Non-Random Adaptive Grid Method for High-Speed Optimization of Highly Dimensional, Badly Behaving Real Time Functions

1997 ◽  
Vol 119 (2) ◽  
pp. 265-272
Author(s):  
K. E. Shahroudi
Keyword(s):  
Real Time ◽  
High Speed ◽  
Solution Space ◽  
Quantitative Measure ◽  
Grid Method ◽  
Optimization Methods ◽  
Optimization Method ◽  
Adaptive Grid ◽  
Optimization Techniques ◽  
Function Evaluation

The majority of optimization methods lose their applicability when solving highly dimensional functions. The required calculation effort usually becomes enormous as dimensions increase, regardless of the elegance of the method. Most methods concern themselves with finding a single optimum that satisfies the required accuracy, but that provides no quantitative measure (i.e., probability of correctness) indicating whether the true optimum is found. Furthermore, there is usually no exact measure of the calculation effort prior to starting the procedure. There is always an unavoidable coupling (i.e., relation) between the accuracy, probability, and calculation effort of an optimization method, but the exact form of this relation is dependent on the procedures followed to reach optimum. Ideally, an optimization method should facilitate the statement of required accuracy, required probability, and the required calculation effort separately and the method should take care of the rest (i.e., total decoupling of the three requirements). Although this ideal case is generally not possible, it is possible to move toward it by finding procedures that reduce the strength of this unwanted coupling. This report derives simple analytical relations between the required accuracy, probability, and calculation effort of a general multidimensional adaptive grid non-gradient guided (NGG) search method where the search points are generated either decisively or randomly. It is then shown that any adaptive method based on reducing the total solution space is heavily penalized. Further, it is analytically illustrated that if the adaptive grid is randomly generated, it is far less successful than the non-random adaptive grid, because the amount of grid adaptation is less decisive at every step, due to the randomness. As with many optimization techniques, the dimensionality problem limits the application of this method to cases where the function evaluation is real time (~milliseconds) and dimensions are lower than say 25, which occurs in conceptual/preliminary design systems such as CAGED (Shahroudi, 1994b). This method is also particularly useful for problems in which the number of optima is known in advance. In this case the required probability can be set to its minimum value, which is required in order to distinguish an absolute optimum from a known (or likely) number of optima. The coupling relations derived in this report will then provide the minimum calculation effort necessary to satisfy accuracy and probability requirements.

Non-Random Adaptive Grid Method for High Speed Optimization of Highly Dimensional Badly Behaving Real Time Functions

1994 ◽  
Author(s):  
Kamran Eftekhari Shahroudi
Keyword(s):  
Real Time ◽  
High Speed ◽  
Solution Space ◽  
Quantitative Measure ◽  
Grid Method ◽  
Optimization Methods ◽  
Optimization Method ◽  
Adaptive Grid ◽  
Optimization Techniques ◽  
Function Evaluation

The majority of optimization methods lose their applicability when solving Highly Dimensional Functions. The required calculation effort usually becomes enormous as dimensions increase, regardless of the elegance of the method. Most methods concern themselves with finding a single optimum which satisfies the required Accuracy, but which provide no quantitative measure (i.e. Probability of correctness) indicating whether the true optimum is found). Furthermore, there is usually no exact measure of the Calculation Effonprior to starting the procedure. There is always an unavoidable coupling (i.e. relation) between the Accuracy, Probability and Calculation Effort of an optimization method but the exact form of this relation is dependant on the procedures followed to reach optimum. Ideally, an optimization method should facilitate the statement of required accuracy, required probability and the required calculation effort separately and the method should take care of the rest (i.e. total decoupling of the three requirements). Although this ideal case is generally not possible, it is possible to move towards it by finding procedures that reduce the strength of this unwanted coupling. This report derives simple analytical relations between the required accuracy, probability and calculation effort of a general multidimensional adaptive grid Non-Gradient Guided (NGG) search method where the search points are generated either decisively or randomly. It is then shown that any adaptive method based on reducing the total solution space is heavily penalized. Further, it is analytically illustrated that if the adaptive grid is randomly generated, it is far less successful than the non random adaptive grid, because the amount of grid adaptation is less decisive at every step., due to the randomness. As with many optimization techniques, the Dimensionality Problem limits the application of this method to cases where the function evaluation is real time (∼ milliseconds) and dimensions are lower than say 25, which occurs in Conceptual/Preliminary Design systems such as CAGEDR [Shahroudi, K.E. (Ref. 4)].

scholarly journals Robust Topology Optimization Under Load and Geometry Uncertainties by Using New Sparse Grid Collocation Method

2019 ◽  
Author(s):  
Seyyed Ali Latifi Rostami ◽  
Ali Ghoddosian
Keyword(s):  
Topology Optimization ◽  
Applied Load ◽  
Grid Method ◽  
Optimization Methods ◽  
Optimization Method ◽  
Monte Carlo Sampling ◽  
Sparse Grid ◽  
Benchmark Problems ◽  
Robust Topology Optimization ◽  
Cheap Alternative

In this paper, a robust topology optimization method presents that insensitive to the uncertainty in geometry and applied load. Geometric uncertainty can be introduced in the manufacturing variability. Applied load uncertainty is occurring in magnitude and angle of force. These uncertainties can be modeled as a random field. A memory-less transformation of random fields used to random variation modeling. The Adaptive Sparse Grid Collocation (ASGC) method combined with the uncertainty models provides robust designs by utilizing already developed deterministic solvers. The proposed algorithm provides a computationally cheap alternative to previously introduced stochastic optimization methods based on Monte Carlo sampling by using the adaptive sparse grid method. Numerical examples, such as a 2D simply supported beam and cantilever beam as benchmark problems, are used to show the effectiveness and superiority of the ASGC method.

scholarly journals Optimal design of symmetric switching CMOS inverter using symbiotic organisms search algorithm

2020 ◽  
Vol 10 (1) ◽  
pp. 171
Author(s):  
Nihad Dib ◽  
Umar Al-Sammarraie
Keyword(s):  
Optimal Design ◽  
High Speed ◽  
Search Algorithm ◽  
Fitness Function ◽  
Logic Gate ◽  
Optimization Methods ◽  
Optimization Method ◽  
Cmos Inverter ◽  
Symbiotic Organisms Search ◽  
Symbiotic Organisms

This paper investigates the optimal design of symmetric switching CMOS inverter using the Symbiotic Organisms Search (SOS) algorithm. SOS has been recently proposed as an effective evolutionary global optimization method that is inspired by the symbiotic interaction strategies between different organisms in an ecosystem. In SOS, the three common types of symbiotic relationships (mutualism, commensalism, and parasitism) are modeled using simple expressions, which are used to find the global minimum of the fitness function. Unlike other optimization methods, SOS has no parameters to be tuned, which makes it an attractive and easy-to-implement optimization method. Here, SOS is used to design a high speed symmetric switching CMOS inverter, which is considered the most fundamental logic gate. SOS results are compared to those obtained using several optimization methods, like particle swarm optimization (PSO), genetic algorithm (GA), differential evolution (DE), and other ones, available in the literature. It is shown that the SOS is a robust straight-forward evolutionary algorithm that can compete with other well-known advanced methods.

scholarly journals An Empirical Study on Low Emission Taxiing Path Optimization of Aircrafts on Airport Surfaces from the Perspective of Reducing Carbon Emissions

Energies ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1649 ◽  
Author(s):  
Nan Li ◽  
Yu Sun ◽  
Jian Yu ◽  
Jian-Cheng Li ◽  
Hong-fei Zhang ◽  
...  
Keyword(s):  
Real Time ◽  
Emission Reduction ◽  
Trajectory Optimization ◽  
Optimization Methods ◽  
Optimization Method ◽  
Path Optimization ◽  
Pollutant Emissions ◽  
Future Research ◽  
Aircraft Emissions ◽  
Fuel Consumption And Emissions

Aircraft emissions are the main cause of airport air pollution. One of the keys to achieving airport energy conservation and emission reduction is to optimize aircraft taxiing paths. The traditional optimization method based on the shortest taxi time is to model the aircraft under the assumption of uniform speed taxiing. Although it is easy to solve, it does not take into account the change of the velocity profile when the aircraft turns. In view of this, this paper comprehensively considered the aircraft’s taxiing distance, the number of large steering times and collision avoidance in the taxi, and established a path optimization model for aircraft taxiing at airport surface with the shortest total taxi time as the target. The genetic algorithm was used to solve the model. The experimental results show that the total fuel consumption and emissions of the aircraft are reduced by 35% and 46%, respectively, before optimization, and the taxi time is greatly reduced, which effectively avoids the taxiing conflict and reduces the pollutant emissions during the taxiing phase. Compared with traditional optimization methods that do not consider turning factors, energy saving and emission reduction effects are more significant. The proposed method is faster than other complex algorithms considering multiple factors, and has higher practical application value. It is expected to be applied in the more accurate airport surface real-time running trajectory optimization in the future. Future research will increase the actual interference factors of the airport, comprehensively analyze the actual situation of the airport’s inbound and outbound flights, dynamically adjust the taxiing path of the aircraft and maintain the real-time performance of the system, and further optimize the algorithm to improve the performance of the algorithm.

Significance of Biologically Inspired Optimization Techniques in Real-Time Applications

2017 ◽  
pp. 150-180
Author(s):  
Sushruta Mishra ◽  
Brojo Kishore Mishra ◽  
Hrudaya Kumar Tripathy
Keyword(s):  
Real Time ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Biologically Inspired ◽  
Swarm Optimization ◽  
Genetic Search ◽  
Artificial Bee Colony Optimization ◽  
Bee Colony ◽  
Bee Colony Optimization

The techniques inspired from the nature based evolution and aggregated nature of social colonies have been promising and shown excellence in handling complicated optimization problems thereby gaining huge popularity recently. These methodologies can be used as an effective problem solving tool thereby acting as an optimizing agent. Such techniques are called Bio inspired computing. Our study surveys the recent advances in biologically inspired swarm optimization methods and Evolutionary methods, which may be applied in various fields. Four real time scenarios are demonstrated in the form of case studies to show the significance of bio inspired algorithms. The techniques that are illustrated here include Differential Evolution, Genetic Search, Particle Swarm optimization and artificial bee Colony optimization. The results inferred by implanting these techniques are highly encouraging.

A sequential hybrid method to establish practical sizing systems based on anthropometric data

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Amir Tjolleng ◽  
Kihyo Jung ◽  
Hyunsook Han ◽  
Hyunjung Han ◽  
Jayoung Cho
Keyword(s):  
Hybrid Method ◽  
Grid Method ◽  
Initial Step ◽  
Optimization Methods ◽  
Optimization Method ◽  
Anthropometric Data ◽  
Content Type ◽  
Subsequent Step ◽  
Sizing System ◽  
Sizing Systems

PurposeSize fit and economic efficiency are two crucial aspects that need to be considered in designing a sizing system. However, there could exist a trade-off between those aspects in order to establish a practical sizing system. The purpose of this paper is to develop a sequential hybrid method of grid and optimization to generate a practical sizing system using anthropometric data.Design/methodology/approachThe proposed sequential hybrid method consisted of two sequential steps, which employs grid method and optimization method. In the initial step, the grid method creates primary grids that accommodate a designated percentage (e.g. 90%) of users with best size fit. In the subsequent step, the optimization method generated additional grids to provide acceptable fit, with minimum fit penalty scores for users unaccommodated by the primary grids. Our method was applied to the development of a sizing system for men's military jackets. The proposed method performances were evaluated in terms of accommodation percentage, size fit and number of sizing categories.FindingsOur proposed method resulted in 26 primary grids during the initial step, which cover 90% of users. Next, we generated six additional grids during the subsequent step that provide minimum fit penalty scores for the rest (10%) users.Originality/valueThe main contributions of this paper are as follows: consider accommodation percentage, size fit and number of sizing categories in the design of sizing system; combine the grid and optimization methods and evaluate a sizing system for men's military jackets. The proposed method is applicable to develop optimal sizing systems for multiple-size products.

scholarly journals Evaluation of optimization methods for solving the receptor model for chemical mass balance

2015 ◽  
Vol 80 (2) ◽  
pp. 253-264 ◽  
Author(s):  
N. Anu ◽  
S. Rangabhashiyam ◽  
Antony Rahul ◽  
N. Selvaraju
Keyword(s):  
Genetic Algorithm ◽  
Air Quality ◽  
Optimization Methods ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Quality Analysis ◽  
Algorithm Optimization ◽  
Chi Square ◽  
Source Contribution ◽  
Source Contributions

Balance (CMB) model has been extensively used in order to determine source contribution for particulate matters (size diameters less than 10 ?m and 2.5 ?m) in the air quality analysis. A comparison of the source contribution estimated from the three CMB models (CMB 8.2, CMB-fmincon and CMB-GA) have been carried out through optimization techniques such as ?fmincon? (CMB-fmincon) and genetic algorithm (CMB-GA) using MATLAB. The proposed approach has been validated using San Joaquin Valley Air Quality Study (SJVAQS) California Fresno and Bakersfield PM10 and PM2.5 followed with Oregon PM10 data. The source contribution estimated from CMB-GA was better in source interpretation in comparison with CMB8.2 and CMB-fmincon. The performance accuracy of three CMB approaches were validated using R-square, reduced chi-square and percentage mass tests. The R-square (0.90, 0.67 and 0.81, 0.83), Chi-square (0.36, 0.66 and 0.65, 0.43) and percentage mass (67.36 %, 55.03 % and 94.24 %, 74.85 %) of CMB-GA showed high correlation for PM10, PM2.5 Fresno and Bakersfield data respectively. To make a complete decision, the proposed methodology has been bench marked with Portland, Oregon PM10 data with best fit with R2 (0.99), Chi-square (1.6) and percentage mass (94.4 %) from CMB-GA. Therefore, the study revealed that CMB with genetic algorithm optimization method holds better stability in determining the source contributions.

scholarly journals Smoothness preserving layout for dynamic labels by hybrid optimization

2021 ◽  
Vol 8 (1) ◽  
pp. 149-163
Author(s):  
Yu He ◽  
Guo-Dong Zhao ◽  
Song-Hai Zhang
Keyword(s):  
Global Optimization ◽  
High Speed ◽  
Optimization Methods ◽  
Optimization Method ◽  
Streaming Data ◽  
Resultant Force ◽  
Hybrid Optimization ◽  
Global Optimization Method ◽  
Trade Off ◽  
Global Optimization Methods

AbstractStable label movement and smooth label trajectory are critical for effective information understanding. Sudden label changes cannot be avoided by whatever forced directed methods due to the unreliability of resultant force or global optimization methods due to the complex trade-off on the different aspects. To solve this problem, we proposed a hybrid optimization method by taking advantages of the merits of both approaches. We first detect the spatial-temporal intersection regions from whole trajectories of the features, and initialize the layout by optimization in decreasing order by the number of the involved features. The label movements between the spatial-temporal intersection regions are determined by force directed methods. To cope with some features with high speed relative to neighbors, we introduced a force from future, called temporal force, so that the labels of related features can elude ahead of time and retain smooth movements. We also proposed a strategy by optimizing the label layout to predict the trajectories of features so that such global optimization method can be applied to streaming data.

Significance of Biologically Inspired Optimization Techniques in Real-Time Applications

2020 ◽  
pp. 224-248
Author(s):  
Sushruta Mishra ◽  
Brojo Kishore Mishra ◽  
Hrudaya Kumar Tripathy
Keyword(s):  
Real Time ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Biologically Inspired ◽  
Swarm Optimization ◽  
Genetic Search ◽  
Artificial Bee Colony Optimization ◽  
Bee Colony ◽  
Bee Colony Optimization

The techniques inspired from the nature based evolution and aggregated nature of social colonies have been promising and shown excellence in handling complicated optimization problems thereby gaining huge popularity recently. These methodologies can be used as an effective problem solving tool thereby acting as an optimizing agent. Such techniques are called Bio inspired computing. Our study surveys the recent advances in biologically inspired swarm optimization methods and Evolutionary methods, which may be applied in various fields. Four real time scenarios are demonstrated in the form of case studies to show the significance of bio inspired algorithms. The techniques that are illustrated here include Differential Evolution, Genetic Search, Particle Swarm optimization and artificial bee Colony optimization. The results inferred by implanting these techniques are highly encouraging.

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