Constraints Separation Based Evolutionary Multitasking for Constrained Multi-Objective Optimization Problems

Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.

Energy-Saving Distributed Flexible Job Shop Scheduling Optimization with Dual Resource Constraints Based on Integrated Q-Learning Multi-Objective Grey Wolf Optimizer

The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worker constraints.As one critical factor of production,effective utilization of worker resources can increase productivity.Meanwhile,energy consumption is a growing concern due to the increasingly serious environmental issues.Therefore,the distributed flexible job shop scheduling problem with dual resource constraints(DFJSP-DRC)for minimizing makespan and total energy consumption is studied in this paper.To solve the problem,we present a multi-objective mathematical model for DFJSP-DRC and propose a Q-learning-based multi-objective grey wolf optimizer(Q-MOGWO).In Q-MOGWO,high-quality initial solutions are generated by a hybrid initialization strategy,and an improved active decoding strategy is designed to obtain the scheduling schemes.To further enhance the local search capability and expand the solution space,two wolf predation strategies and three critical factory neighborhood structures based on Q-learning are proposed.These strategies and structures enable Q-MOGWO to explore the solution space more efficiently and thus find better Pareto solutions.The effectiveness of Q-MOGWO in addressing DFJSP-DRC is verified through comparison with four algorithms using 45 instances.The results reveal that Q-MOGWO outperforms comparison algorithms in terms of solution quality.

An Improved Data-Driven Topology Optimization Method Using Feature Pyramid Networks with Physical Constraints

Deep learning for topology optimization has been extensively studied to reduce the cost of calculation in recent years.However,the loss function of the above method is mainly based on pixel-wise errors from the image perspective,which cannot embed the physical knowledge of topology optimization.Therefore,this paper presents an improved deep learning model to alleviate the above difficulty effectively.The feature pyramid network(FPN),a kind of deep learning model,is trained to learn the inherent physical law of topology optimization itself,of which the loss function is composed of pixel-wise errors and physical constraints.Since the calculation of physical constraints requires finite element analysis(FEA)with high calculating costs,the strategy of adjusting the time when physical constraints are added is proposed to achieve the balance between the training cost and the training effect.Then,two classical topology optimization problems are investigated to verify the effectiveness of the proposed method.The results show that the developed model using a small number of samples can quickly obtain the optimization structure without any iteration,which has not only high pixel-wise accuracy but also good physical performance.

Cooperative task allocation for heterogeneous multi-UAV using multi-objective optimization algorithm

The application of multiple UAVs in complicated tasks has been widely explored in recent years.Due to the advantages of flexibility,cheapness and consistence,the performance of heterogeneous multi-UAVs with proper cooperative task allocation is superior to over the single UAV.Accordingly,several constraints should be satisfied to realize the efficient cooperation,such as special time-window,variant equipment,specified execution sequence.Hence,a proper task allocation in UAVs is the crucial point for the final success.The task allocation problem of the heterogeneous UAVs can be formulated as a multi-objective optimization problem coupled with the UAV dynamics.To this end,a multi-layer encoding strategy and a constraint scheduling method are designed to handle the critical logical and physical constraints.In addition,four optimization objectives:completion time,target reward,UAV damage,and total range,are introduced to evaluate various allocation plans.Subsequently,to efficiently solve the multi-objective optimization problem,an improved multi-objective quantum-behaved particle swarm optimization(IMOQPSO)algorithm is proposed.During this algorithm,a modified solution evaluation method is designed to guide algorithmic evolution;both the convergence and distribution of particles are considered comprehensively;and boundary solutions which may produce some special allocation plans are preserved.Moreover,adaptive parameter control and mixed update mechanism are also introduced in this algorithm.Finally,both the proposed model and algorithm are verified by simulation experiments.

Evolutionary Multi-objective Portfolio Optimization in Practical Context

This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search process. The former is essential to enhance the realism of the classical mean-variance model proposed by Harry Markowitz, since portfolio managers often face a number of realistic constraints arising from business and industry regulations, while the latter reflects the fact that portfolio managers are ultimately interested in specific regions or points along the efficient frontier during the actual execution of their investment orders. For the former, this paper proposes an order-based representation that can be easily extended to handle various realistic constraints like floor and ceiling constraints and cardinality constraint. An experimental study, based on benchmark problems obtained from the OR-library, demonstrates its capability to attain a better approximation of the efficient frontier in terms of proximity and diversity with respect to other conventional representations. The experimental results also illustrated its viability and practicality in handling the various realistic constraints. A simple strategy to incorporate preferences into the multi-objective optimization process is highlighted and the experimental study demonstrates its capability in driving the evolutionary search towards specific regions of the efficient frontier.

CEE-Gr:A Global Router with Performance Optimization Under Multi-Constraints

A global routing algorithm with performance optimization under multi constraints is proposed,which studies RLC coupling noise,timing performance,and routability simultaneously at global routing level.The algorithm is implemented and the global router is called CEE Gr.The CEE Gr is tested on MCNC benchmarks and the experimental results are promising.

A hybrid discrete particle swarm optimization-genetic algorithm for multi-task scheduling problem in service oriented manufacturing systems

To cope with the task scheduling problem under multi-task and transportation consideration in large-scale service oriented manufacturing systems(SOMS), a service allocation optimization mathematical model was established, and then a hybrid discrete particle swarm optimization-genetic algorithm(HDPSOGA) was proposed. In SOMS, each resource involved in the whole life cycle of a product, whether it is provided by a piece of software or a hardware device, is encapsulated into a service. So, the transportation during production of a task should be taken into account because the hard-services selected are possibly provided by various providers in different areas. In the service allocation optimization mathematical model, multi-task and transportation were considered simultaneously. In the proposed HDPSOGA algorithm, integer coding method was applied to establish the mapping between the particle location matrix and the service allocation scheme. The position updating process was performed according to the cognition part, the social part, and the previous velocity and position while introducing the crossover and mutation idea of genetic algorithm to fit the discrete space. Finally, related simulation experiments were carried out to compare with other two previous algorithms. The results indicate the effectiveness and efficiency of the proposed hybrid algorithm.

Robust design and optimization for autonomous PV-wind hybrid power systems

This study presents a robust design method for autonomous photovoltaic (PV)-wind hybrid power systems to obtain an optimum system configuration insensitive to design variable variations. This issue has been formulated as a constraint multi-objective optimization problem, which is solved by a multi-objective genetic algorithm, NSGA-II. Monte Carlo Simulation (MCS) method, combined with Latin Hypercube Sampling (LHS), is applied to evaluate the stochastic system performance. The potential of the proposed method has been demonstrated by a conceptual system design. A comparative study between the proposed robust method and the deterministic method presented in literature has been conducted. The results indicate that the proposed method can find a large mount of Pareto optimal system configurations with better compromising performance than the deterministic method. The trade-off information may be derived by a systematical comparison of these configurations. The proposed robust design method should be useful for hybrid power systems that require both optimality and robustness.

面向物理约束的机器人运动学标定最优位姿集规划方法研究

在物理约束下的工业机器人运动学标定过程中,标定精度受到位姿集的影响,而位姿集的选取又受到标定装置的约束,针对以上问题,提出了一种采样区间评价结合位姿集优选的最优位姿集规划方法。首先建立了机器人运动学模型及距离约束标定模型,计算了机器人系统参数误差约束方程及误差雅可比矩阵;然后对机器人工作空间进行空间网格划分,应用拉丁超立方采样结合可观测指标对各个网格区间进行评价,得到最优采样区间;再次基于离线数据建立标定精度预测模型,在最优采样区间内实现最优位姿集的搜索;最后对中瑞RT-608机器人进行最优位姿集的规划及验证,结果表明:基于最优位姿集标定后的平均拟合球半径为0.3947 mm,较随机位姿集减小了57.98%。

信息共享条件下多MIMO对象的协同与优化控制

针对信息物理系统(cyber-physical system,CPS)中多个MIMO对象存在协同效率低、控制算法收敛速度慢的问题,提出一种在信息共享条件下多个MIMO对象协同优化控制策略。利用一种仅有物理层与信息层的新型网络控制系统结构,实现了多个MIMO对象的状态变量、控制和检测信息实时共享。在信息共享的条件下,n个MIMO对象通过CPS分配的性能指标和各对象间的物理约束,采用极小值原理设计的协同控制器实现了系统间的自主协同控制,并利用特征值方法证明了多个MIMO对象在控制器自主协同作用下能够实现子系统与CPS性能整体稳定。通过3个相互存在物理约束的双输入双输出对象进行仿真,验证了控制策略的有效性。

Aerodynamic optimization of rotor airfoil based on multi-layer hierarchical constraint method

Rotor airfoil design is investigated in this paper. There are many difficulties for this highdimensional multi-objective problem when traditional multi-objective optimization methods are used. Therefore, a multi-layer hierarchical constraint method is proposed by coupling principal component analysis(PCA) dimensionality reduction and e-constraint method to translate the original high-dimensional problem into a bi-objective problem. This paper selects the main design objectives by conducting PCA to the preliminary solution of original problem with consideration of the priority of design objectives. According to the e-constraint method, the design model is established by treating the two top-ranking design goals as objective and others as variable constraints. A series of bi-objective Pareto curves will be obtained by changing the variable constraints, and the favorable solution can be obtained by analyzing Pareto curve spectrum. This method is applied to the rotor airfoil design and makes great improvement in aerodynamic performance. It is shown that the method is convenient and efficient, beyond which, it facilitates decision-making of the highdimensional multi-objective engineering problem.

Differences and relations of objectives, constraints, and decision parameters in the optimization of individual heat exchangers and thermal systems

Performance improvement of heat exchangers and the corresponding thermal systems benefits energy conservation, which is a multi-parameters, multi-objectives and multi-levels optimization problem. However, the optimized results of heat exchangers with improper decision parameters or objectives do not contribute and even against thermal system performance improvement. After deducing the inherent overall relations between the decision parameters and designing requirements for a typical heat exchanger network and by applying the Lagrange multiplier method, several different optimization equation sets are derived, the solutions of which offer the optimal decision parameters corresponding to different specific optimization objectives, respectively. Comparison of the optimized results clarifies that it should take the whole system, rather than individual heat exchangers, into account to optimize the fluid heat capacity rates and the heat transfer areas to minimize the total heat transfer area, the total heat capacity rate or the total entropy generation rate, while increasing the heat transfer coefficients of individual heat exchangers with different given heat capacity rates benefits the system performance. Besides, different objectives result in different optimization results due to their different intentions, and thus the optimization objectives should be chosen reasonably based on practical applications, where the inherent overall physical constraints of decision parameters are necessary and essential to be built in advance.

基于混合准则的IMRT计划优化

在适形调强放射治疗计划优化方法中,基于广义等效均匀剂量(g EUD)的生物优化不能较好地控制靶区剂量覆盖特性,基于剂量体积(DV)的物理优化不能反映组织对剂量的非线性反应,为此提出一种基于g EUD生物准则和物理准则(最小剂量和平均剂量)混合准则约束的方法,结合两类准则的优势,更好地兼顾靶区剂量覆盖特性和保护危及器官。采用10例前列腺病例数据仿真,从剂量学和生物学两方面比较和评价。混合准则优化较物理准则优化能够在保证靶区剂量覆盖特性相似的前提下,降低危及器官的剂量,直肠的平均剂量、V_(50)和V_(60),膀胱的平均剂量、V_(65)、V_(70)、V_(75)、正常组织并发症概率(NTCP)和g EUD有统计学显著差异(P<0.05)。混合准则优化与生物准则优化相比,一方面靶区剂量覆盖特性得到很大改善,靶区剂量统计指标和生物指标均有显著性差异(P<0.05);另一方面危及器官得到保护,表现在直肠平均剂量、V_(50)、V_(60)、V_(75)、NTCP和g EUD,膀胱V_(75)和g EUD有显著性差异(P<0.05)。总之,在保证靶区放疗剂量的同时,基于g EUD的混合准则放疗优化能够减少危及器官的照射剂量,为进一步改善靶区剂量覆盖特性、提高治疗增益比提供可能。

基于粗精调技术的求解带平衡约束圆形Packing问题的拟物算法

带平衡约束的圆形Packing问题是以卫星舱布局为背景的具有NP难度的布局优化问题.文中建立了此问题相应的数学模型,同时提出了两个新的物理模型,并受工艺加工过程中"粗精加工"现象的启发,提出了基于粗精调技术的拟物算法QPCFA.该算法既兼顾了搜索空间的多样性以利于全局搜索,又能对有前途的局部区域进行精细搜索以找到相应的局部最优解.同时,在计算过程中引入禁忌技术和跳坑策略,以提高算法的求解质量.对国际上11个代表性的算例进行了计算,QPCFA更新了其中7个算例的最好记录,其余4个与目前的最好记录基本持平,且与目前的最好结果相比在计算精度上均有较大的提高.

广义等效均匀剂量优化法在左侧乳腺癌调强放疗中的剂量学研究

目的:探讨左侧乳腺癌根治术后调强放疗中广义等效均匀剂量的生物优化法的剂量学优势。方法:选取我院2020年01月到2020年12月30例接受调强放射治疗的左侧乳腺癌患者,每例患者计划靶区均采用剂量-体积的物理优化法;并行危及器官左肺和心脏采用单约束物理优化法(Plan1)、多约束物理优化法(Plan2)以及广义等效均匀剂量的生物优化法(Plan3),右肺、脊髓及其外放的约束条件保持不变,分别评价三组计划的优劣;串行危及器官脊髓及其外放仅采用单约束物理优化法(Plan3)以及广义等效均匀剂量的生物优化法(Plan4),左右肺、心脏的约束条件保持不变,分别评价两组计划的优劣。结果:采用不同优化方法的三组计划Plan1、Plan2和Plan3;以及采用不同优化方法的两组计划Plan3和Plan4靶区的适形度指数CI和均匀性指数HI差异均无统计学意义(P>0.05)。并行危及器官左肺和心脏的剂量Plan3最优,其次是Plan2,最差是Plan1;串行危及器官脊髓及其外放的剂量Plan4优于Plan3且差异均有统计学意义(P<0.05)。结论:广义等效均匀剂量的生物优化法可有效降低危及器官受量且不影响靶区的适形度指数CI以及均匀性指数HI,值得临床中推广使用。

一种混凝土重力坝分区弹模反演新方法

建立了一种解决实际工程中测点数少于待反演参数个数的混凝土重力坝分区弹模反演问题的新方法 .这种方法利用已知的补充信息作为反演问题的物理约束条件 ,建立参数反演的多目标优化数学模型 ,解决了反演结果的惟一性问题 ;并且使用改进的模拟退火算法这种全局最优算法来求解大坝的分区弹模 .数值算例表明 ,这种方法对大坝反演问题具有较高的识别精度 ,反演结果可靠 ,可以应用于实际工程 .

高超声速飞行器多目标复杂约束滑翔弹道优化

针对气动热、过载、动压、控制量、航路点、禁飞区以及终端状态等复杂约束条件,提出高超声速飞行器多目标滑翔弹道优化方案。建立换极运动模型,简化部分约束条件的处理,并规避了传统运动模型的奇异问题;在此基础上,引入物理规划方法将多目标优化问题转换为反映设计者不同偏好的单目标优化问题;进一步基于分段Gauss伪谱方法将弹道单目标优化的最优控制问题转换为非线性规划问题进行求解。仿真结果表明,该方法获得的滑翔优化弹道能满足复杂约束要求,同时能够反映设计者的不同偏好。

基于地质体空间位置优化约束的航空重力梯度数据三维物性反演

重力数据的物性反演面临着严重的多解性问题,降低多解性的有效手段是加入约束条件.而边界识别、深度估计及成像方法可获取地质体的水平位置、深度范围等几何参数信息,本文将基于数据本身挖掘的地质体几何参数信息约束到物性反演中,以降低反演的多解性.通过引入基于深度信息的深度加权函数及基于水平位置的水平梯度加权函数建立优化约束条件,有效地提高了反演结果的横向及纵向分辨率.重力梯度数据包含更多的地质体空间特征信息,将优化约束反演方法应用到全张量数据的反演中,模型试验表明本文方法反演结果与理论模型更加吻合.最后对美国路易斯安那州文顿盐丘实测航空重力梯度数据的应用表明,本文方法在其他地球物理、地质资料不足的情况下获得更可靠的反演结果.

基于模糊机会约束的物流配送路径优化

在建立基于模糊机会约束的物流配送路径优化问题的数学模型基础上,构造了求解该问题的模糊模拟遗传算法。并用实例验证,结果表明用此算法可以有效的求解此类不确定问题,具有良好的寻优能力。

基于R2指标的拟态物理学约束多目标优化算法

针对拟态物理学优化(APO)算法在解决复杂约束多目标问题时,容易陷入局部最优,无法在可行域内进行全局搜索,导致解集分布不均匀的问题。依据约束多目标优化问题的特点,在APO算法的基础上,构造出了一种基于R2指标的拟态物理学约束多目标优化(R2-ICRMOAPO)算法。算法将非支配排序和R2指标相结合,并利用R2指标贡献值作为外部存储集的更新机制,删减贡献值较低的个体,选择出效用更好的候选解。将R2-ICRMOAPO算法与四种多目标群体智能进化算法进行了对比实验,结果表明:R2-ICRMOAPO算法所得到的最优非支配解集所覆盖的目标空间区域更大,Pareto解集更加逼近真实解集。该算法为求解约束多目标优化问题提供了新的思路与方法。