较快的收敛速度和较强的全局搜索能力,能有效地处理复杂函数优化问题。最后,将SFSOA用于求解特征选择问题,获得了满意的结果。     

An effective cellular particle swarm optimization for parameters optimization of a multi-pass milling process

In the milling process, the selection of machining parameters is very important as these parameters determine the processing time, quality, cost and so on, especially in the high-accuracy machine tools. However, the parameters optimization of a multi-pass milling process is a nonlinear constrained optimization problem which is difficult to be solved by the traditional optimization techniques. Therefore, in order to solve this problem effectively, this paper proposes a novel parameters optimization method based on the cellular particle swarm optimization (CPSO). To address the constraints efficiently, the proposed method combines two constraints handling techniques, including the penalty function method and the constraints handling strategy of PSO. In the proposed CPSO, the smart cell constructs its neighborhood with self-adaptive function and constraints handling techniques, which guide the unfeasible particles to move to the feasible regions and search for better solutions. A case is adopted and solved to illustrate the effectiveness of the proposed CPSO algorithm. The results of the experiment study are analyzed and compared with those of the previous algorithms. The experimental results show that the proposed approach outperforms other algorithms and has achieved significant improvement.     

基于多策略的多目标粒子群优化算法

针对目前多目标粒子群优化算法的收敛性能和非劣解的多样性不能同时得到满足等缺陷,提出一种基于多策略的多目标粒子群优化算法（Multi-Objective Particle Swarm Optimization algorithm for Multi-Strategy,MS-MOPSO）。采用非支配排序和拥挤距离排序相结合策略,重新划分外部种群和进化种群;采用小生境选择策略,在外部种群中选择最佳粒子作为领导粒子,用于领导进化种群中粒子的进化;在进化种群中利用多尺度高斯变异策略,平衡算法的全局搜索和局部精确搜索;采用邻域认知个体极值更新策略,不断更新个体极值。将该算法应用到典型的多目标测试函数,并与其他多目标优化算法进行对比分析,测试结果表明该算法中四个策略的有效性和互补性,同时验证了该算法不但具有较好的收敛性和收敛速度,而且该算法最优解的分布具有良好的均匀性和多样性。     

Cellular particle swarm optimization

This paper proposes a cellular particle swarm optimization (CPSO), hybridizing cellular automata (CA) and particle swarm optimization (PSO) for function optimization. In the proposed CPSO, a mechanism of CA is integrated in the velocity update to modify the trajectories of particles to avoid being trapped in the local optimum. With two different ways of integration of CA and PSO, two versions of CPSO, i.e. CPSO-inner and CPSO-outer, have been discussed. For the former, we devised three typical lattice structures of CA used as neighborhood, enabling particles to interact inside the swarm; and for the latter, a novel CA strategy based on “smart-cell” is designed, and particles employ the information from outside the swarm. Theoretical studies are made to analyze the convergence of CPSO, and numerical experiments are conducted to compare the proposed algorithm with different variants of PSO. According to the experimental results, the proposed method performs better than other variants of PSO on benchmark test functions.     

基于混合反向学习策略的鲸鱼优化算法

针对鲸鱼优化算法(WOA)在解决高维复杂问题时存在收敛速度慢、全局搜索能力不足的问题,提出一种最优最差个体混合反向学习的WOA(M WOA).首先,引入一种自适应惯性权重,用于调节寻优前期的步长和寻优后期的种群多样性;其次,提出一种混合反向学习策略并将其融入WOA,以提高算法的收敛精度;最后,引入一种参数非线性衰减策略...     

修正免疫克隆约束多目标优化算法

针对约束多目标优化问题,提出修正免疫克隆约束多目标优化算法.该算法通过引进一个约束处理策略,用一个修正算法对个体的目标函数值进行修正,并对修正后的目标函数值采用免疫克隆算法进行优化,用一个精英种群对可行非支配解进行存储.该算法在优化过程中,既保留了非支配可行解,也充分利用了约束偏离值小的非可行解,同时引进整体克隆策略来提高解分布的多样性.通过对约束多目标问题的各项性能指标的测试以及和对比算法的比较可以看出:该算法在处理约束多目标优化测试问题时,所得解的多样性得到了一定的提高.同时,解的收敛性和均匀性也得到了一定的改进.     

求解工程约束优化问题的PSO-ABC混合算法*

针对包含约束条件的工程优化问题,提出了基于人工蜂群的粒子群优化PSO-ABC算法。将PSO中较优的粒子作为ABC算法的蜜源,并使用禁忌表存储其局部极值,克服粒子群优化算法易陷入局部最优的缺陷。采用可行性规则进行约束处理,将粒子种群分为可行子群和不可行子群,并在ABC算法产生蜜源的过程中保留部分较优的可行解和不可行解的信息,弥补了可行性规则处理最优点位于约束边界附近的问题时存在的不足。四个典型工程优化设计的实验结果表明,该算法能够寻得更优的约束最优化解,且稳健性更强。     

基于混合策略的双种群约束优化算法

提出一种基于混合策略的双种群约束优化算法.利用双种群存储机制处理约束条件,并采用约束支配更新不可行解集,同时采用混合策略进化种群:在进化前期利用Deb准则产生可行解,并保留一部分非劣不可行解参与进化,保持种群多样性;在进化后期让最优个体和次优个体参与进化,使种群快速收敛.仿真实验结果表明,所提出的算法在保证种群多样性的同时,能够较好地收敛到全局最优解,且鲁棒性较好.     

A new chaotic multi-verse optimization algorithm for solving engineering optimization problems

Multi-verse optimization algorithm (MVO) is one of the recent meta-heuristic optimization algorithms. The main inspiration of this algorithm came from multi-verse theory in physics. However, MVO like most optimization algorithms suffers from low convergence rate and entrapment in local optima. In this paper, a new chaotic multi-verse optimization algorithm (CMVO) is proposed to overcome these problems. The proposed CMVO is applied on 13 benchmark functions and 7 well-known design problems in the engineering and mechanical field; namely, three-bar trust, speed reduce design, pressure vessel problem, spring design, welded beam, rolling element-bearing and multiple disc clutch brake. In the current study, a modified feasible-based mechanism is employed to handle constraints. In this mechanism, four rules were used to handle the specific constraint problem through maintaining a balance between feasible and infeasible solutions. Moreover, 10 well-known chaotic maps are used to improve the performance of MVO. The experimental results showed that CMVO outperforms other meta-heuristic optimization algorithms on most of the optimization problems. Also, the results reveal that sine chaotic map is the most appropriate map to significantly boost MVO’s performance.     

基于元胞粒子群算法的数控切削参数优化

针对数控切削参数优化问题的非线性和多约束性质,采用一种元胞粒子群算法（CPSO）进行优化。在基本粒子群算法（PSO）思想的基础上,引入邻居的概念,以搜索解空间的局部信息,并将粒子的信息交流范围扩展到种群外部,从而能搜索到更有希望的解空间;在罚函数机制的基础上,引入标志变量记录粒子是否曾经满足过所有约束条件,根据标志变量进行粒子个体极值与种群全局极值的更新。通过比较CPSO算法与其他算法取得的结果,验证该算法解决数控切削参数优化问题的有效性和优越性。     

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 efficient algorithm for constrained global optimization and application to mechanical engineering design: League championship algorithm (LCA)

The league championship algorithm (LCA) is a new algorithm originally proposed for unconstrained optimization which tries to metaphorically model a League championship environment wherein artificial teams play in an artificial league for several weeks (iterations). Given the league schedule, a number of individuals, as sport teams, play in pairs and their game outcome is determined given known the playing strength (fitness value) along with the team formation (solution). Modelling an artificial match analysis, each team devises the required changes in its formation (a new solution) for the next week contest and the championship goes for a number of seasons. In this paper, we adapt LCA for constrained optimization. In particular: (1) a feasibility criterion to bias the search toward feasible regions is included besides the objective value criterion; (2) generation of multiple offspring is allowed to increase the probability of an individual to generate a better solution; (3) a diversity mechanism is adopted, which allows infeasible solutions with a promising objective value precede the feasible solutions. Performance of LCA is compared with comparator algorithms on benchmark problems where the experimental results indicate that LCA is a very competitive algorithm. Performance of LCA is also evaluated on well-studied mechanical design problems and results are compared with the results of 21 constrained optimization algorithms. Computational results signify that with a smaller number of evaluations, LCA ensures finding the true optimum of these problems. These results encourage that further developments and applications of LCA would be worth investigating in the future studies.     

An evolutionary algorithm with directed weights for constrained multi-objective optimization

When solving constrained multi-objective optimization problems (CMOPs), keeping infeasible individuals with good objective values and small constraint violations in the population can improve the performance of the algorithms, since they provide the information about the optimal direction towards Pareto front. By taking the constraint violation as an objective, we propose a novel constraint-handling technique based on directed weights to deal with CMOPs. This paper adopts two types of weights, i.e. feasible and infeasible weights distributing on feasible and infeasible regions respectively, to guide the search to the promising region. To utilize the useful information contained in infeasible individuals, this paper uses infeasible weights to maintain a number of well-diversified infeasible individuals. Meanwhile, they are dynamically changed along with the evolution to prefer infeasible individuals with better objective values and smaller constraint violations. Furthermore, 18 test instances and 2 engineering design problems are used to evaluate the effectiveness of the proposed algorithm. Several numerical experiments indicate that the proposed algorithm outperforms four compared algorithms in terms of finding a set of well-distributed non-domination solutions.     

一个蚁群优化模型的期望性能分析

用蚁群优化求解组合优化问题时, 信息素模型及其规则可能使问题的各组件之间的竞争失衡, 从而有可能使蚁群搜索停滞在最差解。 研究了蚁群优化求解k-最小生成树问题时的信息素模型及其更新规则对性能的影响,对原有的信息素模型作出了新的解释:直接表示k-最小生成树问题的边被选择的概率。基于新的信息素模型设计了一种新的解的构造过程,这种过程不仅产生可行解, 也产生不可行解;同时研究了使用可行解和全部解更新信息素模型时算法的迭代期望质量随时间的增减情况,其结果表明, 只使用可行解时迭代期望质量随时间连续降低, 而使用全