Date of Award

Spring 2021

Document Type


Degree Name

Master of Science (MS)


Mechanical & Aerospace Engineering


Mechanical Engineering

Committee Director

Gene Hou

Committee Member

Miltos Kotinis

Committee Member

Duc Nguyen


This research presents a formal method for gradient based tradeoff design including methods that extend to cases with singularities and cases with more performance characteristics then design variables. The goal is to find revised design variables that can achieve the targeted performance characteristics and remove any violations to the constraint functions. The tradeoff design problem is formulation in the framework of the Sequential Quadratic Programming and is solved using the gradient based method. The optimal solution is the search direction, s, which represents the most effective way to reduce the current objective and correct the current violation. In this research the search direction is broken up into two parts, ��1 and ��2. Where ��1 can reduce the objective function or functions without changing the value of the constraints and ��2 is responsible to reduce the constraint violations. Additionally, a scalar factor �� is introduced in the search direction to produce a search direction that can achieve the targeted change in the objective function. This paper presents a new method to calculate alpha to adjust the cost function instead of reducing the penalized objective function. The details of the mathematical formulation are presented and discussed here, along with three design examples. The first demonstrative example is the design of a cubic box, the second is a control problem with three targeted eigenvalues, and the third is the design of an I-beam. The design examples demonstrate and validate the use of single objective approach, the constraint only approach and the multi-objective approach. These examples also show that smaller changes produce better results, an iterative process can achieve more accurate results, additional performance characteristics can be added during the design process, methods for handle cases with linearly dependent constraint functions, and, finally, methods for handling cases with more performance characteristics then design variables. Additionally, the third example includes the use of a finite element method demonstrating that this method can be extended to finite element applications.