Variant of optimality criteria method for multiple state optimal design problems

2018 ◽  
Vol 16 (6) ◽  
pp. 1597-1614 ◽  
Author(s):  
Krešimir Burazin ◽  
Ivana Crnjac ◽  
Marko Vrdoljak
Keyword(s):  
Optimal Design ◽  
Optimality Criteria ◽  
Design Problems ◽  
Optimality Criteria Method ◽  
Multiple State

scholarly journals Sequential laminates in multiple-state optimal design problems

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
Nenad Antonic ◽  
Marko Vrdoljak
Keyword(s):  
Composite Materials ◽  
Optimal Design ◽  
Optimality Conditions ◽  
Matrix Phase ◽  
Numerical Treatment ◽  
State Equations ◽  
Design Problems ◽  
Stationary Diffusion ◽  
Multiple State ◽  
Diffusion Problems

In the study of optimal design related to stationary diffusion problems with multiple-state equations, the description of the setH={(Aa1,...,Aam):A∈K(θ)}for given vectorsa1,...,am∈ℝd(m<d) is crucial.K(θ)denotes all composite materials (in the sense of homogenisation theory) with given local proportionθof the first material. We prove that the boundary ofHis attained by sequential laminates of rank at mostmwith matrix phaseαIand coreβI(α<β). Examples showing that the information on the rank of optimal laminate cannot be improved, as well as the fact that sequential laminates with matrix phaseαIare preferred to those with matrix phaseβI, are presented. This result can significantly reduce the complexity of optimality conditions, with obvious impact on numerical treatment, as demonstrated in a simple numerical example.

Gradient methods for multiple state optimal design problems

2007 ◽  
Vol 53 (2) ◽  
pp. 177-187 ◽  
Author(s):  
Nenad Antonić ◽  
Marko Vrdoljak
Keyword(s):  
Optimal Design ◽  
Gradient Methods ◽  
Design Problems ◽  
Multiple State

scholarly journals THE STATIC OPTIMIZATION TASK OF OPTIMAL DESIGN OF NONLINEAR ELECTRONIC SCHEME

2019 ◽  
pp. 109-115
Author(s):  
Didmanidze Ibraim ◽  
Donadze Mikheil
Keyword(s):  
Optimal Design ◽  
Optimality Criteria ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Design Task ◽  
Optimization Task ◽  
Minimum Capacity ◽  
Optimal Values ◽  
The Given ◽  
Selection Of

The article deals with such an important selection of the elements of electronic scheme of the given configuration, when the certain requirements of technical task are satisfied and at the same time the selected optimality criteria reach the extreme value. The gives task has been solved by the method of one-criterion optimization, in particular, the method of center gravity. To formalize the given scheme we have compiled a mathematical model of optimization, which considers the requirements of technical task. The optimal design task of the presented electronic scheme was brought to the task of multi criteria optimization. The computational experiments have been resulted in the Pareto-optimal solutions, from which there was selected a compromise on that corresponds to the minimum capacity, required by the scheme. According to the optimal values of resistors, we have conducted a computerized analysis of the transient process of the given electronic scheme with the help of a computer program Electronics Workbench.

scholarly journals A Highly D‑efficient Spring Balance Weighing Design for an Even Number of Objects

2019 ◽  
Vol 5 (344) ◽  
pp. 17-27
Author(s):  
Małgorzata Graczyk ◽  
Bronisław Ceranka
Keyword(s):  
Optimal Design ◽  
Sufficient Conditions ◽  
Optimality Criteria ◽  
Point Of View ◽  
Necessary And Sufficient Conditions ◽  
Optimal Designs ◽  
Efficient Design ◽  
Spring Balance ◽  
Experimental Errors ◽  
Necessary And Sufficient

The problem of determining unknown measurements of objects in the model of spring balance weighing designs is presented. These designs are considered under the assumption that experimental errors are uncorrelated and that they have the same variances. The relations between the parameters of weighing designs are deliberated from the point of view of optimality criteria. In the paper, designs in which the product of the variances of estimators is possibly the smallest one, i.e. D‑optimal designs, are studied. A highly D‑efficient design in classes in which a D‑optimal design does not exist are determined. The necessary and sufficient conditions under which a highly efficient design exists and methods of its construction, along with relevant examples, are introduced.

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