一种快速构造非支配集的方法--擂台法则

多目标进化算法是用来解决多目标优化问题的,为了提高多目标算法的效率,提出了一种快速构造非支配集的方法——擂台法则。它的时间耗费要低于Deb和Jensen提出的构造非支配集的方法。在实验中将擂台法则同Deb和Jensen的方法进行了比较,最后实验结果证明前者在运行时间上要优于后两者。     

平流层飞艇的多目标优化与决策

该文建立了以平流层飞艇阻力最小、自重最轻、极限承载力最大及刚度最大为优化目标的多目标优化模型;采用强度Pareto进化算法(SPEA)进行了多目标优化设计;基于优化所得的Pareto解集,采用基于信噪比的决策方法选择满足实际需要的最终方案。结果表明：采用的SPEA算法是合理有效的,可以得到非劣解分布较均匀的Pareto曲面;通过基于信噪比的决策方法,可从非劣解集中获得满足实际要求的最稳健设计方案。     

A bi-objective optimization approach for exclusive bus lane selection and scheduling design

This study proposes a methodology to solve the integrated problems of selection and scheduling of the exclusive bus lane. The selection problem intends to determine which roads (links) should have a lane reserved for buses while the scheduling problem intends to find the time period of the application. It is formulated as a bi-objective optimization model that aims to minimize the total travel time of non-bus traffic and buses simultaneously. The proposed model formulation is solved by the hybrid non-dominated sorting genetic algorithm with Paramics. The results show that the proposed methodology is workable. Sets of Pareto solutions are obtained indicating that a trade-off between buses and non-bus traffic for the improvement of the bus transit system is necessary when the exclusive bus lane is applied. This allows the engineer to choose the best solutions that could balance the performance of both modes in a multimode transport system environment to achieve a sustainable transport system.     

Remanufacturing-oriented process planning and scheduling: mathematical modelling and evolutionary optimisation

Remanufacturing has been widely studied for its potential to achieve sustainable production in recent years. In the literature of remanufacturing research, process planning and scheduling are typically treated as two independent parts. However, these two parts are in fact interrelated and often interact with each other. Doing process planning without considering scheduling related factors can easily introduce contradictions or even infeasible solutions. In this work, we propose a mathematical model of integrated process planning and scheduling for remanufacturing (IPPSR), which simultaneously considers the process planning and scheduling problems. An effective hybrid multi-objective evolutionary algorithm (HMEA) is presented to solve the proposed IPPSR. For the HMEA, a multidimensional encoding operator is designed to get a high-quality initial population. A multidimensional crossover operator and a multidimensional mutation operator are also proposed to improve the convergence speed of the algorithm and fully exploit the solution space. Finally, a specific legalising method is used to ‘legalise’ possible infeasible solutions generated by the initialisation method and mutation operator. Extensive computational experiments carried out to compare the HMEA with some well-known algorithms confirm that the proposed HMEA is able to obtain more and better Pareto solutions for IPPSR.     

基于改进NSGA-II的多项目多技能人力资源调度研究

针对以往装配式建筑调度研究主要基于每项活动只有确定的活动时间和一种执行模式,而实际调度过程中存在不确定的活动时间和多种执行模式,建立多目标多模式资源约束下的模糊工期调度模型,提出一种改进的非支配排序遗传算法 (INSGA-II) 来求解 (时间−成本) 双目标优化模型。该算法根据活动的优先级关系进行种群初始化和交叉操作,同时提出新的包含活动列表、模式列表和资源列表的3段编码。最后,通过装配式建筑施工现场实际案例分析和算法性能对比,证明本文构建的调度模型和算法设计能有效地解决多模式资源约束下的模糊工期调度模型,为施工调度计划的设计提供科学的思路和方法。

     

生产调度与维护集成的多目标Lorenz非劣遗传优化

研究了一种单机环境下集成生产和维护的双目标优化调度问题。机床的故障间隔时间和平均维修时间服从指数分布,同时结合加工序列相关准备时间。预防性维护活动不能与作业加工同时进行,但与准备时间不相冲突。调度目标是同时最小化作业总计完成时间和机床不可得性。在问题建模的基础上,构造了一种基于Lorenz非劣关系的分类遗传算法(表示为L-NSGA-Ⅱ),详细设计了算法的核心部分。最后,通过大量计算实验,将L-NSGA-II算法与NSGA-II算法进行了比较分析,说明了L-NSGA-II算法的有效性。     

Optimizing the static–dynamic performance of the body-in-white using a modified non-dominated sorting genetic algorithm coupled with grey relational analysis

This article presents a hybrid method combining a modified non-dominated sorting genetic algorithm (MNSGA-II) with grey relational analysis (GRA) to improve the static–dynamic performance of a body-in-white (BIW). First, an implicit parametric model of the BIW was built using SFE-CONCEPT software, and then the validity of the implicit parametric model was verified by physical testing. Eight shape design variables were defined for BIW beam structures based on the implicit parametric technology. Subsequently, MNSGA-II was used to determine the optimal combination of the design parameters that can improve the bending stiffness, torsion stiffness and low-order natural frequencies of the BIW without considerable increase in the mass. A set of non-dominated solutions was then obtained in the multi-objective optimization design. Finally, the grey entropy theory and GRA were applied to rank all non-dominated solutions from best to worst to determine the best trade-off solution. The comparison between the GRA and the technique for order of preference by similarity to ideal solution (TOPSIS) illustrated the reliability and rationality of GRA. Moreover, the effectiveness of the hybrid method was verified by the optimal results such that the bending stiffness, torsion stiffness, first order bending and first order torsion natural frequency were improved by 5.46%, 9.30%, 7.32% and 5.73%, respectively, with the mass of the BIW increasing by 1.30%.     

一种基于“探测"与“开采"的多目标进化算法

针对实践中多目标优化问题(MOPs)的Pareto解集(PS)未知且比较复杂的特性,提出了一种基于"探测"(Exploration)与"开采"(Exploitation)的多目标进化算法(MOEA)——MOEA/2E。该算法在进化过程中采用"探测"与"开采"相结合的方法,用进化操作不断地探测新的搜索区域,用局部搜索充分开采优秀的解区域,并用隐最优个体保留机制保存每一代的最优个体。与目前最流行且有效的多目标进化算法NSGA-Ⅱ及SPEA-Ⅱ进行的比较实验结果表明,MOEA/2E获得的Pareto最优解集具有更好的收敛性与分布性。     

原油一次加工过程的多目标调度优化

在制定原油一次加工过程详细调度时,往往需要考虑多个优化目标。本文提出一种基于改进的骨干粒子群算法和II代非支配遗传算法协同进化的双种群算法,并通过Pareto差熵控制种群的交流,优化了供油罐使用成本、供油罐的切换成本、管道中原油混合成本以及供油罐罐底混合成本4个目标。通过一个工业实例,将本文算法与现有的几种具有代表性的进化多目标优化算法进行对比,验证本文算法的可行性和有效性。     

考虑动态新增订单需求的快递物流即时配送优化方法研究

目的 针对传统快递物流即时配送中存在难以准时服务动态客户和配送时效性差等问题,提出动态订单插入策略和时间窗指派策略,研究考虑动态新增订单需求的快递物流即时配送优化问题。方法 首先,结合快递物流即时配送网络的周期性需求和新增订单需求,构建以物流运营成本最小和车辆使用数目最少的双目标车辆路径优化模型。其次,设计改进的多目标蚁群优化算法求解优化模型,该算法通过局部优化策略和外部档案更新机制来增强帕累托优化解的求解质量,进而提出动态订单插入策略和时间窗指派策略,进一步提升算法的整体搜索性能。再次,将改进的多目标蚁群优化算法与多目标粒子群算法、多目标灰狼优化算法和多目标多元宇宙优化算法进行对比分析,验证了提出算法的有效性。最后,结合重庆市某快递物流即时配送网络进行实例优化研究,并分析探讨了不同服务时间段的划分对物流运营成本、车辆使用数目和惩罚成本等指标的影响。结果 优化后的物流运营成本下降48%,车辆使用数目减少12辆,将配送中心服务时间分为3个时间段的优化方案效果最好。结论 提出的模型和算法有助于降低物流运营成本并减少配送车辆的使用数目,为考虑动态新增订单需求的快递物流即时配送优化提供方法支持和决策参考。     

水平轴风力机叶片最优体型设计

从降低风力机成本及提高风力机运行可靠性的角度,建立以最小的叶片质量获得最大的年发电量两个目标函数,以叶片体型参数及运行参数等关键参数为设计变量,以叶片的强度为主要约束条件的多目标优化设计数学模型,采用Pareto遗传算法对某1.5MW风力机叶片进行最优体型设计研究。与原设计叶片相比,最优体型设计方案提高了风力机的年发电量、减轻了叶片质量,说明优化设计模型合理有效。     

中国铁路发展战略研究

以总工期最短和总费用最低为目标,针对包含线性活动、条状活动、块状活动等多种施工场景的铁路工程项目,基于RSM方法构建铁路项目多目标优化模型,并提出一种改进的NSGA-II算法对模型进行求解。算法设计一种分层次选取种群个体的均匀进化精英选择策略,以提高种群多样性和收敛性;同时引入差分进化算法的变异、交叉算子,构造分层多策略自适应变异、交叉算子,以平衡整个种群的局部搜索能力和全局搜索能力。结果表明,增加对特殊活动和施工方向的考虑,可增强模型对铁路项目的适用性;改进后的算法收敛速度快,运行稳定,得到的结果更优,能够满足较大规模铁路项目进度计划优化。

     

A lexicographic weighted Tchebycheff approach for multi-constrained multi-objective optimization of the surface grinding process

In this article a multi-objective mathematical model is developed to minimize total time and cost while maximizing the production rate and surface finish quality in the grinding process. The model aims to determine optimal values of the decision variables considering process constraints. A lexicographic weighted Tchebycheff approach is developed to obtain efficient Pareto-optimal solutions of the problem in both rough and finished conditions. Utilizing a polyhedral branch-and-cut algorithm, the lexicographic weighted Tchebycheff model of the proposed multi-objective model is solved using GAMS software. The Pareto-optimal solutions provide a proper trade-off between conflicting objective functions which helps the decision maker to select the best values for the decision variables. Sensitivity analyses are performed to determine the effect of change in the grain size, grinding ratio, feed rate, labour cost per hour, length of workpiece, wheel diameter and downfeed of grinding parameters on each value of the objective function.     

Local Pareto approximation for multi-objective optimization

The design process of complex systems often resorts to solving an optimization problem, which involves different disciplines and where all design criteria have to be optimized simultaneously. Mathematically, this problem can be reduced to a vector optimization problem. The solution of this problem is not unique and is represented by a Pareto surface in the objective function space. Once a Pareto solution is obtained, it may be very useful for the decision-maker to be able to perform a quick local approximation in the vicinity of this Pareto solution for sensitivity analysis. In this article, new linear and quadratic local approximations of the Pareto surface are derived and compared to existing formulas. The case of non-differentiable Pareto points (solutions) in the objective space is also analysed. The concept of a local quick Pareto analyser based on local sensitivity analysis is proposed. This Pareto analysis provides a quantitative insight into the relation between variations of the different objective functions under constraints. A few examples are considered to illustrate the concept and its advantages.