基于移动可变形孔洞方法的超弹性结构拓扑优化

现有隐式拓扑优化方法在进行超弹性结构拓扑优化设计时，具有设计变量多、中间设计有限元分析存在严重的收敛性和设计结果无法直接导入CAD/CAE系统等问题。为解决这些问题，提出了一种基于移动可变形孔洞的显式拓扑优化方法来进行承受大变形的超弹性结构设计，材料本构采用常用的Mooney-Rivlin模型。首先，介绍了移动可变形孔洞方法的基本思想和可变形孔洞的显式描述方法；其次，构造了基于移动可变形孔洞方法的超弹性结构拓扑优化的数学列式，给出了相应的灵敏度结果；最后，通过数值算例验证了本方法的有效性。数值结果表明，该方法可以通过较少的设计变量和非常稳健的优化过程，给出边界由B样条曲线描述且可与CAD/CAE软件无缝连接的超弹性结构设计。     

Shape morphing and topology optimization of fluid channels by explicit boundary tracking

An integrated shape morphing and topology optimization approach based on the deformable simplicial complex methodology is developed to address Stokes and Navier‐Stokes flow problems. The optimized geometry is interpreted by a set of piecewise linear curves embedded in a well‐formed triangular mesh, resulting in a physically well‐defined interface between fluid and impermeable regions. The shape evolution is realized by deforming the curves while maintaining a high‐quality mesh through adaption of the mesh near the structural boundary, rather than performing global remeshing. Topological changes are allowed through hole merging or splitting of islands. The finite element discretization used provides smooth and stable optimized boundaries for simple energy dissipation objectives. However, for more advanced problems, boundary oscillations are observed due to conflicts between the objective function and the minimum length scale imposed by the meshing algorithm. A surface regularization scheme is introduced to circumvent this issue, which is specifically tailored for the deformable simplicial complex approach. In contrast to other filter‐based regularization techniques, the scheme does not introduce additional control variables, and at the same time, it is based on a rigorous sensitivity analysis. Several numerical examples are presented to demonstrate the applicability of the approach.     

A Flexible Framework for Cubic Regularization Algorithms for Nonconvex Optimization in Function Space

We propose a cubic regularization algorithm that is constructed to deal with nonconvex minimization problems in function space. It allows for a flexible choice of the regularization term and thus accounts for the fact that in such problems one often has to deal with more than one norm. Global and local convergence results are established in a general framework.     

Assortment optimization under the multinomial logit model with product synergies

In synergistic assortment optimization, a product’s attractiveness changes as a function of which other products are offered. We represent synergy structure graphically. Vertices denote products. An edge denotes synergy between two products, which increases their attractiveness when both are offered. Finding an assortment to maximize retailer’s expected profit is NP-hard in general. We present efficient algorithms when the graph is a path, a tree, or has low treewidth. We give a linear program to recover the optimal assortment for paths.     

Generalized sensitivity analysis of nonlinear programs using a sequence of quadratic programs

ABSTRACT

Local sensitivity information is obtained for KKT points of parametric NLPs that may exhibit active set changes under parametric perturbations; under appropriate regularity conditions, computationally relevant generalized derivatives of primal and dual variable solutions of parametric NLPs are calculated. Ralph and Dempe obtained directional derivatives of solutions of parametric NLPs exhibiting active set changes from the unique solution of an auxiliary quadratic program. This article uses lexicographic directional derivatives, a newly developed tool in nonsmooth analysis, to generalize the classical NLP sensitivity analysis theory of Ralph and Dempe. By viewing said auxiliary quadratic program as a parametric NLP, the results of Ralph and Dempe are applied to furnish a sequence of coupled QPs, whose unique solutions yield generalized derivative information for the NLP. A practically implementable algorithm is provided. The theory developed here is motivated by widespread applications of nonlinear programming sensitivity analysis, such as in dynamic control and optimization problems.     

Piezoelectric property improvement of polyethylene ferroelectrets using postprocessing thermal‐pressure treatment

In this work, biaxially stretched polymer foams with well‐defined cellular structures were prepared from polyethylene via blown‐film extrusion and subjected to corona charging to produce a piezoelectric response. The charging parameters were first optimized in terms of charging voltage and needle distance, as well as the gas type and pressure to investigate their effect on the piezoelectric coefficient (d₃₃). The results show that samples charged under nitrogen (N₂) at 100 kPa had better d₃₃ coefficient than those charged under ambient air or N₂ at 20 kPa. Moreover, 2 different thermal pressure treatments were imposed to obtain an optimized eye‐like cellular structure with different cell aspect ratios (AR). The results showed that when the cells were elongated in both the longitudinal and transverse directions (higher AR), higher d₃₃ coefficients were achieved. From all the samples produced, the best results were obtained for a longitudinal aspect ratio (AR‐L) of 7.1, a transversal aspect ratio (AR‐T) of 4.6, and a relative foam density of 0.52 leading to a d₃₃ coefficient of 935 pC/N. This coefficient was further increased using reverse charging and multilayered films, reaching a maximum of 2550 pC/N. This value is much higher than typical ones reported so far for any polyethylene and polypropylene ferroelectrets. These results could increase the use of polyethylene in piezoelectric applications as these materials are very attractive for the large‐scale production of electret‐based sensors and transducers due to their low cost and easy processing.     

不确定环境下基于时间、费用及鲁棒性权衡的多目标项目调度优化

项目调度中的时间和费用是两个重要的指标,而在不确定环境下进度计划的鲁棒性则是保证项目平稳实施的关键。本文研究不确定环境下的多目标项目调度优化问题,以优化项目的工期、鲁棒值和成本为目标安排各活动的开始时间。基于此,作者构建多目标项目调度优化模型,将模型分解为三个子模型分析目标间的权衡关系,然后设计非劣排序遗传算法进行求解,应用精英保留策略和基于子模型权衡关系的优化策略优化算法,进行算法测试和算例参数敏感性分析。最后,应用上述方法研究一个项目实例,计算得到非劣解集,实例的敏感性分析结果进一步验证了三个目标间的权衡关系,据此提出资源的有效利用策略。本文的研究可以为多目标项目调度制定进度计划提供定量化决策支持。     

Decision diagrams for solving traveling salesman problems with pickup and delivery in real time

The Traveling Salesman Problem with Pickup and Delivery seeks a minimum cost path with pickups preceding deliveries. It is important in on-demand last-mile logistics, such as ride sharing and meal delivery. We examine the use of low-width Decision Diagrams in a branch-and-bound with and without Assignment Problem inference duals as a primal heuristic for finding good solutions within strict time budgets. We show these diagrams can be more effective than similarly structured hybrid Constraint Programming techniques for real-time decision making.     

Optimal time delays in a class of reaction-diffusion equations

ABSTRACT

A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best approximation of a desired state function. The differentiability of the mapping is proved that associates the solution of the delay equation to the vector of weights and delays. Based on an adjoint calculus, first-order necessary optimality conditions are derived. Numerical test examples show the applicability of the concept of optimizing time delays.