MO-FG-CAMPUS-TeP3-04: Deliverable Robust Optimization in IMPT Using Quadratic Objective Function

In view of robustness of objective function and constraints in robust design, the method of maximum variation analysis is adopted to improve the robust design. In this method, firstly, we analyses the effect of uncertain factors in design variables and design parameters on the objective function and constraints, then calculate maximum variations of objective function and constraints. A two-level optimum mathematical model is constructed by adding the maximum variations to the original constraints. Different solving methods are used to solve the model to study the influence to robustness. As a demonstration, we apply our robust optimization method to an engineering example, the design of a machine tool spindle. The results show that, compared with other methods, this method of HPSO(hybrid particle swarm optimization) algorithm is superior on solving efficiency and solving results, and the constraint robustness and the objective robustness completely satisfy the requirement, revealing that excellent solving method can improve robustness.

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Robust Optimization in Possibility Theory

ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg ◽

10.1115/1.4044037 ◽

2019 ◽

Vol 5 (4) ◽

Cited By ~ 1

Author(s):

Dominik Hose ◽

Markus Mäck ◽

Michael Hanss

Keyword(s):

Decision Making ◽

Robust Optimization ◽

Objective Function ◽

Optimization Problems ◽

Initial Conditions ◽

Multicriteria Decision Making ◽

Possibility Theory ◽

Linear Quadratic Regulator ◽

Linear Quadratic ◽

Multicriteria Decision

Abstract In this contribution, the optimization of systems under uncertainty is considered. The possibilistic evaluation of the fuzzy-valued constraints and the adoption of a multicriteria decision making technique for the fuzzy-valued objective function enable a meaningful solution to general fuzzy-valued optimization problems. The presented approach is universally applicable, which is demonstrated by reformulating and solving the linear quadratic regulator problem for fuzzy-valued system matrices and initial conditions.

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Constructing a quasi-concave quadratic objective function from interviewing a decision maker

European Journal of Operational Research ◽

10.1016/s0377-2217(01)00185-0 ◽

2002 ◽

Vol 141 (3) ◽

pp. 608-640 ◽

Cited By ~ 3

Author(s):

A.S. Tangian

Keyword(s):

Objective Function ◽

Decision Maker ◽

Quadratic Objective Function

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Robust Design Optimization Under Mixed Uncertainties With Stochastic Expansions

Journal of Mechanical Design ◽

10.1115/1.4024230 ◽

2013 ◽

Vol 135 (8) ◽

Cited By ~ 11

Author(s):

Yi Zhang ◽

Serhat Hosder

Keyword(s):

Monte Carlo ◽

Robust Optimization ◽

Objective Function ◽

Design Optimization ◽

Robust Design ◽

Optimization Technique ◽

Response Surfaces ◽

Robust Design Optimization ◽

Stochastic Expansions ◽

Mixed Uncertainties

The objective of this paper is to introduce a computationally efficient and accurate approach for robust optimization under mixed (aleatory and epistemic) uncertainties using stochastic expansions that are based on nonintrusive polynomial chaos (NIPC) method. This approach utilizes stochastic response surfaces obtained with NIPC methods to approximate the objective function and the constraints in the optimization formulation. The objective function includes a weighted sum of the stochastic measures, which are minimized simultaneously to ensure the robustness of the final design to both inherent and epistemic uncertainties. The optimization approach is demonstrated on two model problems with mixed uncertainties: (1) the robust design optimization of a slider-crank mechanism and (2) robust design optimization of a beam. The stochastic expansions are created with two different NIPC methods, Point-Collocation and Quadrature-Based NIPC. The optimization results are compared to the results of another robust optimization technique that utilizes double-loop Monte Carlo sampling (MCS) for the propagation of mixed uncertainties. The optimum designs obtained with two different optimization approaches agree well in both model problems; however, the number of function evaluations required for the stochastic expansion based approach is much less than the number required by the Monte Carlo based approach, indicating the computational efficiency of the optimization technique introduced.

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