Remarks on Conditions for the Validity of Parametric Decomposition in Optimal Design

1990 ◽  
Author(s):  
J. R. Jagannatha Rao ◽  
Panos Y. Papalambros
Keyword(s):  
Optimal Design ◽  
Present Article ◽  
Original Problem ◽  
Necessary Conditions ◽  
Special Problem ◽  
Problem Structure ◽  
Globally Convergent ◽  
Parametric Decomposition ◽  
Practical Design ◽  
Decomposition Strategies

Abstract Decomposition strategies are used in a variety of practical design optimization applications. Such decompositions are valid, if the solution of the decomposed problem is in fact also the solution to the original one. Conditions for such validity are not always obvious. In the present article, we develop conditions for two-level parametric decomposition under which: (1) isolated minima at the two levels imply an isolated minimum for the original problem; (2) necessary conditions at the two-levels are equivalent to the necessary conditions for the original problem; and, (3) a descent algorithm for computing Karush-Kuhn-Tucker points in decomposition formulations is globally convergent. Since no special problem structure is assumed, the results are general and could be used to evaluate the suitability of a variety of approaches and algorithms for decomposition strategies.

Momentum exchange impact damper design methodology for object-wall-collision problems

2017 ◽  
Vol 24 (14) ◽  
pp. 3206-3218
Author(s):  
Yohei Kushida ◽  
Hiroaki Umehara ◽  
Susumu Hara ◽  
Keisuke Yamada
Keyword(s):  
Optimal Design ◽  
Design Methodology ◽  
Design Parameters ◽  
Momentum Exchange ◽  
Impact Damper ◽  
One Dimensional ◽  
Practical Design ◽  
Wall Collision ◽  
Damper Design ◽  
And Control

Momentum exchange impact dampers (MEIDs) were proposed to control the shock responses of mechanical structures. They were applied to reduce floor shock vibrations and control lunar/planetary exploration spacecraft landings. MEIDs are required to control an object’s velocity and displacement, especially for applications involving spacecraft landing. Previous studies verified numerous MEID performances through various types of simulations and experiments. However, previous studies discussing the optimal design methodology for MEIDs are limited. This study explicitly derived the optimal design parameters of MEIDs, which control the controlled object’s displacement and velocity to zero in one-dimensional motion. In addition, the study derived sub-optimal design parameters to control the controlled object’s velocity within a reasonable approximation to derive a practical design methodology for MEIDs. The derived sub-optimal design methodology could also be applied to MEIDs in two-dimensional motion. Furthermore, simulations conducted in the study verified the performances of MEIDs with optimal/sub-optimal design parameters.

scholarly journals On the kolmogorov system with fourth-degree homogeneous nonlinearities

2020 ◽  
Vol 64 (3) ◽  
pp. 268-272
Author(s):  
A. P. Sadovskii
Keyword(s):  
Singular Point ◽  
Present Article ◽  
Necessary Conditions ◽  
Fourth Degree ◽  
Kolmogorov System

The necessary conditions of the center at the singular point O (0, 0) for the kolmogorov system with fourth-degree homogeneous nonlinearities are found in the work of B. Ferenc, J. Dzheny, W. Liu, V. G. Romanovsky. For all these cases, with the exception of two, sufficiency is also proved. In the present article, sufficiency is proved for two cases of the center that were not proved in the above-mentioned work. In addition, the sufficiency of two other conditions of the center is proved in another way.

scholarly journals Optimality conditions via scalarization for approximate quasi efficiency in multiobjective optimization

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 671-680 ◽  
Author(s):  
Mehrdad Ghaznavi
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Original Problem ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Multiobjective Optimization Problem ◽  
Alternative Theorem ◽  
Convexity Assumptions ◽  
Interesting Area

Approximate problems that scalarize and approximate a given multiobjective optimization problem (MOP) became an important and interesting area of research, given that, in general, are simpler and have weaker existence requirements than the original problem. Recently, necessary conditions for approximation of several types of efficiency for MOPs have been obtained through the use of an alternative theorem. In this paper, we use these results in order to extend them to sufficient conditions for approximate quasi (weak, proper) efficiency. For this, we use two scalarization techniques of Tchebycheff type. All the provided results are established without convexity assumptions.

Necessary conditions for optimal design of structures with a nonsmooth eigenvalue based criterion

1995 ◽  
Vol 9 (1) ◽  
pp. 52-56 ◽  
Author(s):  
H. C. Rodrigues ◽  
J. M. Guedes ◽  
M. P. Bendsøe
Keyword(s):  
Optimal Design ◽  
Necessary Conditions

The Optimal Design of Multi-Level Planetary Gear Reducer

2010 ◽  
Vol 139-141 ◽  
pp. 1308-1311 ◽  
Author(s):  
Jing Bing Wu ◽  
Lun Shu ◽  
He Ming Cheng
Keyword(s):  
Mathematical Model ◽  
Optimal Design ◽  
Load Capacity ◽  
Planetary Gear ◽  
Maximum Load ◽  
Practical Design ◽  
Optimal Function ◽  
Multi Level ◽  
The Mathematical Model ◽  
Center Distance

Based on the analysis and study of the composite reducer, the allocation of transmission ratio is considered to be the key to optimal design of multi-level planetary gear reducer. In view of so many discussion and study of the minimum volume as the optimization objective existed, this paper regards the maximum load capacity as the optimal goal on condition that the center distance or size is given, and then establishes the optimal mathematical model. The related constraints are given according to the theoretical knowledge and practical design experience. In this paper, an optimal function procedure that based on genetic is used to optimize the mathematical model. The satisfied result has been worked out combined with the practical example. Compared to the original program, the load capacity of 17.8% is improved. In addition, some references are provided to the optimal design of planetary gear reducer.

Indirect Solution of Inequality Constrained and Singular Optimal Control Problems Via a Simple Continuation Method

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Brian C. Fabien
Keyword(s):  
Optimal Control ◽  
Original Problem ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Continuation Method ◽  
Singular Control ◽  
Inequality Constraints ◽  
Control Problems ◽  
Quadratic Loss ◽  
State Variable

This paper develops a simple continuation method for the approximate solution of optimal control problems. The class of optimal control problems considered include (i) problems with bounded controls, (ii) problems with state variable inequality constraints (SVIC), and (iii) singular control problems. The method used here is based on transforming the state variable inequality constraints into equality constraints using nonnegative slack variables. The resultant equality constraints are satisfied approximately using a quadratic loss penalty function. Similarly, singular control problems are made nonsingular using a quadratic loss penalty function based on the control. The solution of the original problem is obtained by solving the transformed problem with a sequence of penalty weights that tends to zero. The penalty weight is treated as the continuation parameter. The paper shows that the transformed problem yields necessary conditions for a minimum that can be written as a boundary value problem involving index-1 differential–algebraic equations (BVP-DAE). The BVP-DAE includes the complementarity conditions associated with the inequality constraints. It is also shown that the necessary conditions for optimality of the original problem and the transformed problem differ by a term that depends linearly on the algebraic variables in the DAE. Numerical examples are presented to illustrate the efficacy of the proposed technique.

scholarly journals Development of Practical Design Approaches for Water Distribution Systems

2019 ◽  
Vol 9 (23) ◽  
pp. 5117
Author(s):  
Young Hwan Choi ◽  
Ho Min Lee ◽  
Jiho Choi ◽  
Do Guen Yoo ◽  
Joong Hoon Kim
Keyword(s):  
Optimal Design ◽  
Distribution Systems ◽  
Water Distribution ◽  
Design Method ◽  
Water Distribution Systems ◽  
Computation Time ◽  
Practical Design ◽  
Previous Design ◽  
Design Factors ◽  
Pipe Size

The optimal design of water distribution systems (WDSs) should be economical, consider practical field applicability, and satisfy hydraulic constraints such as nodal pressure and flow velocity. However, the general optimal design of a WDSs approach using a metaheuristic algorithm was difficult to apply for achieving pipe size continuity at the confluence point. Although some studies developed the design approaches considering the pipe continuity, these approaches took many simulation times. For these reasons, this study improves the existing pipe continuity search method by reducing the computation time and enhancing the ability to handle pipe size continuity at complex joints that have more than three nodes. In addition to more practical WDSs designs, the approach considers various system design factors simultaneously in a multi-objective framework. To verify the proposed approach, the three well-known WDSs to apply WDS design problems are applied, and the results are compared with the previous design method, which used a pipe continuity research algorithm. This study can reduce the computation time by 87% and shows an ability to handle complex joints. Finally, the application of this practical design technique, which considers pipe continuity and multiple design factors, can reduce the gap between the theoretical design and the real world because it considers construction conditions and abnormal situations.

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