面向复杂约束优化问题的进化算法综述

约束优化是多数实际工程应用优化问题的呈现方式.进化算法由于其高效的表现,近年来被广泛应用于约束优化问题求解.但约束条件使得问题解空间离散、缩小、改变,给进化算法求解约束优化问题带来极大挑战.在此背景下,融合约束处理技术的进化算法成为研究热点.此外,随着研究的深入,近年来约束处理技术在复杂工程应用问题优化中得到了广泛发展,例如多目标、高维、等式优化等.根据复杂性的缘由,将面向复杂约束优化问题的进化优化分为面向复杂目标的进化约束优化算法和面向复杂约束场景的进化算法两种类别进行综述,其中,重点探讨了实际工程应用的复杂性对约束处理技术的挑战和目前研究的最新进展,并最后总结了未来的研究趋势与挑战.     

改进的约束优化多目标遗传算法及工程应用

利用多目标法处理约束条件,提出一种改进的基于多目标优化的遗传算法用于求解约束优化问题。该算法将约束优化问题转化为两个目标的多目标优化问题; 利用庄家法构造非劣个体,将种群分为支配子种群和非支配子种群,以一定概率分别从支配子种群和非支配子种群中选择个体进行算术交叉操作,引导个体逐步向极值点靠近,增强算法的局部搜索能力,对非支配子种群进行多样性变异操作。8个标准测试函数和3个工程应用的仿真实验结果表明了该算法的有效性。     

双局部粒子群算法解决环境经济调度问题

提出一种基于双局部最优的多目标粒子群优化算法,与可行解为优的约束处理方法相结合,来求解决非线性带约束的多目标电力系统环境经济调度问题。该算法针对传统多目标粒子群算法多样性低的局限性,通过对搜索空间的分割归类来增加帕累托最优解的多样性;并采用一种新的双局部最优来引导粒子的搜索,从而增强了算法的全局搜索能力。算法加入了可行解为优的约束处理方法对IEEE30节点六发电机电力系统环境经济负荷分配模型分别在几个不同复杂性问题的情况进行仿真测试,并与文献中的其他算法进行了比较。结果表明,改进的算法能够在保持帕累托最优解多样性的同时具有良好的收敛性能,更有效地解决电力系统环境经济调度问题。     

一类带约束动态多目标优化问题的进化算法

动态多目标约束优化问题是一类NP-Hard问题,定义了动态环境下进化种群中个体的序值和个体的约束度,结合这两个定义给出了一种选择算子.在一种环境变化判断算子下给出了求解环境变量取值于正整数集Z+的一类带约束动态多目标优化问题的进化算法.通过几个典型的Benchmark函数对算法的性能进行了测试,其结果表明新算法能够较好地求出带约束动态多目标优化问题在不同环境下质量较好、分布较均匀的Pareto最优解集.     

求解约束优化问题的改进自适应mu约束处理技术

针对当前的约束处理技术存在易陷入局部最优解、难以满足等式约束和多控制参数的问题,在mu约束处理技术的基础上,以梯度下降法和多目标拥挤距离为理论依据,设计反映种群约束违反度分布信息的omega参数,它可以自适应地调节约束违反度阈值mu的松弛进而有效地解决约束问题.此外,改进了mu阈值比较准则以提高种群的多样性.经对CEC2017的标准约束优化问题(Constraint optimization problems,COP)进行求解,并与其他先进算法相比较,结果表明,改进的mu约束处理技术能够高效地处理含等式约束的COP.     

一种改进的多目标约束优化差分进化算法

提出一种新的多目标优化差分进化算法用于求解约束优化问题.该算法利用佳点集方法初始化个体以维持种群的多样性.将约束优化问题转化为两个目标的多目标优化问题.基于Pareto支配关系,将种群分为Pareto子集和Non-Pareto子集,结合差分进化算法两种不同变异策略的特点,对Non-Pareto子集和Pareto子集分别采用DE/best/1变异策略和DE/rand/1变异策略.数值实验结果表明该算法具有较好的寻优效果.     

约束进化算法及其应用研究综述

约束优化问题广泛存在于科学研究和工程实践中,其对应的约束优化进化算法也成为了进化领域的重要研究方向。约束优化进化算法的本质问题是如何有效地利用不可行解和可行解的信息,平衡目标函数和约束条件,使得算法更加高效。首先对约束优化问题进行定义;然后详细分析了目前主流的约束进化算法,同时,基于不同的约束处理机制,将这些机制分为约束和目标分离法、惩罚函数法、多目标优化法、混合法和其他算法,并对这些方法进行了详细的分析和总结;接着指出约束进化算法亟待解决的问题,并明确指出未来需要进一步研究的方向;最后对约束进化算法在工程优化、电子和通信工程、机械设计、环境资源配置、科研领域和管理分配等方面的应用进行了介绍。     

求解约束优化问题的多目标粒子群算法*

提出一种多目标粒子群算法处理约束优化问题(MOCPSO). 首先将约束优化问题转化为多目标问题, 然后给出一个不可行阈值来充分地利用不可行粒子的信息引导种群的飞行; 并提出一种粒子间的比较准则以比较它们的优劣; 最后, 为了增加种群的多样性, 提升种群跳出局部最优解的能力, 引入高斯白噪声扰动. 选取有代表性的标准测试函数对MOCPSO算法的性能进行仿真实验, 相比较其它算法, 结果显示MOCPSO算法是求解约束优化问题的有效算法.     

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.     

Structural topology design optimization using Genetic Algorithms with a bit-array representation

In this paper, a bit-array representation method for structural topology optimization using the Genetic Algorithm (GA) is implemented. The importance of structural connectivity in a design is further emphasized by considering the total number of connected objects of each individual explicitly in an equality constraint function. To evaluate the constrained objective function, Deb’s constraint handling approach is further developed to ensure that feasible individuals are always better than infeasible ones in the population to improve the efficiency of the GA. A violation penalty method is proposed to drive the GA search towards the topologies with higher structural performance, less unusable material and fewer separate objects in the design domain. An identical initialization method is also proposed to improve the GA performance in dealing with problems with long narrow design domains. Numerical results of structural topology optimization problems of minimum weight and minimum compliance designs show the success of this bit-array representation method and suggest that the GA performance can be significantly improved by handling the design connectivity properly.     

一种新型约束多目标帝国竞争算法

针对约束多目标优化问题，提出了一种基于约束违背程度和Pareto支配的有效约束处理策略，并设计了一种新型多目标帝国竞争算法（MOICA）.该算法采用一种简化的初始帝国构建过程，在同化过程引入了向外部档案内非劣解学习的机制，并基于帝国势力新定义的帝国竞争新方法以获取问题高质量的解.选用了7个测试问题CF1~CF7进行计算实验并和多种算法进行对比.计算结果表明， MOICA在求解约束多目标优化问题方面具有较强的搜索能力和优势.     

Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization

During the last five years, several methods have been proposed for handling nonlinear constraints using evolutionary algorithms (EAs) for numerical optimization problems. Recent survey papers classify these methods into four categories: preservation of feasibility, penalty functions, searching for feasibility, and other hybrids. In this paper we investigate a new approach for solving constrained numerical optimization problems which incorporates a homomorphous mapping between n-dimensional cube and a feasible search space. This approach constitutes an example of the fifth decoder-based category of constraint handling techniques. We demonstrate the power of this new approach on several test cases and discuss its further potential.     

基于新模型的多目标Memetic算法及收敛分析

将多目标函数优化问题转化成单目标约束优化问题.对转化后的问题提出了基于约束主导原理的选择方法,克服了多数方法只使用Pareto优胜关系作为选择策略而没有采用偏好信息这一缺陷;Memetic算法是求解多目标优化问题最有效的方法之一,它融合了局部搜索和进化计算.新的多目标Memetic算法引进C-metric,将模拟退火算法与遗传算法结合起米,改善了全局搜索能力.用概率论的有关知识证明了算法的收敛性.仿真结果表明该方法对不同的试验函数均可求出一组沿着Pareto前沿分布均匀且散布广泛的非劣解.     

基于改进粒子群优化算法的约束多目标优化

针对约束多目标优化问题,提出一种改进的粒子群优化算法,采用距离量度和自适应惩罚函数相结合的约束处理技术,通过可行解比例有效均衡目标函数和约束条件,提高算法的边界搜索能力。定义新的k最近邻聚集密度,保持解集分布性,并将聚集密度和轮盘赌选择相结合选取全局最优粒子。仿真结果表明,该算法在Pareto解集均匀性及逼近性方面均具有优势。     

基于个人偏好的多目标优化问题目标权重计算方法

针对多目标优化过程中如何根据个人偏好确定各目标权重的问题,提出一种约束优化方法以获得各目标的最佳权重.首先,将目标权重计算问题转化为综合适应度最大方差计算问题;然后,将个人偏好转化为最大方差问题不等式约束条件;最后,利用遗传算法和梯度投影法求解约束优化问题以获得最佳的目标权重.在电力机车故障维修策略决策过程中应用该算法计算各部件经济性、安全性等目标权重,实验结果验证了所提出方法能够获得满足个人偏好的最佳目标权重.     

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.

     

A surrogate-assisted evolution strategy for constrained multi-objective optimization

In many real-world optimization problems, several conflicting objectives must be achieved and optimized simultaneously and the solutions are often required to satisfy certain restrictions or constraints. Moreover, in some applications, the numerical values of the objectives and constraints are obtained from computationally expensive simulations. Many multi-objective optimization algorithms for continuous optimization have been proposed in the literature and some have been incorporated or used in conjunction with expert and intelligent systems. However, relatively few of these multi-objective algorithms handle constraints, and even fewer, use surrogates to approximate the objective or constraint functions when these functions are computationally expensive. This paper proposes a surrogate-assisted evolution strategy (ES) that can be used for constrained multi-objective optimization of expensive black-box objective functions subject to expensive black-box inequality constraints. Such an algorithm can be incorporated into an intelligent system that finds approximate Pareto optimal solutions to simulation-based constrained multi-objective optimization problems in various applications including engineering design optimization, production management and manufacturing. The main idea in the proposed algorithm is to generate a large number of trial offspring in each generation and use the surrogates to predict the objective and constraint function values of these trial offspring. Then the algorithm performs an approximate non-dominated sort of the trial offspring based on the predicted objective and constraint function values, and then it selects the most promising offspring (those with the smallest predicted ranks from the non-dominated sort) to become the actual offspring for the current generation that will be evaluated using the expensive objective and constraint functions. The proposed method is implemented using cubic radial basis function (RBF) surrogate models to assist the ES. The resulting RBF-assisted ES is compared with the original ES and to NSGA-II on 20 test problems involving 2–15 decision variables, 2–5 objectives and up to 13 inequality constraints. These problems include well-known benchmark problems and application problems in manufacturing and robotics. The numerical results showed that the RBF-assisted ES generally outperformed the original ES and NSGA-II on the problems used when the computational budget is relatively limited. These results suggest that the proposed surrogate-assisted ES is promising for computationally expensive constrained multi-objective optimization.     

多目标约束处理方法求解泊位岸桥联合分配问题

为了制定合理高效的泊位岸桥联合分配方案,加快船舶周转,本文针对船舶动态到港的连续泊位建立了以船舶总在港时间最短为目标的泊位岸桥联合分配混合整数非线性模型.通过多目标约束处理策略将复杂约束的违反程度转化为另一个目标,从而将原单目标优化模型转化为双目标优化模型,并用基于快速非支配排序的多目标遗传算法(NSGA-II)对其进行求解.同时,针对问题特点,分别设计了基于调整、惩罚函数、可行解优先和综合约束处理策略的单目标遗传算法对原模型进行求解.通过多组不同规模的标准算例对本文的方法进行测试,验证了基于多目标约束处理策略的方法求解效果相较于单目标约束处理策略的方法更加高效和稳定.     

蒸馏与换热协同的约束多目标在线操作优化方法

针对蒸馏装置与换热网络间缺乏协同优化导致的分馏精度差和能耗高的问题,提出了一种基于代理模型的约束多目标在线协同操作优化方法.为了解决蒸馏装置与换热网络操作参数协同优化时存在的计算耗时和约束的问题,构建Kriging代理模型来近似目标函数和约束条件,提出了基于随机欠采样和Adaboost的分类代理模型（RUSBoost）来解决类别不平衡的收敛判定预测问题.提出了基于多阶段自适应约束处理的代理模型的模型管理方法,该方法采用基于参考向量激活状态的最大化改善期望准则和可行概率准则更新机制来平衡优化初始阶段种群的多样性和可行性,采用支配参考点的置信下限准则更新机制加快收敛速度.通过不断与机理模型交互来在线更新代理模型,实现在线操作优化.通过测试函数和仿真实例验证了本文方法的有效性.     

A multi-objective optimization based solution for the combined economic-environmental power dispatch problem

The combined economic-environmental dispatch issue is multidimensional, non-linear, non-convex and highly constrained problem. It involves multiple and often conflicting optimization criteria for which no unique optimal solution can be determined with respect to all criteria. In this paper a multi-objective optimization based solution to the combined economic-environmental power dispatch is proposed. The derivation of the optimal solution is based on the weighted sum method for which improvements are made in direction of penalty function integration. For that purpose a modified dynamic normalization is suggested. A penalization method based on membership functions is introduced in order to calculate the constraint violations. The objective of the proposed method is gaining an optimal solution for the dynamic combined economic-environmental dispatch problem associated to real power systems. Therefore, the algorithm is applied on different test power systems. The obtained results are analyzed and compared with various optimization techniques presented in the literature. The results demonstrate the efficiency of the proposed method in finding solutions toward global optimum.