On Unique Solutions of Multiple-State Optimal Design Problems on an Annulus

2018 ◽  
Vol 177 (2) ◽  
pp. 329-344 ◽  
Author(s):  
Krešimir Burazin
Keyword(s):  
Optimal Design ◽  
Design Problems ◽  
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.

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

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

Optimal Design of a Gas Turbine Cogeneration Plant by a Hierarchical Optimization Method With Parallel Computing

2018 ◽  
Author(s):  
Ryohei Yokoyama ◽  
Yuji Shinano ◽  
Yuki Wakayama ◽  
Tetsuya Wakui
Keyword(s):  
Optimal Design ◽  
Energy Supply ◽  
Optimization Method ◽  
Optimal Operation ◽  
Hierarchical Optimization ◽  
Cogeneration Plant ◽  
Design Problems ◽  
Computation Efficiency ◽  
Supply Systems ◽  
Energy Supply Systems

To attain the highest performance of energy supply systems, it is necessary to rationally determine types, capacities, and numbers of equipment in consideration of their operational strategies corresponding to seasonal and hourly variations in energy demands. Mixed-integer linear programming (MILP) approaches have been applied widely to such optimal design problems. The authors have proposed a MILP method utilizing the hierarchical relationship between design and operation variables to solve the optimal design problems of energy supply systems efficiently. In addition, some strategies to enhance the computation efficiency have been adopted: bounding procedures at both the levels and ordering of the optimal operation problems at the lower level. In this paper, as an additional strategy to enhance the computation efficiency, parallel computing is adopted to solve multiple optimal operation problems in parallel at the lower level. In addition, the effectiveness of each and combinations of the strategies adopted previously and newly is investigated. This hierarchical optimization method is applied to an optimal design of a gas turbine cogeneration plant, and its validity and effectiveness are clarified through some case studies.

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