scholarly journals Variability Map of Objective Function for Analysis of Global Optimization Problem Characteristic Features

2019 ◽  
pp. 4-21
Author(s):  
T.A. Agasiev
Keyword(s):  
Objective Function ◽  
Information Content ◽  
Optimization Problem ◽  
Target Function ◽  
Search Space ◽  
Experiment Design ◽  
Generalized Information ◽  
Problem Characteristic ◽  
Characteristic Features

Methods of landscape analysis are developed to estimate various characteristic features of the objective function in the optimization problem. The accuracy of the estimates largely depends on the chosen method of experiment design for the landscape sampling, i.e. on the number and location of points in the search space forming a discrete representation of the objective function landscape. The method of information content is the most resistant to changes in the experiment design but requires route building to bypass the obtained points of landscape sampling. A method of characterization of the optimization problem objective function is proposed on the base of landscape sampling without building a route to bypass its points. The notion of a variability map of objective function is introduced. The informativeness criteria are formulated for groups of points of a landscape sample. A method of constructing the so-called full variability map is proposed as well as the function of generalized information content for the analysis of the characteristic features of the objective function. The method allows obtaining more accurate estimates of target function characteristics which are resistant to variations of the experiment design

scholarly journals METHODS OF FORMULATING AND SOLVING OPTIMIZATION PROBLEMS OF CUTTING LOGS OF LARGE SIZE BY BAR-SAWING METHOD WITH CUTTING OUT ONE BAR AND FIVE PAIRS OF SIDE EDGING BOARDS WITH SUBSEQUENT SAWING LUMBER FOR EDGED BOARDS

2017 ◽  
Vol 7 (1) ◽  
pp. 137-150
Author(s):  
Агапов ◽  
Aleksandr Agapov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Target Function ◽  
Cross Sectional ◽  
Optimization Task ◽  
Cutting Out ◽  
The Mathematical Model ◽  
The Relationship

For the first time the mathematical model of task optimization for this scheme of cutting logs, including the objective function and six equations of connection. The article discusses Pythagorean area of the logs. Therefore, the target function is represented as the sum of the cross-sectional areas of edging boards. Equation of the relationship represents the relationship of the diameter of the logs in the vertex end with the size of the resulting edging boards. This relationship is described through the use of the Pythagorean Theorem. Such a representation of the mathematical model of optimization task is considered a classic one. However, the solution of this mathematical model by the classic method is proved to be problematic. For the solution of the mathematical model we used the method of Lagrange multipliers. Solution algorithm to determine the optimal dimensions of the beams and side edging boards taking into account the width of cut is suggested. Using a numerical method, optimal dimensions of the beams and planks are determined, in which the objective function takes the maximum value. It turned out that with the increase of the width of the cut, thickness of the beam increases and the dimensions of the side edging boards reduce. Dimensions of the extreme side planks to increase the width of cut is reduced to a greater extent than the side boards, which are located closer to the center of the log. The algorithm for solving the optimization problem is recommended to use for calculation and preparation of sawing schedule in the design and operation of sawmill lines for timber production. When using the proposed algorithm for solving the optimization problem the output of lumber can be increased to 3-5 %.

REDUCING DIMENSION IN GLOBAL OPTIMIZATION

2011 ◽  
Vol 08 (03) ◽  
pp. 535-544 ◽  
Author(s):  
BOUDJEHEM DJALIL ◽  
BOUDJEHEM BADREDDINE ◽  
BOUKAACHE ABDENOUR
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Optimization Problem ◽  
Low Cost ◽  
Main Idea ◽  
Search Space ◽  
Global Optimum ◽  
Local Optima ◽  
Interesting Idea ◽  
Narrow Space

In this paper, we propose a very interesting idea in global optimization making it easer and a low-cost task. The main idea is to reduce the dimension of the optimization problem in hand to a mono-dimensional one using variables coding. At this level, the algorithm will look for the global optimum of a mono-dimensional cost function. The new algorithm has the ability to avoid local optima, reduces the number of evaluations, and improves the speed of the algorithm convergence. This method is suitable for functions that have many extremes. Our algorithm can determine a narrow space around the global optimum in very restricted time based on a stochastic tests and an adaptive partition of the search space. Illustrative examples are presented to show the efficiency of the proposed idea. It was found that the algorithm was able to locate the global optimum even though the objective function has a large number of optima.

scholarly journals Characteristic feature analysis of continuous optimization problems based on Variability Map of objective function for optimization algorithm configuration

2020 ◽  
Vol 10 (1) ◽  
pp. 97-111
Author(s):  
Taleh Agasiev
Keyword(s):  
Objective Function ◽  
Optimization Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Landscape Analysis ◽  
Decomposition Approach ◽  
Analysis Methods ◽  
Algorithm Configuration ◽  
Sample Points ◽  
Characteristic Features

AbstractAdvanced optimization algorithms with a variety of configurable parameters become increasingly difficult to apply effectively to solving optimization problems. Appropriate algorithm configuration becomes highly relevant, still remaining a computationally expensive operation. Development of machine learning methods allows to model and predict the efficiency of different solving strategies and algorithm configurations depending on properties of optimization problem to be solved. The paper suggests the Dependency Decomposition approach to reduce computational complexity of modeling the efficiency of optimization algorithm, also considering the amount of computational resources available for optimization problem solving. The approach requires development of explicit Exploratory Landscape Analysis methods to assess a variety of significant characteristic features of optimization problems. The results of feature assessment depend on the number of sample points analyzed and their location in the design space, on top of that some of methods require additional evaluations of objective function. The paper proposes new landscape analysis methods based on given points without the need of any additional objective function evaluations. An algorithm of building a so-called Full Variability Map is suggested based on informativeness criteria formulated for groups of sample points. The paper suggests Generalized Information Content method for analysis of Full Variability Map which allows to get accurate and stable estimations of objective function features. The Sectorization method of Variability Map analysis is proposed to assess characteristic features reflecting such properties of objective function that are critical for optimization algorithm efficiency. The resulting features are invariant to the scale of objective function gradients which positively affects the generalizing ability of problems classification algorithm. The procedure of the comparative study of effectiveness of landscape analysis algorithms is introduced. The results of computational experiments indicate reliability of applying the suggested landscape analysis methods to optimization problem characterization and classification.

Shape Optimization of Hydraulic Structures: an Example of an Optimum Design of a Fish Passage

10.29007/2k64 ◽  
2018 ◽  
Author(s):  
Pat Prodanovic ◽  
Cedric Goeury ◽  
Fabrice Zaoui ◽  
Riadh Ata ◽  
Jacques Fontaine ◽  
...  
Keyword(s):  
Numerical Model ◽  
Shape Optimization ◽  
Objective Function ◽  
Optimum Design ◽  
Optimization Problem ◽  
A Priori ◽  
Coupled System ◽  
Fish Passage ◽  
Hydraulic Structures ◽  
Design Variables

This paper presents a practical methodology developed for shape optimization studies of hydraulic structures using environmental numerical modelling codes. The methodology starts by defining the optimization problem and identifying relevant problem constraints. Design variables in shape optimization studies are configuration of structures (such as length or spacing of groins, orientation and layout of breakwaters, etc.) whose optimal orientation is not known a priori. The optimization problem is solved numerically by coupling an optimization algorithm to a numerical model. The coupled system is able to define, test and evaluate a multitude of new shapes, which are internally generated and then simulated using a numerical model. The developed methodology is tested using an example of an optimum design of a fish passage, where the design variables are the length and the position of slots. In this paper an objective function is defined where a target is specified and the numerical optimizer is asked to retrieve the target solution. Such a definition of the objective function is used to validate the developed tool chain. This work uses the numerical model TELEMAC- 2Dfrom the TELEMAC-MASCARET suite of numerical solvers for the solution of shallow water equations, coupled with various numerical optimization algorithms available in the literature.

scholarly journals Very Fast and Accurate Procedure for the Characterization of Photovoltaic Panels from Datasheet Information

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Antonino Laudani ◽  
Francesco Riganti Fulginei ◽  
Alessandro Salvini ◽  
Gabriele Maria Lozito ◽  
Salvatore Coco
Keyword(s):  
Numerical Methods ◽  
Search Space ◽  
Extraction Process ◽  
Reduced Form ◽  
Photovoltaic Panels ◽  
Approximation Techniques ◽  
Computational Costs ◽  
Minimization Technique ◽  
Accurate Procedure

In recent years several numerical methods have been proposed to identify the five-parameter model of photovoltaic panels from manufacturer datasheets also by introducing simplification or approximation techniques. In this paper we present a fast and accurate procedure for obtaining the parameters of the five-parameter model by starting from its reduced form. The procedure allows characterizing, in few seconds, thousands of photovoltaic panels present on the standard databases. It introduces and takes advantage of further important mathematical considerations without any model simplifications or data approximations. In particular the five parameters are divided in two groups, independent and dependent parameters, in order to reduce the dimensions of the search space. The partitioning of the parameters provides a strong advantage in terms of convergence, computational costs, and execution time of the present approach. Validations on thousands of photovoltaic panels are presented that show how it is possible to make easy and efficient the extraction process of the five parameters, without taking care of choosing a specific solver algorithm but simply by using any deterministic optimization/minimization technique.

Aerodynamic Characterization of Transonic Turbine Vanes Optimized to Attenuate Rotor Forcing

2011 ◽  
Author(s):  
R. Puente ◽  
G. Paniagua ◽  
T. Verstraete
Keyword(s):  
High Efficiency ◽  
Prediction Method ◽  
Optimization Procedure ◽  
3D Design ◽  
Turbine Vanes ◽  
Turbine Vane ◽  
Loss Prediction ◽  
Transonic Turbine ◽  
Characteristic Features

A multi-objective optimization procedure is applied to the 3D design of a transonic turbine vane row, considering efficiency and stator outlet pressure distortion, which is directly related to induced rotor forcing. The characteristic features that define different individuals along the Pareto Front are described, analyzing the differences between high efficiency airfoils and low interaction. Pressure distortion is assessed by means of a model that requires only of the computation the steady flow field in the domain of the stator. The reduction of aerodynamic rotor forcing is checked via unsteady multistage aerodynamic computations. A well known loss prediction method is used to drive the efficiency of one optimization run, while CFD analysis is used for another, in order to assess the reliability of both methods. In both cases, the decomposition of total losses is performed to quantify the influence on efficiency of reducing rotor forcing. Results show that when striving for efficiency, the rotor is affected by few, but intense shocks. On the other hand, when the objective is the minimization of distortion, multiple shocks will appear.

scholarly journals A characterization of optimal multiprocessor schedules and new dominance rules

2020 ◽  
Vol 40 (4) ◽  
pp. 876-900
Author(s):  
Rico Walter ◽  
Alexander Lawrinenko
Keyword(s):  
Parallel Machines ◽  
Computational Study ◽  
Search Space ◽  
Point Of View ◽  
Theoretical Point ◽  
Optimal Solutions ◽  
Identical Parallel Machines ◽  
Makespan Minimization ◽  
Structural Pattern

Abstract The paper on hand approaches the classical makespan minimization problem on identical parallel machines from a rather theoretical point of view. Using an approach similar to the idea behind inverse optimization, we identify a general structural pattern of optimal multiprocessor schedules. We also show how to derive new dominance rules from the characteristics of optimal solutions. Results of our computational study attest to the efficacy of the new rules. They are particularly useful in limiting the search space when each machine processes only a few jobs on average.

scholarly journals Nonnegative Signal Decomposition with Supervision

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Teng Li ◽  
Huan Chang ◽  
Jun Wu
Keyword(s):  
Objective Function ◽  
Image Classification ◽  
Pattern Classification ◽  
Optimization Problem ◽  
Real Data ◽  
Classification Performance ◽  
Signal Decomposition ◽  
Weak Supervision ◽  
Training Samples ◽  
Novel Algorithm

This paper presents a novel algorithm to numerically decompose mixed signals in a collaborative way, given supervision of the labels that each signal contains. The decomposition is formulated as an optimization problem incorporating nonnegative constraint. A nonnegative data factorization solution is presented to yield the decomposed results. It is shown that the optimization is efficient and decreases the objective function monotonically. Such a decomposition algorithm can be applied on multilabel training samples for pattern classification. The real-data experimental results show that the proposed algorithm can significantly facilitate the multilabel image classification performance with weak supervision.

scholarly journals Optimal design of a DC MHD pump by simulated annealing method

2014 ◽  
Vol 11 (2) ◽  
pp. 339-350
Author(s):  
Khadidja Bouali ◽  
Fatima Kadid ◽  
Rachid Abdessemed
Keyword(s):  
Simulated Annealing ◽  
Optimal Design ◽  
Objective Function ◽  
Design Problem ◽  
Design Methodology ◽  
Optimization Problem ◽  
Optimization Procedure ◽  
Simulated Annealing Method ◽  
Direct Interpretation ◽  
Annealing Method

In this paper a design methodology of a magnetohydrodynamic pump is proposed. The methodology is based on direct interpretation of the design problem as an optimization problem. The simulated annealing method is used for an optimal design of a DC MHD pump. The optimization procedure uses an objective function which can be the minimum of the mass. The constraints are both of geometrics and electromagnetic in type. The obtained results are reported.

scholarly journals Table cartogram generation as an optimization problem

2019 ◽  
Vol 1 ◽  
pp. 1-2 ◽  
Author(s):  
Mao Li ◽  
Ryo Inoue
Keyword(s):  
Objective Function ◽  
Least Squares ◽  
Optimization Problem ◽  
Data Representation ◽  
Linear Least Squares ◽  
Original Table ◽  
Outer Border ◽  
Limited Degree ◽  
The Difference ◽  
Operation Results

<p><strong>Abstract.</strong> A table cartogram, visualization of table-form data, is a rectangle-shaped table in which each cell is transformed to express the magnitude of positive weight by its area while maintaining the adjacency relationship of cells in the original table. Winter (2011) applies an area cartogram generation method of Gastner and Newman (2004) for their generation, and Evans et al. (2018) proposes a new geometric procedure. The rows and columns on a table cartogram should be easily recognized by readers, however, no methods have focused to enhance the readability. This study proposes a method that defines table cartogram generation as an optimization problem and attempts to minimize vertical and horizontal deformation. Since the original tables are comprised of regular quadrangles, this study uses quadrangles to express cells in a table cartogram and fixes the outer border to attempt to retain the shape of a standard table.</p><p>This study proposes a two-step approach for table cartogram generation with cells that begin as squares and with fixed outer table borders. The first step only adjusts the vertical and horizontal borders of cells to express weights to the greatest possible degree. All cells maintain their rectangular shape after this step, although the limited degree of freedom of this operation results in low data representation accuracy. The second step adapts the cells of the low-accuracy table cartogram to accurately fit area to weight by relaxing the constraints on the directions of borders of cells. This study utilizes an area cartogram generation method proposed by Inoue and Shimizu (2006), which defines area cartogram generation as an optimization problem. The formulation with vertex coordinate parameters consists of an objective function that minimizes the difference between the given data and size of each cell, and a regularization term that controls the changes of bearing angles. It is formulated as non-linear least squares, and is solved through the iteration of linear least squares by linearizing the problem at the coordinates of vertices and updating the estimated coordinates until the value of the objective function becomes small enough.</p>

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