Analysis of Photothermal Characterization of Layered Materials – Design of Optimal Experiments

In this paper numerical calculations are presented for the steady-periodic temperature in layered materials and functionally-graded materials to simulate photothermal methods for the measurement of thermal properties. No laboratory experiments were performed. The temperature is found from a new Green's function formulation which is particularly well-suited to machine calculation. The simulation method is verified by comparison with literature data for a layered material. The method is applied to a class of two-component functionally-graded materials, and results for temperature and sensitivity coefficients are presented. An optimality criterion, based on the sensitivity coefficients, is used for choosing what experimental conditions will be needed for photothermal measurements to determine the spatial distribution of thermal properties. This method for optimal experiment design is completely general and may be applied to any photothermal technique and to any material with spatial variation of thermal properties.     

Properly efficient solutions for vectorial norm approximation

In the present paper a general vectorial best approximation problem using vectorial norms with respect to properly efficient solutions is considered. Necessary and sufficient optimality conditions for such solutions are derived. This is done on base of scalarization and studying a corresponding dual problem to the scalar optimization problem. Also optimality conditions in subdifferential form are formulated. For the necessity of the optimality conditions especially convexity assumptions are essential. But under only very weak supposition these conditions are sufficient.     

基于动态规划的动载荷时域识别方法研究

提出一种基于动态规划方程的动态载荷时域方法。首先从系统的状态空间方程出发,利用最小二乘法建立系统响应的实际测量值与识别值之间的目标函数。将Bellman最优化原理运用到目标函数的最小化当中,推导出动态优化载荷识别公式。通过一个多自由度数值算例对本方法进行验证,表明方法对含有噪声的动态载荷识别问题适应性强,具有较高的识别精度。     

Inverse fracture problems in piezoelectric solids by local integral equation method

The meshless local Petrov–Galerkin (MLPG) method is used to solve the inverse fracture problems in two-dimensional (2D) piezoelectric body. Electrical boundary conditions on the crack surfaces are not specified due to unknown dielectric permittivity of the medium inside the crack. Both stationary and transient dynamic boundary conditions are considered here. The analyzed domain is covered by small circular subdomains surrounding nodes spread randomly over the analyzed domain. A unit step function is chosen as test function in deriving the local integral equations (LIE) on the boundaries of the chosen subdomains. The Laplace-transform technique is applied to eliminate the time variation in the governing equation. The local integral equations are nonsingular and take a very simple form. The spatial variation of the Laplace transforms of displacements and electrical potential are approximated on the local boundary and in the interior of the subdomain by means of the moving least-squares (MLS) method. The singular value decomposition (SVD) is applied to solve the ill-conditioned linear system of algebraic equations obtained from the LIE after MLS approximation. The Stehfest algorithm is applied for the numerical Laplace inversion to retrieve the time-dependent solutions.     

A hybrid optimization model for proficient bidding strategies with no Karush–Kuhn–Tucker optimality conditions

The computational complexity behind the bi‐level optimization problem has led the researchers to adopt Karush–Kuhn–Tucker (KKT) optimality conditions. However, the problem function has more number of complex constraints to be satisfied. Classical optimization algorithms are impotent to handle the function. This paper presents a simplified minimization function, in which both the profit maximization problem and the ISO market clearance problem are considered, but with no KKT optimality conditions. Subsequently, this paper solves the minimization function using a hybrid optimization algorithm. The hybrid optimization algorithm is developed by combining the operations of group search optimizer (GSO) and genetic algorithm (GA). The hybridization enables the dispersion process of GSO to be a new mutated dispersion process for improving the convergence rate. We evaluate the methodology by experimenting on IEEE 14 and IEEE 30 bus systems. The obtained results are compared with the outcomes of bidding strategies that are based on GSO, PSO, and GA. The results demonstrate that the hybrid optimization algorithm solves the minimization function better than PSO, GA, and GSO. Hence, the profit maximization in the proposed methodology is relatively better than that of the conventional algorithms. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal Control of Polymer Morphologies

This paper is devoted to the optimal design of polymeric materials through control of the cooling during the crystallization process. The optimality is defined in terms of optimal mechanical properties, which are directly related to the morphology of the solidified polymeric material. As a characterizing mathematical entity to be controlled the contact interface density is introduced and its relations to other structure variables such as temperature and crystallinity is discussed. Not only a general optimal control approach is presented, but also some relevant special cases are discussed, for which a more detailed analysis can be carried out. It is shown that under reasonable conditions on the parameters and the process, these optimal-control problems have solutions in appropriate function spaces and the optimality conditions derived from the Lagrangian formulation are discussed. Finally, the numerical approximation is discussed and results for some test examples are presented.     

非线性规划的非完全Lagrange函数与最优性条件

非线性规划问题（P）“minf(x)suject to hj(x)≤0，j=1,2,……，m”的非完全Lagrange函数定义为L（x,λJ）=f(x) (λJ）^tHj(x)其中，J包含等于{1，2，……，m}。当J={1，2，……，m}时，它即为通常的Lagrange函数。在一类广义凸意义下考虑非线性规划问题的非完全Lagrange函数及其鞍点最优性条件。在某种意义上，本语言的结果推广了文^[1,2,4,5]中的有关结果。     

一类不可微广义凸多目标规划的最优性条件和对偶

本文研究带不等式约束的不可微多目标规划问题,引入了广义d-I型一致不变凸函数的概念,证明了Pareto有效解和Pareto弱有效解的Karush-Kuhn-Tucker型充分条件.构造出了混合对偶模型,并证明了相应的对偶定理.     

集合函数多目标规划的二阶最优性条件

在给出了集合函数多目标规划的一阶最优性条件的基础上,进一步给出了集合函数多目标规划问题弱有效解的二阶充分条件和强有效解的二阶充分条件以及局部弱有效解的二阶充分条件。     

Decomposition method for solving optimal material orientation problems

The strain energy density is considered as a measure of the stiffness/flexibility of the composite structure. A methodology for determining the stationary points of the strain energy density in anisotropic solids is developed. The methodology proposed is based on new problem formulation, derivation and analysis of optimality conditions, and decomposition method. The optimal material orientation problem is formulated in terms of strains. The optimality conditions derived cover different material symmetries, linear and also some non-linear material models. The complexity analysis of the optimality conditions has been performed. The proposed approach allows to divide the solution of the optimal material orientation problem into less complicated subtasks.     

异质行为偏好对供应链决策及协调的影响

考虑零售商的异质行为偏好,研究供应链的生产决策及协调问题。引入新的决策参考点探究异质行为偏好问题,构建考虑损失规避及公平关切的效用函数,研究零售商损失规避及公平关切对供应链最优决策及供应链协调性的影响。理论分析及数值算例表明：当批发价格满足不同条件时,零售商的损失规避及公平关切行为对其最优订货量的影响是不同的;在分散情形下,供应链不能达到系统最优,引进保险契约可以使供应链双方达到Pareto最优。     

The effects of relative food item size on optimal tooth cusp sharpness during brittle food item processing

Teeth are often assumed to be optimal for their function, which allows researchers to derive dietary signatures from tooth shape. Most tooth shape analyses normalize for tooth size, potentially masking the relationship between relative food item size and tooth shape. Here, we model how relative food item size may affect optimal tooth cusp radius of curvature (RoC) during the fracture of brittle food items using a parametric finite-element (FE) model of a four-cusped molar. Morphospaces were created for four different food item sizes by altering cusp RoCs to determine whether optimal tooth shape changed as food item size changed. The morphospaces were also used to investigate whether variation in efficiency metrics (i.e. stresses, energy and optimality) changed as food item size changed. We found that optimal tooth shape changed as food item size changed, but that all optimal morphologies were similar, with one dull cusp that promoted high stresses in the food item and three cusps that acted to stabilize the food item. There were also positive relationships between food item size and the coefficients of variation for stresses in food item and optimality, and negative relationships between food item size and the coefficients of variation for stresses in the enamel and strain energy absorbed by the food item. These results suggest that relative food item size may play a role in selecting for optimal tooth shape, and the magnitude of these selective forces may change depending on food item size and which efficiency metric is being selected.     

Cycle time analysis in reentrant robotic cells with swap ability

In this paper, reentrant robotic cells composed of a robot with swap ability for a single part type is studied. In this regard, we restrict our attention to the two-machine reentrant cell scheduling problem. In the cell, a part visits the machines at least once. To minimise the cycle time, the sequence of robot moves must be optimised. Based on our previous study on the optimality of robotic cells, we restrict our investigation to only one-unit cycles. Therefore, all one-unit cycles are generated and their cycle time formulae are developed. Initially, we determine both essential and sufficient conditions for different cycles to be optimal and present the regions of optimality when each part reenters the first machine two times. We determine optimality conditions for different cycles when each part reenters both machines two times. Finally, sensitivity analysis is performed for both cases and the influence of the parameter values in the regions of optimality for each cycle is shown.     

Optimal Price-Inventory Decisions: Profit vs. ROII

Making optimal price-inventory decisions in the face of alternate criteria is studied for a monopoly firm. When the firm's demand function belongs to the logarithmic concave class, necessary and sufficient optimality conditions are obtained for profit and return on inventory investment criteria. It is shown that decentralized price-inventory decision-making is optimal when the return criterion is used. The theoretical developments are elucidated with a detailed study of linear demand and a comprehensive numerical example.     

Optimal search of distributed arrival time control

Distributed arrival time control (DATC) is a heuristic feedback control algorithm for scheduling which has been developed for a real-time distributed scheduling of heterarchical systems. It has been renowned not only for its fast solution searching algorithm but also for its flexibility to changing environment. However, the optimality of this heuristic method has not been analytically explained until recently because it has been designed to discover a near optimal solution instead of the true optimum. In this paper, we provide a novel optimal search method for the DATC scheduling problem by introducing a scalar cost function over the vector space of time and show the existence and location of true optima for the DATC scheduling problem through geometric approach. This geometrical interpretation enables us to find the true optimal by direct projection without iterations like previous DATC approaches. Based on the true optimum found, we evaluate the optimality of DATC algorithms by examining their dependency on initial conditions and explain their intrinsic causality mechanism for the discrepancy with true optimum. The implication of this study is on the new viewpoint over the vector space of DATC, which not only solves the optimality issue of DATC but also provides a new direction of direct search approach like projection method for the true optimum.     

Fractional Optimal Control of Navier-Stokes Equations

In this paper, the non-stationary incompressible fluid flows governed by the Navier-Stokes equations are studied in a bounded domain. This study focuses on the timefractional Navier-Stokes equations in the optimal control subject, where the control is distributed within the domain and the time-fractional derivative is proposed as RiemannLiouville sort. In addition, the control object is to minimize the quadratic cost functional. By using the Lax-Milgram lemma with the assistance of the fixed-point theorem, we demonstrate the existence and uniqueness of the weak solution to this system. Moreover, for a quadratic cost functional subject to the time-fractional Navier-Stokes equations, we prove the existence and uniqueness of optimal control. Also, via the variational inequality upon introducing the adjoint linearized system, some inequalities and identities are given to guarantee the first-order necessary optimality conditions. A direct consequence of the results obtained here is that when α → 1, the obtained results are valid for the classical optimal control of systems governed by the Navier-Stokes equations.     

An Algorithm for Project Cost-Duration Analysis Problem with Quadratic and Convex Cost Functions

Kuhn-Tucker necessary and sufficient conditions for the nonlinear programming problem are applied to the project cost-duration analysis problem for project networks with convex costs. These conditions give an optimality curve for the problem. A solution is optimal if and only if when the values for activities are plotted on their optimality diagram, the values lie on the optimality curve. An algorithm is given here when the cost is convex and quadratic. The algorithm is also generalized to the case when the cost is convex and piecewise quadratic. The algorithm can be used to solve problems with convex cost functions by approximating them by piecewise quadratic functions.     

Dynamic programming and the solution of the biharmonic equation

The numerical solution of the biharmonic equation in a rectangular domain is presented in the context of continuous dynamic programming techniques. The equations are specialized to the solution of elastic rectangular plates. A suitable approximate expression of a certain functional equation containing derivatives only in one direction is used to derive equations for the stiffness and flexibility matrices of the plate. It is shown that those matrices satisfy matrix Riccati equations subject to suitable initial conditions. It is also shown that the condition of optimality in the Hamilton-Jacobi-Bellman equation directly expresses a classical variational principle, i.e. the principle of complementary energy. Some numerical examples are finally presented.     

ROBUSTNESS OPTIMIZATION FOR CONSTRAINED NONLINEAR PROGRAMMING PROBLEMS∗

In realistic situations engineering designs should take into consideration random aberrations from the stipulated design variables arising from manufacturing variability. Moreover, many environmental parameters are often stochastic in nature. Traditional nonlinear optimization attempts to find a deterministic optimum of a cost function and does not take into account the effect of these random variations on the objective. This paper attempts to devise a technique for finding optima of constrained nonlinear functions that are robust with respect to such variations. The expectation of the function over a domain of aberrations in the parameters is taken as a measure of ‘robustness’ of the function value at a point. It is pointed out that robustness optimization is ideally an attempt to trade off between ‘optimality’ and ‘robustness’. A newly-developed multi-criteria optimization technique known as Normal-Boundary Intersection is used to find evenly-spaced points on the Pareto curve for the ‘optimality’ and ‘robustness’ criteria. This Pareto curve enables the user to make the trade-off decision explicitly, free of arbitrary ‘weighting’ parameters.

This paper also formulates a derivative-based approximation for evaluating the expected value of the objective function on the nonlinear manifold defined by the state equations for the system. Existing procedures for evaluating the expectation usually involve numerical integration techniques requiring many solutions of the state equations for one evaluation of the expectation. The procedure presented here bypasses the need for multiple solutions of the state equations and hence provides a cheaper and more easily optimizable approximation to the expectation. Finally, this paper discusses how nonlinear inequality constraints should be treated in the presence of random parameters in the design. Computational results are presented for finding a robust optimum of a nonlinear structural optimization problem.     

Post-buckling analysis of composite beams: A simple intuitive formulation

Post-buckling analysis of composite beams with axially immovable ends is investigated using an Intuitive formulation. Intuitive formulation uses two parameters namely critical buckling load and axial stretching force developed in the post-buckled domain of composite beam. Geometric nonlinearity of von-Karman type is taken into consideration which accounts for membrane stretching action of the beam. Axial stretching force developed in post-buckled domain of composite beam is evaluated by using an axial governing equation and is expressed either in terms of lateral displacement function as an integrated value, or as a function of both axial and lateral displacement functions at any discrete location of the beam. The available expressions of critical buckling load and derived expressions of axial stretching force developed in the beam are used for obtaining an approximate closed-form expressions for the post-buckling loads of various beam boundary conditions. Numerical accuracy of the proposed analytical closed-form expressions obtained from the intuitive formulation are compared to the available finite element solutions for symmetric and asymmetric lay-up schemes of laminated composite beam. Effect of central amplitude ratio and lay-up orientation on post-buckling load variation is briefly discussed for various beam boundary conditions considered in this study.