Common Optimization Methods Research Articles

Optimization Methods and Algorithms for Solving Of HydroThermal Scheduling Problems.

Different optimization methods have been applied to solve hydrothermal scheduling problems. This study reviews some of the common optimization methods and algorithms their strengths and weaknesses. The study found out that with time, old methods are improved upon and novel methods are developed to provide for more efficiency, faster convergence, robustness, and adaptability.

Potential of the Pseudo-Inverse Method as a Constrained Static Optimization for Musculo-Tendon Forces Prediction

Inverse dynamics combined with a constrained static optimization analysis has often been proposed to solve the muscular redundancy problem. Typically, the optimization problem consists in a cost function to be minimized and some equality and inequality constraints to be fulfilled. Penalty-based and Lagrange multipliers methods are common optimization methods for the equality constraints management. More recently, the pseudo-inverse method has been introduced in the field of biomechanics. The purpose of this paper is to evaluate the ability and the efficiency of this new method to solve the muscular redundancy problem, by comparing respectively the musculo-tendon forces prediction and its cost-effectiveness against common optimization methods. Since algorithm efficiency and equality constraints fulfillment highly belong to the optimization method, a two-phase procedure is proposed in order to identify and compare the complexity of the cost function, the number of iterations needed to find a solution and the computational time of the penalty-based method, the Lagrange multipliers method and pseudo-inverse method. Using a 2D knee musculo-skeletal model in an isometric context, the study of the cost functions isovalue curves shows that the solution space is 2D with the penalty-based method, 3D with the Lagrange multipliers method and 1D with the pseudo-inverse method. The minimal cost function area (defined as the area corresponding to 5% over the minimal cost) obtained for the pseudo-inverse method is very limited and along the solution space line, whereas the minimal cost function area obtained for other methods are larger or more complex. Moreover, when using a 3D lower limb musculo-skeletal model during a gait cycle simulation, the pseudo-inverse method provides the lowest number of iterations while Lagrange multipliers and pseudo-inverse method have almost the same computational time. The pseudo-inverse method, by providing a better suited cost function and an efficient computational framework, seems to be adapted to the muscular redundancy problem resolution in case of linear equality constraints. Moreover, by reducing the solution space, this method could be a unique opportunity to introduce optimization methods for a posteriori articulation of preference in order to provide a palette of solutions rather than a unique solution based on a lot of hypotheses.

Optimal structural design of the midship of a VLCC based on the strategy integrating SVM and GA

In this paper a hybrid process of modeling and optimization, which integrates a support vector machine (SVM) and genetic algorithm (GA), was introduced to reduce the high time cost in structural optimization of ships. SVM, which is rooted in statistical learning theory and an approximate implementation of the method of structural risk minimization, can provide a good generalization performance in metamodeling the input-output relationship of real problems and consequently cuts down on high time cost in the analysis of real problems, such as FEM analysis. The GA, as a powerful optimization technique, possesses remarkable advantages for the problems that can hardly be optimized with common gradient-based optimization methods, which makes it suitable for optimizing models built by SVM. Based on the SVM-GA strategy, optimization of structural scantlings in the midship of a very large crude carrier (VLCC) ship was carried out according to the direct strength assessment method in common structural rules (CSR), which eventually demonstrates the high efficiency of SVM-GA in optimizing the ship structural scantlings under heavy computational complexity. The time cost of this optimization with SVM-GA has been sharply reduced, many more loops have been processed within a small amount of time and the design has been improved remarkably.

Effect of diatomic molecular properties on binary laser pulse optimizations of quantum gate operations

The importance of the ro-vibrational state energies on the ability to produce high fidelity binary shaped laser pulses for quantum logic gates is investigated. The single frequency 2-qubit ACNOT(1) and double frequency 2-qubit NOT(2) quantum gates are used as test cases to examine this behaviour. A range of diatomics is sampled. The laser pulses are optimized using a genetic algorithm for binary (two amplitude and two phase parameter) variation on a discretized frequency spectrum. The resulting trends in the fidelities were attributed to the intrinsic molecular properties and not the choice of method: a discretized frequency spectrum with genetic algorithm optimization. This is verified by using other common laser pulse optimization methods (including iterative optimal control theory), which result in the same qualitative trends in fidelity. The results differ from other studies that used vibrational state energies only. Moreover, appropriate choice of diatomic (relative ro-vibrational state arrangement) is critical for producing high fidelity optimized quantum logic gates. It is also suggested that global phase alignment imposes a significant restriction on obtaining high fidelity regions within the parameter search space. Overall, this indicates a complexity in the ability to provide appropriate binary laser pulse control of diatomics for molecular quantum computing.

C^4: Exploring Multiple Solutions in Graphical Models by Cluster Sampling

This paper presents a novel Markov Chain Monte Carlo (MCMC) inference algorithm called C(4)--Clustering with Cooperative and Competitive Constraints--for computing multiple solutions from posterior probabilities defined on graphical models, including Markov random fields (MRF), conditional random fields (CRF), and hierarchical models. The graphs may have both positive and negative edges for cooperative and competitive constraints. C(4) is a probabilistic clustering algorithm in the spirit of Swendsen-Wang. By turning the positive edges on/off probabilistically, C(4) partitions the graph into a number of connected components (ccps) and each ccp is a coupled subsolution with nodes connected by positive edges. Then, by turning the negative edges on/off probabilistically, C(4) obtains composite ccps (called cccps) with competing ccps connected by negative edges. At each step, C(4) flips the labels of all nodes in a cccp so that nodes in each ccp keep the same label while different ccps are assigned different labels to observe both positive and negative constraints. Thus, the algorithm can jump between multiple competing solutions (or modes of the posterior probability) in a single or a few steps. It computes multiple distinct solutions to preserve the intrinsic ambiguities and avoids premature commitments to a single solution that may not be valid given later context. C(4) achieves a mixing rate faster than existing MCMC methods, such as various Gibbs samplers and Swendsen-Wang cuts. It is also more "dynamic" than common optimization methods such as ICM, LBP, and graph cuts. We demonstrate the C(4) algorithm in line drawing interpretation, scene labeling, and object recognition.

Shape, sizing optimization and material selection based on mixed variables and genetic algorithm

In this work, we explore simultaneous designs of materials selection and structural optimization. As the material selection turns out to be a discrete process that finds the optimal distribution of materials over the design domain, it cannot be performed with common gradient-based optimization methods. In this paper, material selection is considered together with the shape and sizing optimization in a framework of multiobjective optimization of tracking the Pareto curve. The idea of mixed variables is often introduced in the case of mono-objective optimization. However, in the case of multi-objective optimization, we still face some hard key points related to the convexity and the continuity of the Pareto domain, which underline the originality of this work. In addition to the above aspect, there is a lack in the literature concerning the industrial applications that consider the mixed parameters. Continuous variables refer to structural parameters such as thickness, diameter and spring elastic constants while material ID is defined as binary design variable for each material. Both mechanical and thermal loads are considered in this work with the aim of minimizing the maximum stress and structural weight simultaneously. The efficiency of the design procedure is demonstrated through various numerical examples.

Performance analysis of reset control systems

AbstractIn this paper we present a general linear matrix inequality‐based analysis method to determine the performance of a SISO reset control system in both the ℒ︁2 gain and ℋ︁2 sense. In particular, we derive convex optimization problems in terms of LMIs to compute an upperbound on the ℒ︁2 gain performance and the ℋ︁2 norm, using dissipativity theory with piecewise quadratic Lyapunov functions. The results are applicable to for all LTI plants and linear‐based reset controllers, thereby generalizing the available results in the literature. Furthermore, we provide simple though convincing examples to illustrate the accuracy of our proposed ℒ︁2 gain and ℋ︁2 norm calculations and show that, for an input constrained ℋ︁2 problem, reset control can outperform a linear controller designed by a common nonlinear optimization method. Copyright © 2009 John Wiley & Sons, Ltd.

Automated seeding for the optimization of crystal quality

With the advent of structural genomics a variety of crystallization techniques have been automated and applied to high-throughput pipelines, yet seeding, which is the most common and successful optimization method, is still being performed predominantly manually. The aim of this study was to devise simple automated seeding techniques that can be applied in a routine manner using existing robots and not requiring special tools. Two alternative protocols for automated seeding experiments are described. One involves the delivery of microcrystals from stock to target wells using the robot dispensing tip as a seeding tool. The second harnesses an animal whisker as the seeding tool. Larger and better ordered crystals were obtained using both techniques.

Algorithmic strategies for full waveform inversion: 1D experiments

Full-waveform seismic inversion, i.e., the iterative minimization of the misfit between observed seismic data and synthetic data obtained by a numerical solution of the wave equation provides a systematic, flexible, general mechanism for reconstructing earth models from observed ground motion. However, many difficulties arise for highly resolved models and the associated large-dimensional parameter spaces and high-frequency sources. First, the least-squares data-misfit functional suffers from spurious local minima, which necessitates an accurate initial guess for the smooth background model. Second, total variation regularization methods that are used to resolve sharp interfaces create significant numerical difficulties because of their nonlinearity and near-degeneracy. Third, bound constraints on continuous model parameters present considerable difficulty for commonly used active-set or interior-point methods for inequality constraints because of the infinite-dimensional nature of the parameters. Finally, common gradient-based optimization methods have difficulties scaling to the many model parameters that result when the continuous parameter fields are discretized. We have developed an optimization strategy that incorporates several techniques address these four difficulties, including grid, frequency, and time-window continuation; primal-dual methods for treating bound inequality constraints and total variation regularization; and inexact matrix-free Newton-Krylov optimization. Using this approach, several computations were performed effectively for a 1D setting with synthetic observations.

Gate Location Optimization in Injection Molding Based on Empirical Search Method

In injection mold, design of gate location is among the most critical factors in achieving dimensionally accurate parts and high productivity of the molding process, since it influences the manner in which the plastic flows into the mold cavity. To automatically predict the optimal gate location of injection molds based on injection-molding simulation, a new and practical method: empirical search method according to the analysis of common optimization methods has been presented in this article. In this method, the gate location scope is initiated by the practical experience of mold designer so that the core for the gate location optimization is construction of empirical library. In order to build the empirical library, in terms of shape and function characteristic of injection-molding part, all the parts are classified six kinds: shell, container, plate, structural part, ornamental part and transparent part, and the corresponding design rules are kept in the empirical library. In addition, this article combines the empirical search method and numerical simulation technique, builds the mathematics model for the gate location optimization of plate part in empirical library and obtains the gate location optimization scheme for this kind of part through one concrete numerical example. The analysis and verification by adopting the software Moldflow testify the optimization mathematics model is effective.

Informed multi‐objective decision‐making in environmental management using Pareto optimality

Summary Effective decision‐making in environmental management requires the consideration of multiple objectives that may conflict. Common optimization methods use weights on the multiple objectives to aggregate them into a single value, neglecting valuable insight into the relationships among the objectives in the management problem. We present a multi‐objective optimization procedure that approximates the non‐dominated Pareto frontier without the use of weightings, allowing for visualization of the trade‐offs among objectives. The non‐dominated Pareto frontier is approximated by the simultaneous optimization of a vector objective function; two vector objective functions are defined as non‐dominated if improvement with respect to one objective is at the detriment of another objective. We demonstrate the method with a case study for the optimum distribution of forest fuels treatments that reduce the impact of fire on a forest. The multiple objectives are to protect habitat of an endangered species, protect late successional forest reserves and minimize the total area treated. In the comparison of three optimization searches, the number of non‐dominated solutions increases with the dimensions of the objective space, but with only two objectives the search is ineffective in minimizing fire impact in the different landscape types. Key challenges include the extensive computation time required to approximate the non‐dominated set, and reducing the number of solutions that are analysed in detail. Synthesis and applications. The multi‐objective optimization program presented can be adapted to other environmental management problems, and easily incorporates a wide range of quantifiable objectives. This tool provides decision‐makers with a set of alternatives that estimates the full range of trade‐offs among multiple objectives and provides a common ground from which dialogue can come to an informed compromise and decision in environmental management problems.

Simulation optimization with qualitative variables and structural model changes: A genetic algorithm approach

In many common simulation optimization methods the structure of the system stays the same and only the set of values for certain parameters of the system such as the number of machines in a station or the in-process inventory is varied from one evaluation to the next. The methodology described in this paper is a simulation-optimization process where the qualitative variables and the structure of the system are the subjects of optimization. Here, the optimum response sought is a function of design and operation characteristics of the system such as the type of machines to use, dispatching rules, sequence of processing operations, etc. In the methodology developed here simulation models are automatically generated through an object-oriented process and are evaluated for various candidate configurations of the system. These candidates are suggested by a Genetic Algorithm (GA) that automatically guides the system towards better solutions. After simulating the alternatives, the results are returned to the GA to be utilized in selection of the next generation of configurations to be evaluated. This process continues until a satisfactory solution is obtained for the system.

Multiobjective Optimization of Bridge Deck Rehabilitation Using a Genetic Algorithm

The solution methods of multiobjective optimization have undergone constant development over the past three decades. However, the methods available to date are not particularly robust. Because of the complicated relationship between the rehabilitation cost and deterioration degree of infrastructure systems, it is difficult to find a near‐optimal solution using common optimization methods. Since genetic algorithms work with a population of points, they can capture a number of solutions simultaneously and easily incorporate the concept of Pareto optimality. In this paper a simple genetic algorithm with two additional techniques, Pareto optimality ranking and fitness sharing, is implemented for the deck rehabilitation plan of network‐level bridges, aiming to minimize the total rehabilitation cost and deterioration degree. This approach is illustrated by a simple example and then applied to a practical bridge system with a large number of bridges.

A Comparison of Selection Schemes Used in Evolutionary Algorithms

Evolutionary algorithms are a common probabilistic optimization method based on the model of natural evolution. One important operator in these algorithms is the selection scheme, for which in this paper a new description model, based on fitness distributions, is introduced. With this, a mathematical analysis of tournament selection, truncation selection, ranking selection, and exponential ranking selection is carried out that allows an exact prediction of the fitness values after selection. The correspondence of binary tournament selection and ranking selection in the expected fitness distribution is proved. Furthermore, several properties of selection schemes are derived (selection intensity, selection variance, loss of diversity), and the three selection schemes are compared using these properties.