A Design Methodology for Nonlinear Systems Containing Parameter Uncertainty

1984 ◽  
Vol 106 (1) ◽  
pp. 15-20 ◽  
Author(s):  
G. E. Young ◽  
D. M. Auslander
Keyword(s):  
Nonlinear Systems ◽  
Parameter Uncertainty ◽  
Design Methodology ◽  
Search Strategy ◽  
Random Search ◽  
Adjustable Parameter ◽  
Performance Indices ◽  
Adaptive Random Search ◽  
Generalized Sensitivity ◽  
Parameter Values

A design methodology capable of dealing with nonlinear systems containing parameter uncertainty is presented. A generalized sensitivity analysis is incorporated which utilizes sampling of the parameter space and statistical inference. For a system with j adjustable and k nonadjustable parameters, this methodology (which includes an adaptive random search strategy) is used to determine the combination of j adjustable parameter values which maximizes the probability of the performance indices simultaneously satisfying design criteria given the uncertainty in the k nonadjustable parameters.

scholarly journals Optimization Algorithms for Detection of Social Interactions

Algorithms ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 139 ◽  
Author(s):  
Vincenzo Cutello ◽  
Georgia Fargetta ◽  
Mario Pavone ◽  
Rocco A. Scollo
Keyword(s):  
Social Networks ◽  
Local Search ◽  
Social Interactions ◽  
Community Detection ◽  
Experimental Analysis ◽  
Search Strategy ◽  
Random Search ◽  
Optimization Methods ◽  
Research Areas ◽  
Greedy Optimization

Community detection is one of the most challenging and interesting problems in many research areas. Being able to detect highly linked communities in a network can lead to many benefits, such as understanding relationships between entities or interactions between biological genes, for instance. Two different immunological algorithms have been designed for this problem, called Opt-IA and Hybrid-IA, respectively. The main difference between the two algorithms is the search strategy and related immunological operators developed: the first carries out a random search together with purely stochastic operators; the last one is instead based on a deterministic Local Search that tries to refine and improve the current solutions discovered. The robustness of Opt-IA and Hybrid-IA has been assessed on several real social networks. These same networks have also been considered for comparing both algorithms with other seven different metaheuristics and the well-known greedy optimization Louvain algorithm. The experimental analysis conducted proves that Opt-IA and Hybrid-IA are reliable optimization methods for community detection, outperforming all compared algorithms.

Creative Design Methodology and the SIT Method

1997 ◽  
Author(s):  
Roni Horowitz ◽  
Oded Maimon
Keyword(s):  
Design Methodology ◽  
Search Strategy ◽  
Sufficient Conditions ◽  
Strategy Selection ◽  
Step Procedure ◽  
Creative Solutions ◽  
General Search ◽  
Problem Reformulation ◽  
Creative Problem ◽  
The Given

Abstract The paper presents SIT (Structured Inventive Thinking) — a structured method for enhancing creative problem solving in engineering design. The method is a three step procedure: problem reformulation, general search strategy selection, and an application of idea provoking techniques. The most innovative part of the method is the problem reformulation stage. The given problem is modified through the application of objectively defined and empirically tested set of sufficient conditions for creative solutions. The paper describes the sufficient conditions and the empirical study that demonstrates their appropriateness. Then the whole SIT mechanism is presented with illustrative examples.

scholarly journals Constructing Synthetic Samples

2016 ◽  
Vol 32 (1) ◽  
pp. 113-127
Author(s):  
Hua Dong ◽  
Glen Meeden
Keyword(s):  
Optimization Problem ◽  
Search Algorithm ◽  
Random Search ◽  
The United States ◽  
Simulation Studies ◽  
Synthetic Sample ◽  
Population Means ◽  
Adaptive Random Search ◽  
Random Search Algorithm ◽  
Two Populations

Abstract We consider the problem of constructing a synthetic sample from a population of interest which cannot be sampled from but for which the population means of some of its variables are known. In addition, we assume that we have in hand samples from two similar populations. Using the known population means, we will select subsamples from the samples of the other two populations which we will then combine to construct the synthetic sample. The synthetic sample is obtained by solving an optimization problem, where the known population means, are used as constraints. The optimization is achieved through an adaptive random search algorithm. Simulation studies are presented to demonstrate the effectiveness of our approach. We observe that on average, such synthetic samples behave very much like actual samples from the population of interest. As an application we consider constructing a one-percent synthetic sample for the missing 1890 decennial sample of the United States.

Numerical Optimization of the Thermoelectric Cooling Devices

2006 ◽  
Vol 129 (3) ◽  
pp. 339-347 ◽  
Author(s):  
Boris Abramzon
Keyword(s):  
Electric Current ◽  
Optimization Problems ◽  
Random Search ◽  
Thermal Conductance ◽  
Numerical Approach ◽  
Physical Parameters ◽  
Optimization Approach ◽  
Independent Variables ◽  
Adaptive Random Search ◽  
Optimization Search

The present study proposes a unified numerical approach to the problem of optimum design of the thermoelectric devices for cooling electronic components. The standard mathematical model of a single-stage thermoelectric cooler (TEC) with constant material properties is employed. The model takes into account the thermal resistances from the hot and cold sides of the TEC. Values of the main physical parameters governing the TEC performance (Seebeck coefficient, electrical resistance, and thermal conductance) are derived from the manufacturer catalog data on the maximum achievable temperature difference, and the corresponding electric current and voltage. The optimization approach is illustrated with several examples for different design objective functions, variables, and constraints. The objective for the optimization search is the maximization of the total cooling rate or the performance coefficient of the cooling device. The independent variables for the optimization search are as follows: The number of the thermoelectric modules, the electric current, and the cold side temperature of the TEC. Additional independent variables in other cases include the number of thermoelectric couples and the area-to-height ratio of the thermoelectric pellet. In the present study, the optimization problems are solved numerically using the so-called multistart adaptive random search method.

Sensitivity Analysis

2021 ◽  
pp. 251-262
Author(s):  
Timothy E. Essington
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Uncertainty ◽  
Monte Carlo Analysis ◽  
Interactive Effects ◽  
Structure Parameter ◽  
Ecological Processes ◽  
Individual Parameter ◽  
Global Sensitivity ◽  
Versus Parameter ◽  
Parameter Values

The chapter “Sensitivity Analysis” reviews why sensitivity analysis is a critical component of mathematical modeling, and the different ways of approaching it. A sensitivity analysis is an attempt to identify the parts of the model (i.e. structure, parameter values) that are most important for governing the output. It is an important part of modeling because it is used to quantify the degree of uncertainty in the model prediction and, in many cases, is the main goal of the model (i.e. the model was developed to identify the most important ecological processes). The chapter covers the idea of “local” versus “global” sensitivity analysis via individual parameter perturbation, and how interactive effects of parameters can be revealed via Monte Carlo analysis. Structural versus parameter uncertainty is also explained and explored.

Simulation Optimization Using Multi-Time-Scale Adaptive Random Search

2019 ◽  
Vol 36 (06) ◽  
pp. 1940014
Author(s):  
Qi Zhang ◽  
Jiaqiao Hu
Keyword(s):  
Search Algorithm ◽  
Numerical Study ◽  
Random Search ◽  
Solution Space ◽  
Population Based ◽  
Global Optimum ◽  
Adaptive Random Search ◽  
Candidate Solution ◽  
Approximation Type ◽  
Effective Use

We propose a random search algorithm for seeking the global optimum of an objective function in a simulation setting. The algorithm can be viewed as an extension of the MARS algorithm proposed in Hu and Hu (2011) for deterministic optimization, which iteratively finds improved solutions by modifying and sampling from a parameterized probability distribution over the solution space. However, unlike MARS and many other algorithms in this class, which are often population-based, our method only requires a single candidate solution to be generated at each iteration. This is primarily achieved through an effective use of past sampling information by means of embedding multiple nested stochastic approximation type of recursions into the algorithm. We prove the global convergence of the algorithm under general conditions and discuss two special simulation noise cases of interest, in which we show that only one simulation replication run is needed for each sampled solution. A preliminary numerical study is also carried out to illustrate the algorithm.

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