求解约束优化问题的改进灰狼优化算法

针对基本灰狼优化(GWO)算法存在求解精度低、收敛速度慢、局部搜索能力差的问题,提出一种改进灰狼优化(IGWO)算法用于求解约束优化问题。该算法采用非固定多段映射罚函数法处理约束条件,将原约束优化问题转化为无约束优化问题,然后利用IGWO算法对转换后的无约束优化问题进行求解。在IGWO算法中,引入佳点集理论生成初始种群,为算法全局搜索奠定基础;为了提高局部搜索能力和加快收敛,对当前最优灰狼个体执行Powell局部搜索。采用几个标准约束优化测试问题进行仿真实验,结果表明该算法不仅克服了基本GWO的缺点,而且性能优于差分进化和粒子群优化算法。     

求解一类不可微多目标优化问题的社会认知算法*

针对一类不可微多目标优化问题,给出了一个新的算法——极大熵社会认知算法。利用极大熵方法将带有约束的不可微多目标优化问题转化为无约束单目标优化问题,然后利用社会认知算法对其进行求解。该算法是基于社会认知理论,通过一系列的学习代理来模拟人类的社会性和智能性从而完成对目标的优化。利用两个测试算例对其进行测试并与其他算法进行比较,计算结果表明,该算法在求解的准确性和有效性方面均优于其他算法。     

An exact penalty function algorithm for solving general constrained parameter optimization problems

An exact penalty function type of algorithm is proposed to solve a general class of constrained parameter optimization problems. The proposed algorithm has the property that any solution obtained by it will always satisfy the problem constraints, and that it will obtain a solution to the constrained problem, within a given specified tolerance, by solving a single unconstrained problem, i.e. it is not necessary to solve a sequence of unconstrained optimization problems. The algorithm applies a modification of Rosenbrock's (Rosenbrock, 1960) polynomial boundary penalty function, and a negative exponential penalty function with moving parameters, to modify the objective function in the neighborhood of the constrained region; a robust unconstrained algorithm (Davison and Wong, 1975) is then used to solve the resulting unconstrained optimization problem. Some standard test functions are included to show the performance of the algorithhm. Application of the algorithm is then made to solve some computer-aided design problems occurring in the area of control system synthesis.     

基于无约束优化和遗传算法的贝叶斯网络结构学习方法

基于无约束优化和遗传算法,提出一种学习贝叶斯网络结构的限制型遗传算法.首先构造一无约束优化问题,其最优解对应一个无向图.在无向图的基础上,产生遗传算法的初始种群,并使用遗传算法中的选择、交叉和变异算子学习得到最优贝叶斯网络结构.由于产生初始种群的空间是由一些最优贝叶斯网络结构的候选边构成,初始种群具有很好的性质.与直接使用遗传算法学习贝叶斯网络结构的效率相比,该方法的学习效率相对较高.     

ESA: a hybrid bio-inspired metaheuristic optimization approach for engineering problems

In this paper, a hybrid bio-inspired metaheuristic optimization approach namely emperor penguin and salp swarm algorithm (ESA) is proposed. This algorithm imitates the huddling and swarm behaviors of emperor penguin optimizer and salp swarm algorithm, respectively. The efficiency of the proposed ESA is evaluated using scalability analysis, convergence analysis, sensitivity analysis, and ANOVA test analysis on 53 benchmark test functions including classical and IEEE CEC-2017. The effectiveness of ESA is compared with well-known metaheuristics in terms of the optimal solution. The proposed ESA is also applied on six constrained and one unconstrained engineering problems to evaluate its robustness. The results reveal that ESA offers optimal solutions as compared to the other competitor algorithms.

     

非正交联合对角化的罚函数粒子群算法

针对多个矩阵近似联合对角化盲分离问题,提出一种新的非正交近似联合对角化算法.首先采用罚函数法将联合对角化的非线性约束优化模型转化为无约束优化模型;其次将粒子群优化算法引入无约束优化模型中实现目标函数的最优化,从而完成矩阵组的联合对角化.分析了惩罚因子的更新策略及算法的收敛性能,并设计仿真实验进行对比分析以检验算法解决实际盲分离问题的能力.     

基于牛顿法的并行优化算法

针对非线性数值优化问题,提出一种在分布式环境下的基于牛顿法的并行算法。引入松弛变量,将不等式约束转换为等式约束,利用广义拉格朗日乘子将约束优化问题转换为无约束子优化问题。为了并行地求解这些子优化问题,将Newton迭代法中的Hessian矩阵进行适当的分裂,采用简单迭代法求解Newton法中的线性方程组。在理论上对该算法进行了收敛性分析。在HP rx2600集群上进行的数值实验结果表明并行效率达90%以上。     

基于自适应罚函数的QPSO算法的代谢通量评估*

针对代谢通量评估问题属于带约束的优化问题,其目标函数是一个非线性、不可微的并且存在多个局部最小点的复杂函数,提出了使用自适应罚函数的量子粒子群优化算法来解决这个问题。通过自适应罚函数的方法解决约束条件,然后使用QPSO算法最小化内部代谢通量。用此算法评估谷氨酸棒杆菌的内部代谢通量并与传统的优化算法来比较,实验结果证明了该算法的可行性和有效性。     

Vehicle power train optimization using multi-objective bird swarm algorithm

In this paper, a multi-objective bird swarm algorithm (MOBSA) is proposed to cope with multi-objective optimization problems. The algorithm is explored based on BSA which is an evolutionary algorithm suitable for single objective optimization. In this paper, non-dominated sorting approach is used to distinguish optimal solutions and parallel coordinates is applied to evaluate the distribution density of non-dominated solution and further update the external archive when it is full to overflowing, which ensure faster convergence and more widespread of Pareto front. Then, the MOBSA is adopted to optimize benchmark problems. The results demonstrate that MOBSA gets better performance compared with NSGA-II and MOPSO. Since a vehicle power train problem could be treated as a typical multi-objective optimization problem with constraints, with integration of constrained non-dominated solution, MOBSA is adopted to acquire optimal gear ratios and optimize vehicle power train. The results compared with other popular algorithm prove the proposed algorithm is more suitable for constrained multi-objective optimization problem in engineering field.

     

改进灰狼优化算法求解模糊车间调度问题

模糊车间调度问题是复杂调度的经典体现,针对此问题设计优秀的调度方案能提高生产效率。目前对于模糊车间调度问题的研究主要集中在单目标上,因此提出一种改进的灰狼优化算法（improved grey wolf optimization,IGWO）求解以最小化模糊完成时间和最小化模糊机器总负载的双目标模糊柔性作业车间调度问题。该算法首先采用双层编码将IGWO离散化,设计一种基于HV贡献度的策略提高种群多样性;然后使用强化学习方法确定全局和局部的搜索参数,改进两种交叉算子协助个体在不同更新模式下的进化;接着使用两级变邻域和四种替换策略提高局部搜索能力;最后在多个测例上进行多组实验分析验证改进策略的有效性。在多数测例上,IGWO的性能要优于对比算法,具有良好的收敛性和分布性。     

求解多维背包问题的蚁群-拉格朗日松弛混合优化算法

针对多维背包问题(MKP) NP-hard、约束强的特点, 提出一种高效的蚁群-拉格朗日松弛(LR) 混合优化算法. 该算法以蚁群优化(ACO) 为基本框架, 并基于LR 对偶信息定义了一种MKP效用指标. ACO使得整体算法具有全局搜索能力, 所设计的效用指标将MKP的优化目标与约束条件有机地融合在一起. 该指标一方面可以用来定 义MKP核问题, 降低问题规模; 另一方面, 可以用作ACO的启发因子, 引导算法在有希望的解区域中强化搜索. 在大量标准算例上的测试结果表明, 所提出算法的鲁棒性较好; 与其他已有算法相比, 在求解质量和求解效率方面均具有很强的竞争力.

     

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.     

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.

     

Practical application of a penalty function approach to constrained minimax optimization

A practical, penalty function approach to solving constrained minimax problems is applied here. In essence, this approach reformulates the constrained minimax problem as an unconstrained minimax problem. A recently proposed optimization algorithm called grazor search is used to solve the reformulated unconstrained minimax problem. The proposed approach can handle inequality constraints-parameter constraints in particular. A practical transmission-line filter example with parameter constraints illustrates the results.     

An interval space reducing method for constrained problems with particle swarm optimization

In this paper, we propose a method for solving constrained optimization problems using interval analysis combined with particle swarm optimization. A set inverter via interval analysis algorithm is used to handle constraints in order to reduce constrained optimization to quasi unconstrained one. The algorithm is useful in the detection of empty search spaces, preventing useless executions of the optimization process. To improve computational efficiency, a space cleaning algorithm is used to remove solutions that are certainly not optimal. As a result, the search space becomes smaller at each step of the optimization procedure. After completing pre-processing, a modified particle swarm optimization algorithm is applied to the reduced search space to find the global optimum. The efficiency of the proposed approach is demonstrated through comprehensive experimentation involving 100 000 runs on a set of well-known benchmark constrained engineering design problems. The computational efficiency of the new method is quantified by comparing its results with other PSO variants found in the literature.     

协调探索和开发能力的改进灰狼优化算法

提出一种协调探索和开发能力的灰狼优化算法.利用佳点集方法初始化灰狼个体的位置,为全局搜索多样性奠定基础;为协调算法的全局探索和局部开发能力,给出一种基于正切三角函数描述的非线性动态变化控制参数;为加快算法的收敛速度,受粒子群优化算法个体记忆功能的启发,设计一种新的个体位置更新公式.10个标准函数的测试结果表明,改进灰狼优化(IGWO)算法能够有效地协调其对问题搜索空间的探索和开发能力.     

一类非线性极小极大问题的改进粒子群算法

针对一类非线性极小极大问题目标函数非光滑的特点给求解带来的困难,利用改进的粒子群算法并结合极大熵函数法给出了此类问题的一种新的有效算法。首先利用极大熵函数将无约束和有约束极小极大问题转化为一个光滑函数的无约束最优化问题,将此光滑函数作为粒子群算法的适应值函数;然后用数学中的外推方法给出一个新的粒子位置更新公式,并应用这个改进的粒子群算法来优化此问题。数值结果表明,该算法收敛快﹑数值稳定性好,是求解非线性极小极大问题的一种有效算法。     

Constrained particle swarm optimization using a bi-objective formulation

This paper introduces an approach for dealing with constraints when using particle swarm optimization. The constrained, single objective optimization problem is converted into an unconstrained, bi-objective optimization problem that is solved using a multi-objective implementation of the particle swarm optimization algorithm. A specialized bi-objective particle swarm optimization algorithm is presented and an engineering example problem is used to illustrate the performance of the algorithm. An additional set of 13 test problems from the literature is used to further validate the performance of the newly proposed algorithm. For the example problems considered here, the proposed algorithm produced promising results, indicating that it is an approach that deserves further consideration. The newly proposed algorithm provides performance similar to that of a tuned penalty function approach, without having to tune any penalty parameters.     

基于群智能求解带约束问题的时域鲁棒优化算法

针对现有的时域鲁棒优化算法无法解决带约束的优化问题,基于群智能优化方法,提出一种求解带约束优化问题的时域鲁棒优化算法.首先,用约束条件构造罚函数,将带约束优化问题处理成为无约束优化问题;然后,采用一个分段函数作为粒子的适应度评价函数,通过竞争规则筛选粒子,设计带约束问题的时域鲁棒优化算法.以优化碳纤维原丝的性能为背景,将算法在多组参数下进行测试和对比分析,结果表明了所提出算法的有效性.进一步分析AR模型对算法性能的影响,指出预测模型的改进是提升算法性能的一个重要手段.     

Constrained balanced optimization problems

We consider the balanced optimization problem with an additional linear constraint under a general combinatorial optimization setting. It is shown that this Constrained Balanced Optimization Problem (CBOP) can be solved in polynomial time whenever an associated minsum problem can be solved in polynomial time. A modification of this basic algorithm is also suggested with improved average performance. This modified algorithm is applicable to the unconstrained version also and has better average performance than existing algorithms. Computational results are presented which establish the superiority of the modified algorithm on both, constrained and unconstrained models. Some variants of CBOP are also discussed in brief.