一种求解约束优化问题的遗传算法

提出一种求解约束优化问题的遗传算法。通过可行解与不可行解算术交叉的方法对问题的决策空间进行搜索,对可行种群和不可行种群分别按照适应度和约束违反度进行选择。传统变异操作使得解往往偏离了约束区域,因此引入对可行解的边界变异和对不可行解的非均匀变异,并通过维变异方法保持种群的多样性。数值实验结果说明该算法的有效性。     

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.     

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。     

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.     

求解虚拟企业资源结盟博弈的启发式群智能优化算法

通过对求解虚拟企业资源结盟博弈问题与求解经典SAT问题相似性的分析,提出了一种求解虚拟企业资源结盟博弈的启发式群智能优化算法.算法融合萤火虫优化算法与布谷鸟优化算法部分原理,并设计可行的交叉算子以及变异优化算子,能够修复不可行解并保持种群多样性.实验结果表明本文算法的迭代次数与搜索到的稳定联盟数成线性增长,较启发式遗传算法有着更好的爬山性能和搜索能力.     

一种求解约束优化问题的进化算法及其工程应用

提出一种改进的用于求解约束优化问题的进化算法.该算法利用混沌方法初始化个体以保证其均匀分布在搜索空间中.在进化过程中,将种群分为可行子种群和不可行子种群,分别采用不同的交叉和变异操作,以平衡算法的全局和局部搜索能力.标准测试问题的实验结果表明了改进算法的有效性.最后将改进算法应用到两个工程优化设计问题中,得到了满意的结果.     

多模态多目标差分进化算法求解非线性方程组

针对当前算法在求解非线性方程组时面临解的个数不完整、精确度不高、收敛速度慢等问题进行了研究,提出一种多模态多目标差分进化算法。首先将非线性方程组转换为多模态多目标优化问题,初始化一个随机种群并对种群中全部个体进行评价;然后通过非支配解排序和决策空间拥挤距离选择机制,挑选种群中的一半优质个体进行变异;接着在变异过程中采用一种新的变异策略和边界处理方法以增加解的多样性;最后通过交叉和选择机制使优质个体进行进化,直到搜索到全部最优解。在所选测试函数集和工程实例上的实验结果表明,该算法能有效地搜索到非线性方程组的解,并通过与当前四个算法进行比较,该算法在解的数量和成功率上具有优越性。     

改进罚函数法与蝙蝠算法在约束优化中的应用

设计了一种基于自适应罚函数法和改进蝙蝠算法的约束优化问题求解方法。提出了一种自适应罚函数法,该处理方法综合考虑了约束违反的情况和进化过程的特点,如果某个约束违反的次数越多,则证明该约束越强,赋予惩罚系数越大;种群中的不可行解的数量越多,为保持种群的多样性,则约束应该取较小的值,即惩罚系数取较小的值。提出了一种改进的蝙蝠算法,利用混沌的遍历性特点产生初始种群,增强了初始种群的多样性和种群的质量;在考虑了脉冲响度的蝙蝠算法局部搜索中,融入了交叉操作;为防止算法在后期陷入局部最优解,引进了变异操作,保证了群体的多样性。将自适应罚函数法与改进的蝙蝠算法融合起来求解约束优化问题,4个复杂的标准测试函数和2个工程实际问题证明了该约束优化求解方法的可行性和有效性。     

求解约束优化问题的ε-DE 算法

差分进化(differential evolution,简称DE)算法解决约束优化问题(constrained optimization problems,简称COPs)时通常采用可行解优先的比较规则,但是该方法不能利用种群中不可行解的信息.设计了可以利用不可行解信息的ε-DE算法.该算法通过构造一种比较准则,使得进化过程可以充分利用种群中优秀不可行解的信息.该准则通过引入种群约束允许放松程度的概念,在进化初始阶段使可行域边界上且拥有较优目标函数的不可行解进入种群;随着进化代数增加,种群约束允许放松程度不断减小,使得种群中不可行解数量减少,直到种群约束允许放松程度为0,种群完全由可行解组成.此外,还选择了一种改进的DE算法作为搜索算法,使得进化过程具有较快的收敛性.13个标准Benchmark函数实验仿真的结果表明:ε-DE算法是目前利用DE算法解决COPs问题中效果最好的.     

基于遗传策略的过多指定点路由算法的研究

提出了一种求解移动IP中过多指定节点的最短路由问题的分层遗传算法。通过对已有的求解路由模型进行分析,建立了通过多个指定节点的网络模型;根据所给的指定节点来划分解的可行域的层次,来求解移动IP的最短路由问题;该算法采用了可变长度染色体的编码方法,并使用了随机遍历抽样的选择方法,根据网络的拓扑信息进行交叉和变异操作,同时使用修正函数以消除遗传操作中产生的不可行解。各个子种群间独立地并行运行遗传算法,最后得到一条经过多个指定节点的最短路由。并建立随机网络拓扑对该算法进行仿真,实验结果表明,该算法能够有效地求出通过多个指定节点的最短路由,并且受网络规模和问题的复杂性影响比较小。     

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.     

Constrained global optimization via a DIRECT-type constraint-handling technique and an adaptive metamodeling strategy

Recent metamodel-based global optimization algorithms are very promising for box-constrained expensive optimization problems. However, few of them can tackle constrained optimization problems. This article presents an improved constrained optimization algorithm, called eDIRECT-C, for expensive constrained optimization problems. In the eDIRECT-C algorithm, we present a novel DIRECT-type constraint-handling technique that separately handles feasible and infeasible cells. This technique has no user-defined parameter and is beneficial for exploring the undetected feasible regions and boundary of feasible regions. We also employ an adaptive metamodeling strategy to build appropriate metamodel types for objective and constraints respectively. This strategy yields more accurate predictions and therefore significantly speeds up the convergence. To assess the performance of eDIRECT-C, we compare it with some state-of-the-art metamodel-based constrained optimization algorithms and the original DIRECT algorithm on 13 benchmark problems and 4 engineering examples. The comparative results imply that the proposed algorithm is very promising for constrained problems in terms of the convergence speed, quality of final solutions and success rate.     

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.     

基于遗传算法求解约束优化问题的一种算法

在用遗传算法求解约束优化问题时,处理好约束条件是取得好的优化效果的关键.通过考虑遗传算法和约束优化问题的某些特点,提出将直接比较方法和在进化群体中自适应地保持不可行解比例的策略相结合来处理约束条件的一种新方法,并将该方法结合到通用的遗传算法中.数值实验显示了这种方法的有效性.     

Controlling selection areas of useful infeasible solutions for directed mating in evolutionary constrained multi-objective optimization

As an evolutionary approach to solve constrained multi-objective optimization problems (CMOPs), recently an algorithm using the two-stage non-dominated sorting and the directed mating (TNSDM) was proposed. In TNSDM, the directed mating utilizes infeasible solutions dominating feasible solutions in the objective space to generate offspring. The directed mating significantly contributes to the search performance improvement in evolutionary constrained multi-objective optimization. However, the conventional directed mating has two problems. First, since the conventional directed mating selects a pair of parents based on the conventional Pareto dominance, two parents having different search directions may be mated. Second, the directed mating cannot be performed in some cases especially when the population has few useful infeasible solutions. In this case, the conventional mating using only feasible solutions is performed instead. Thus, the effectiveness of the directed mating cannot always be achieved depending on the number of useful infeasible solutions. To overcome these problems and further enhance the effect of the directed mating in TNSDM, in this work we propose a method to control the selection area of useful infeasible solutions by controlling dominance area of solutions (CDAS). We verify the effectiveness of the proposed method in TNSDM, and compare its search performance with the conventional CNSGA-II on discrete m-objective k-knapsack problems and continuous mCDTLZ problems. The experimental results show that the search performance of TNSDM is further improved by controlling the selection area of useful infeasible solutions in the directed mating.