Stochastic multi-site capacity planning of TFT-LCD manufacturing using expected shadow-price based decomposition

This paper presents a stochastic optimization model and efficient decomposition algorithm for multi-site capacity planning under the uncertainty of the TFT-LCD industry. The objective of the stochastic capacity planning is to determine a robust capacity allocation and expansion policy hedged against demand uncertainties because the demand forecasts faced by TFT-LCD manufacturers are usually inaccurate and vary rapidly over time. A two-stage scenario-based stochastic mixed integer programming model that extends the deterministic multi-site capacity planning model proposed by Chen et al. (2010) [1] is developed to discuss the multi-site capacity planning problem in the face of uncertain demands. In addition a three-step methodology is proposed to generate discrete demand scenarios within the stochastic optimization model by approximating the stochastic continuous demand process fitted from the historical data. An expected shadow-price based decomposition, a novel algorithm for the stage decomposition approach, is developed to obtain a near-optimal solution efficiently through iterative procedures and parallel computing. Preliminary computational study shows that the proposed decomposition algorithm successfully addresses the large-scale stochastic capacity planning model in terms of solution quality and computation time. The proposed algorithm also outperforms the plain use of the CPLEX MIP solver as the problem size becomes larger and the number of demand scenarios increases.     

Solving air traffic conflict problems via local continuous optimization

This paper first introduces an original trajectory model using B-splines and a new semi-infinite programming formulation of the separation constraint involved in air traffic conflict problems. A new continuous optimization formulation of the tactical conflict-resolution problem is then proposed. It involves very few optimization variables in that one needs only one optimization variable to determine each aircraft trajectory. Encouraging numerical experiments show that this approach is viable on realistic test problems. Not only does one not need to rely on the traditional, discretized, combinatorial optimization approaches to this problem, but, moreover, local continuous optimization methods, which require relatively fewer iterations and thereby fewer costly function evaluations, are shown to improve the performance of the overall global optimization of this non-convex problem.     

Cell-to-cell mapping method for time-optimal trajectory planning of multiple robot arm systems

This paper presents the results obtained by applying the cell-to-cell mapping method to solve the problem of the time-optimal trajectory planning for coordinated multiple robotic arms handling a common object along a specified geometric path. Based on the structure of the time-optimal trajectory control law, the continuous dynamic model of multiple arms is first approximated by a discrete and finite cell-to-cell mapping on a two-dimensional cell space over a phase plane. The optimal trajectory and the corresponding control are then determined by using the cell-to-cell mapping and a simple search algorithm. To further improve the computational efficiency and to allow for parallel computation, a hierarchical search algorithm consisting of a multiple-variable optimization on the top level and a number of cell-to-cell searches on the bottom level is proposed and implemented in the paper. Besides its simplicity, another distinguishing feature of the cell-to-cell mapping methods is the generation of all optimal trajectories for a given final state and all possible initial states through a single searching process. For most of the existing trajectory planning methods, the planning process can be started only when both the initial and final states have been specified. The cell-to-cell method can be generalized to any optimal trajectory planning problem for a multiple robotic arms system.     

Computational strategies for non-convex multistage MINLP models with decision-dependent uncertainty and gradual uncertainty resolution

In many planning problems under uncertainty the uncertainties are decision-dependent and resolve gradually depending on the decisions made. In this paper, we address a generic non-convex MINLP model for such planning problems where the uncertain parameters are assumed to follow discrete distributions and the decisions are made on a discrete time horizon. In order to account for the decision-dependent uncertainties and gradual uncertainty resolution, we propose a multistage stochastic programming model in which the non-anticipativity constraints in the model are not prespecified but change as a function of the decisions made. Furthermore, planning problems consist of several scenario subproblems where each subproblem is modeled as a nonconvex mixed-integer nonlinear program. We propose a solution strategy that combines global optimization and outer-approximation in order to optimize the planning decisions. We apply this generic problem structure and the proposed solution algorithm to several planning problems to illustrate the efficiency of the proposed method with respect to the method that uses only global optimization.     

Focused ultrasonic therapy planning: Metamodeling,optimization, visualization

We present a generic approach for focused ultrasonic therapy planning on the basis of numerical simulation, multi-objective optimization, stochastic analysis and visualization in virtual environments. A realistic test case is used to demonstrate the approach. RBF metamodeling of simulation results is performed for continuous representation of two optimization objectives. The non-convex Pareto front of the objectives is determined by means of non-dominated set and local improvement algorithms. Uncertainties of metamodeling are estimated by means of a cross-validation procedure. The 3D visualization in virtual environment framework Avango allows detailed inspection of MRT images, the corresponding material model and spatial distribution of the resulting thermal dose.     

Range reduction techniques for improving computational efficiency in global optimization of signomial geometric programming problems

Many global optimization approaches for solving signomial geometric programming problems are based on transformation techniques and piecewise linear approximations of the inverse transformations. Since using numerous break points in the linearization process leads to a significant increase in the computational burden for solving the reformulated problem, this study integrates the range reduction techniques in a global optimization algorithm for signomial geometric programming to improve computational efficiency. In the proposed algorithm, the non-convex geometric programming problem is first converted into a convex mixed-integer nonlinear programming problem by convexification and piecewise linearization techniques. Then, an optimization-based approach is used to reduce the range of each variable. Tightening variable bounds iteratively allows the proposed method to reach an approximate solution within an acceptable error by using fewer break points in the linearization process, therefore decreasing the required CPU time. Several numerical experiments are presented to demonstrate the advantages of the proposed method in terms of both computational efficiency and solution quality.     

Dynamic Capacity Acquisition and Assignment under Uncertainty

Given a set of m resources and n tasks, the dynamic capacity acquisition and assignment problem seeks a minimum cost schedule of capacity acquisitions for the resources and the assignment of resources to tasks, over a given planning horizon of T periods. This problem arises, for example, in the integrated planning of locations and capacities of distribution centers (DCs), and the assignment of customers to the DCs, in supply chain applications. We consider the dynamic capacity acquisition and assignment problem in an environment where the assignment costs and the processing requirements for the tasks are uncertain. Using a scenario based approach, we develop a stochastic integer programming model for this problem. The highly non-convex nature of this model prevents the application of standard stochastic programming decomposition algorithms. We use a recently developed decomposition based branch-and-bound strategy for the problem. Encouraging preliminary computational results are provided.     

基于矩阵变换的聚类集成优化模型

聚类集成方法能够有效综合不同的聚类结果,提高聚类的精确度和稳定性.提出了一个基于矩阵变换的聚类集成优化模型,模型通过矩阵变换代替传统方法中的聚类配准模式,使得优化模型更加简洁,然后给出了求解该优化模型的叠代算法.实验表明,提出的聚类集成方法能够有效提高聚类集成的稳定性和精确度,并且在聚类数目比较少时,算法有着较低的时间复杂度.     

Trajectory Modeling of Robot Manipulators in the Presence of Obstacles

This paper presents two different strategies for the problem of the optimal trajectory planning of robot manipulators in the presence of fixed obstacles. The first strategy is related to the situation where the trajectory must pass through a given number of points. The second strategy corresponds to the case where only the initial and final points are given. The optimal traveling time and the minimum mechanical energy of the actuators are considered together to build a multiobjective function. The trajectories are defined using spline functions and are obtained through offline computation for online operation. Sequential unconstrained minimization techniques (SUMT) have been used for the optimization. The obstacles are considered as three-dimensional objects sharing the same workspace performed by the robot. The obstacle avoidance is expressed in terms of the distances between potentially colliding parts. Simulation results are presented and show the efficiency of the general methodology used in this paper.     

Global optimization of higher order moments in portfolio selection

We discuss the global optimization of the higher order moments of a portfolio of financial assets. The proposed model is an extension of the celebrated mean variance model of Markowitz. Asset returns typically exhibit excess kurtosis and are often skewed. Moreover investors would prefer positive skewness and try to reduce kurtosis of their portfolio returns. Therefore the mean variance model (assuming either normally distributed returns or quadratic utility functions) might be too simplifying. The inclusion of higher order moments has therefore been proposed as a possible augmentation of the classical model in order to make it more widely applicable. The resulting problem is non-convex, large scale, and highly relevant in financial optimization. We discuss the solution of the model using two stochastic algorithms. The first algorithm is Differential Evolution (DE). DE is a population based metaheuristic originally designed for continuous optimization problems. New solutions are generated by combining up to four existing solutions plus noise, and acceptance is based on evolutionary principles. The second algorithm is based on the asymptotic behavior of a suitably defined Stochastic Differential Equation (SDE). The SDE consists of three terms. The first term tries to reduce the value of the objective function, the second enforces feasibility of the iterates, while the third adds noise in order to enable the trajectory to climb hills.     

A dynamic genetic algorithm based on continuous neural networks for a kind of non-convex optimization problems

This paper presents a kind of dynamic genetic algorithm based on a continuous neural network, which is intrinsically the steepest decent method for constrained optimization problems. The proposed algorithm combines the local searching ability of the steepest decent methods with the global searching ability of genetic algorithms. Genetic algorithms are used to decide each initial point of the steepest decent methods so that all the initial points can be searched intelligently. The steepest decent methods are employed to decide the fitness of genetic algorithms so that some good initial points can be selected. The proposed algorithm is motivated theoretically and biologically. It can be used to solve a non-convex optimization problem which is quadratic and even more non-linear. Compared with standard genetic algorithms, it can improve the precision of the solution while decreasing the searching scale. In contrast to the ordinary steepest decent method, it can obtain global sub-optimal solution while lessening the complexity of calculation.     

Accurate and robust body position trajectory tracking of six-legged walking robots with nonsingular terminal sliding mode control method

Many tasks, such as walking in narrow environments, detecting land mines, coordinating with manipulators, and avoiding obstacles, demand multi-legged walking robots to accurately and robustly track predefined body trajectories. Tracking body position trajectory must be accurate and robust in these situations, but research on this topic is rarely carried out. In this study, we propose a nonsingular terminal sliding mode (NTSM) control algorithm to implement accurate and robust body position trajectory tracking of six-legged walking robots. The NTSM control algorithm is constructed on the basis of the body position trajectory tracking model with a new NTSM reaching law. The performance of the NTSM control method is evaluated through several verifications. Results demonstrate that the proposed algorithm is effective for accurate and robust body position trajectory tracking. The findings of this study can provide insights into improving multi-legged walking robots’ walking and operation abilities in special environments and expanding the application fields of these robots.     

Iterative Algorithms for Multiscale State Estimation, Part 1: Concepts

The objective of the present investigation is to explore the potential of multiscale refinement schemes for the numerical solution of dynamic optimization problems arising in connection with chemical process systems monitoring. State estimation is accomplished by the solution of an appropriately posed least-squares problem. To offer at any instant of time an approximate solution, a hierarchy of successively refined problems is designed using a wavelet-based Galerkin discretization. In order to fully exploit at any stage the approximate solution obtained also for an efficient treatment of the arising linear algebra tasks, we employ iterative solvers. In particular, we will apply a nested iteration scheme to the hierarchy of arising equation systems and adapt the Uzawa algorithm to the present context. Moreover, we show that, using wavelets for the formulation of the problem hierarchy, the largest eigenvalues of the resulting linear systems can be controlled effectively with scaled diagonal preconditioning. Finally, we deduce appropriate stopping criteria and illustrate the characteristics of the solver with a numerical example.     

A solution algorithm for non-convex mixed integer optimization problems with only few continuous variables

Geometric branch-and-bound techniques are well-known solution algorithms for non-convex continuous global optimization problems with box constraints. Several approaches can be found in the literature differing mainly in the bounds used.     

全球变暖的宏观经济增长模型

本文研究了全球变暖的减排对策及其对经济环境的影响.运用动态最优化的方法,对该系统进行静态与动态的分析,并且讨论了参数对经济环境的影响.对我国制定全球变暖的对策有一定启发意义.     

Parameter estimation of delay differential equations: An integration-free LS-SVM approach

This paper introduces an estimation method based on Least Squares Support Vector Machines (LS-SVMs) for approximating time-varying as well as constant parameters in deterministic parameter-affine delay differential equations (DDEs). The proposed method reduces the parameter estimation problem to an algebraic optimization problem. Thus, as opposed to conventional approaches, it avoids iterative simulation of the given dynamical system and therefore a significant speedup can be achieved in the parameter estimation procedure. The solution obtained by the proposed approach can be further utilized for initialization of the conventional nonconvex optimization methods for parameter estimation of DDEs. Approximate LS-SVM based models for the state and its derivative are first estimated from the observed data. These estimates are then used for estimation of the unknown parameters of the model. Numerical results are presented and discussed for demonstrating the applicability of the proposed method.     

Testing the topographical global initialization strategy in the framework of an unconstrained optimization method

In general, classical iterative algorithms for optimization, such as Newton-type methods, perform only local search around a given starting point. Such feature is an impediment to the direct use of these methods to global optimization problems, when good starting points are not available. To overcome this problem, in this work we equipped a Newton-type method with the topographical global initialization strategy, which was employed together with a new formula for its key parameter. The used local search algorithm is a quasi-Newton method with backtracking. In this approach, users provide initial sets, instead of starting points. Then, using points sampled in such initial sets (merely boxes in \({\mathbb {R}}^{n}\)), the topographical method selects appropriate initial guesses for global optimization tasks. Computational experiments were performed using 33 test problems available in literature. Comparisons against three specialized methods (DIRECT, MCS and GLODS) have shown that the present methodology is a powerful tool for unconstrained global optimization.     

Parallel solver for trajectory optimization search directions

A key algorithmic element of a real-time trajectory optimization hardware/software implementation is presented, the search step solver. This is one piece of an algorithm whose overall goal is to make nonlinear trajectory optimization fast enough to provide real-time commands during guidance of a vehicle such as an aeromaneuvering orbiter or the National Aerospace Plane. Many methods of nonlinear programming require the solution of a quadratic program (QP) at each iteration to determine the search step. In the trajectory optimization case, the QP has a special dynamic programming structure, an LQR-like structure. The algorithm exploits this special structure with a divide-and-conquer type of parallel implementation. A hypercube message-passing parallel machine, the INTEL iPSC/2, has been used. The algorithm solves a (p·N)-stage problem onN processors inO(p + log₂ N) operations. The algorithm yields a factor of 8 speed-up over the fastest known serial algorithm when solving a 1024-stage test problem on 32 processors.This research was supported in part by the National Aeronautics and Space Administration under Grant No. NAG-1-1009.     

A General Cavitation Model for the Highly Nonlinear Mie-Grüneisen Equation of State

A general one-fluid cavitation model is proposed for a family of Mie-Grüneisen equations of state (EOS), which can provide a wide application of cavitation flows, such as liquid-vapour transformation and underwater explosion. An approximate Riemann problem and its approximate solver for the general cavitation model are developed. The approximate solver, which provides the interface pressure and normal velocity by an iterative method, is applied in computing the numerical flux at the phase interface for our compressible multi-medium flow simulation on Eulerian grids. Several numerical examples, including Riemann problems and underwater explosion applications, are presented to validate the cavitation model and the corresponding approximate solver.     

A numerical study of MIDACO on 100 MINLP benchmarks

This article presents a numerical study on MIDACO, a new global optimization software for mixed integer non-linear programming (MINLP) based on ant colony optimization and the oracle penalty method. Extensive and rigorous numerical tests on a set of 100 non-convex MINLP benchmark problems from the open literature are performed. Results obtained by MIDACO are directly compared to results by a recent study of state-of-the-art deterministic MINLP software on the same test set. Further comparisons with an established MINLP software is undertaken in addition. This study shows that MIDACO is not only competitive to the established MINLP software, but can even outperform those in terms of the number of global optimal solutions found. Moreover, the parallelization capabilities of MIDACO enable it to be even competitive to deterministic software regarding the amount of (serial processed) function evaluation, while the black-box capabilities of MIDACO offer an intriguing new robustness for MINLP.