多目标优化差分进化算法

个体的适应度赋值和群体的多样性维护是进化算法的两个关键问题。首先,一方面,定义了Paretoε-支配关系的相关概念,通过Paretoε-支配关系确定个体的强度Pareto值,根据个体的强度Pareto值对群体进行Pareto分级排序,实现优胜劣汰;另一方面,使用拥挤距离估算个体的拥挤密度,淘汰位于拥挤区的一些个体,维持群体的多样性。然后,根据差分进化算法的特点,使用适当的进化策略和控制参数,给出了一种用于求解多目标优化问题的差分进化算法DEAMO。最后,数值实验表明,DEAMO在求解标准的多目标优化问题时性能表现优良。     

基于粗糙集理论与差分进化的混合多目标优化算法

针对传统算法求解约束多目标优化所得近似解精度不高、分布性能不好的问题,提出一种基于粗糙集理论与差分进化的混合算法.首先利用多目标差分进化生成一个初始的近似 Pareto 前沿;然后利用粗糙集理论提高Pareto 前沿的分布质量.选取一组标准的多目标约束测试问题,采用混合算法与 NSGA-II 算法进行仿真求解,对比结果表明,所提出的算法在求解约束多目标优化问题时具有更好的近似解分布和更优越的近似解性能.     

用于约束多目标优化问题的双群体差分进化算法

首先给出一种改进的差分进化算法,然后提出一种基于双群体搜索机制的求解约束多目标优化问题的差分进化算法.该算法同时使用两个群体,其中一个用于保存搜索过程中找到的可行解,另一个用于记录在搜索过程中得到的部分具有某些优良特性的不可行解,避免了构造罚函数和直接删除不可行解.此外,文中算法、NSGA-Ⅱ和SPEA的时间复杂度的比较表明,NSGA-Ⅱ最优,文中算法与SPEA相当.对经典测试函数的仿真结果表明,与NSGA-Ⅱ相比较,文中算法在均匀性及逼近性方面均具有一定的优势.     

基于多种群差分进化的多目标优化算法

针对差分进化算法(Differential Evolution Algorithm,DE)求解多目标优化问题时易陷入局部最优的问题,设计了一种双向搜索机制,它通过对相反进化方向产生的两个子代个体进行评价,来增强DE算法的局部搜索能力;设计了多种群机制,它可令各子群独立进化一定次数再执行全局进化,以完成子群间进化信息的交流,这一方面降低了算法陷入局部最优的风险,另一方面增强了Pareto解集的多样性,使Pareto前沿面的解集分布更为均匀。实验结果表明,相比于NSGA-II等同类算法,所提方法在搜索Pareto最优解时效率更高,并且Pareto最优解集的精度及分布程度比前者更好。     

基于进化算法的多目标优化方法

进化算法在解决多目标优化问题中有其特有的优势.首先对多目标优化问题进行了描述;然后结合研究现状讨论了目前几种主要的基于进化算法的多目标优化方法,以及它们的优缺点;最后给出了多目标进化优化算法的一些应用,以及进化多目标优化算法的未来发展方向.     

组合分布估计和差分进化的多目标优化算法

为了提高多目标优化算法的收敛能力及求解精度,提出了一种组合分布估计和差分进化的多目标优化算法.该方法用分布估计算法和差分进化算法共同生成种群中的粒子,利用选择因子来控制每个粒子的产生方式,并且根据迭代次数的增加来改变2种算法的使用比例,搜索初期利用分布估计算法进行快速定位,然后用差分进化算法进行精确搜索.并对差分进化算法的变异因子进行了改进,定义了一个可变的变异因子,来控制不同搜索时期中差分进化算法的变异范围.用4个测试函数对算法进行了仿真测试,并同NSGA-Ⅱ和RM-MEDA进行了比较.实验结果表明,该算法具有良好的收敛性和分布性,并且效果稳定.     

一种自适应多目标离散差分进化算法

提出一种自适应多目标离散差分进化算法。该算法将差分进化引入多目标优化领域,采用一种新的自适应离散差分进化策略增强算法的全局搜索能力,以获得更优的Pareto近似解,并结合Pareto快速分层排序策略和基于聚集密度的按层修剪操作对种群进行更新维护,使解集保持良好的多样性。实例测试和算法比较表明,该算法能有效求解离散域和连续域上不同类型的多目标优化问题,且在收敛性、分布性、稳定性方面均表现较好。     

多目标差分进化算法的电力系统无功优化

 在传统电力系统无功优化( Reactive Power Optimization,RPO) 模型中引入电压水平 指标,建立了以网损最小,电压水平最好为目标的多目标差分进化算法( Differential Evolution Algorithm) 的模型。针对基本差分进化算法易陷入局部最优解、收敛速度慢的缺点,提出一种 具有自适应参数策略的改进差分进化算法并首次用于多目标电力系统无功优化问题。通过在 算法进化过程中调整变异因子F 和交叉因子CR,在初期增加种群的多样性、扩大全局搜索区 域; 从而可以避免算法陷入局部最优解; 同时在后期也加快了收敛速度。将该算法用于电力系 统无功优化并仿真计算了IEEE-14 节点标准测试系统,结果验证模型和算法的有效性。     

多目标进化算法研究进展

进化算法具有本质上并行、不需要求导或其他辅助知识、一次运行产生多个解和简单易于实现等优点,被视为求解多目标优化问题的有效方法,目前已经形成了各种不同的多目标进化算法（MOEA）。本文首先回顾了多目标进化算法的研究起源,给出了多目标优化问题的数学描述;其次,详细分析了第一代多目标进化算法,其主要特征是简单易于实现,包括NSGA、NPGA、MOGA等,并指出这一代算法研究的成绩与不足;然后,对第二代多目标进化算法作了全面分析,指出其特征是强调效率,以精英保留策略为实现机制,且对SPEA、PAES、NSGAⅡ、NPGA2、PESA、Micro-GA等方法进行分析比较,还对这一代的研究作了总结;最后,对多目标进化算法的研究趋势作了展望和预测。     

一种改进的基于差分进化的多目标进化算法

近年来运用进化算法（EAs）解决多目标优化问题（Multi-objective Optimization Problems MOPs）引起了各国学者们的关注。作为一种基于种群的优化方法,EAs提供了一种在一次运行后得到一组优化的解的方法。差分进化（DE）算法是EA的一个分支,最开始是用来解决连续函数空间的问题。提出了一种改进的基于差分进化的多目标进化算法（CDE）,并且将它与另外两个经典的多目标进化算法（MOEAs）NSGA-II和SPEA2进行了对比实验。     

Evolutionary multi-objective optimization: some current research trends and topics that remain to be explored

This paper provides a short review of some of the main topics in which the current research in evolutionary multi-objective optimization is being focused. The topics discussed include new algorithms, efficiency, relaxed forms of dominance, scalability, and alternative metaheuristics. This discussion motivates some further topics which, from the author’s perspective, constitute good potential areas for future research, namely, constraint-handling techniques, incorporation of user’s preferences and parameter control. This information is expected to be useful for those interested in pursuing research in this area.     

Evolutionary multi-objective optimization:some current research trends and topics that remain to be explored

This paper provides a short review of some of the main topics in which the current research in evolutionary multi-objective optimization is being focused. The topics discussed include new algorithms, efficiency, relaxed forms of dominance, scalability, and alternative metaheuristics. This discussion motivates some further topics which, from the author’s perspective, constitute good potential areas for future research, namely, constraint-handling techniques, incorporation of user’s preferences and parameter control. This information is expected to be useful for those interested in pursuing research in this area.     

Software prototype for solving multi-objective machining optimization problems: Application in non-conventional machining processes

For an effective and efficient application of machining processes it is often necessary to consider more than one machining performance characteristics for the selection of optimal machining parameters. This implies the need to formulate and solve multi-objective optimization problems. In recent years, there has been an increasing trend of using meta-heuristic algorithms for solving multi-objective machining optimization problems. Although having the ability to efficiently handle highly non-linear, multi-dimensional and multi-modal optimization problems, meta-heuristic algorithms are plagued by numerous limitations as a consequence of their stochastic nature. To overcome some of these limitations in the machining optimization domain, a software prototype for solving multi-objective machining optimization problems was developed. The core of the developed software prototype is an algorithm based on exhaustive iterative search which guarantees the optimality of a determined solution in a given discrete search space. This approach is justified by a continual increase in computing power and memory size in recent years. To analyze the developed software prototype applicability and performance, four case studies dealing with multi-objective optimization problems of non-conventional machining processes were considered. Case studies are selected to cover different formulations of multi-objective optimization problems: optimization of one objective function while all the other are converted into constraints, optimization of a utility function which combines all objective functions and determination of a set of Pareto optimal solutions. In each case study optimization solutions that had been determined by past researchers using meta-heuristic algorithms were improved by using the developed software prototype.     

改进差异演化算法求解约束优化问题

在现实生活中许多实际问题都可以转化为约束优化问题,并且实际问题通常都很复杂,其函数形态各具特色,传统基于梯度信息的各种求解策略对于具有不可微、多峰及非凸的非线性函数约束优化问题很难凑效。而最近兴起的智能类算法却对这类问题的求解效果突出,在借鉴国外的差异演化算法研究成果基础上,运用改进差异演化算法来求解约束优化问题。最后通过实例进行仿真实验,结果表明改进差异演化算法在求解约束优化问题时具有一定的优越性。     

基于混沌的多目标粒子群优化算法

针对多目标优化问题,提出了一种改进的粒子群算法.该算法为了寻找新解,引入了混沌搜索技术,同时采用了一种新的方法--拥挤距离法定义解的适应度.并采取了精英保留策略,在提高非劣解集多样性的同时,使解集更加趋近于Pareto集.最后,把算法应用到4个典型的多目标测试函数.数值结果表明,该算法能够有效的收敛到Pareto非劣最优目标域,并沿着Pareto非劣目标域有很好的分散性.     

Assembly Line Balancing Using Differential Evolution Models

There is a growing research interest on the application of evolutionary computation-based techniques in manufacturing optimization due to the fact that this field is associated with a plethora of complex combinatorial optimization problems. Differential evolution (DE), one of the latest developed evolutionary algorithms, has rarely been applied on manufacturing optimization problems (MOPs). A possible reason for the absence of DE from this research field is that DE was introduced as global optimizer over continuous spaces, while most of MOPs are of combinatorial nature with discrete decision variables. DE maintains and evolves floating-point vectors and therefore its application to MOPs that have solutions represented by permutations is not straightforward. This paper investigates the use of DE for the solution of the simple assembly line balancing problem (SALBP), a well-known NP-hard MOP. Two basic formulation types for SALBP are examined, namely type-1 and type-2: the former attempts to minimize the number of workstations required to manufacture a product in an assembly line for a given fixed cycle time; while the latter attempts to minimize the cycle time of the line for a given number of stations. Extensive experiments carried out over public benchmarks test instances estimate the performance of DE approach.     

A Pareto-optimal genetic algorithm for warehouse multi-objective optimization

The automated warehouse management requires to fulfill objectives that are usually conflicting with each other. The decisions taken must ensure optimized usage of resources, cost reduction and better customer service. The warehouse replenishment task is a typical example of multi-objective optimization. In this paper, a genetic algorithm with a new crossover operator is developed to solve the replenishment problem. This algorithm is applied to real warehouse data and produces Pareto-optimal permutations of the stored products. A fuzzy rule-base is proposed to increase the diversity of the optimal solutions.     

解决高维优化问题的差分进化算法

针对高维优化问题难以解决并且优化耗费时间长的问题,提出了一种解决高维优化问题的差分进化算法。将协同进化思想引入到差分进化领域,采用一种由状态观测器和随机分组策略组成的协同进化方案。其中,状态观测器根据搜索状态反馈信息适时地调用随机分组策略重新分组;随机分组策略将高维优化问题分解为若干较低维的子问题,而后分别进化。该方案有效地增强了算法解决高维优化问题的搜索速度和搜索能力。经典型的实例测试,并与其他一流差分进化算法比较,实验结果表明:所提算法能有效地求解不同类型的高维优化问题,在搜索速度方面有明显提升,尤其对可分解的高维优化问题极具竞争力。