Off-campus University of Miami users: To download campus access theses, please use the following link to log into our proxy server with your University of Miami CaneID and Password.

Non-University of Miami users: Please talk to your librarian about requesting this thesis through interlibrary loan.

Publication Date



UM campus only

Degree Type


Degree Name

Master of Science (MS)


Mechanical Engineering (Engineering)

Date of Defense


First Committee Member

Singiresu S. Rao

Second Committee Member

Burt Rosenberg

Third Committee Member

Jizhou Song


This thesis is aimed at the optimum design of uncertain mechanical components and systems involving multiple objectives and constraints. There are various mechanical and design problems that are encountered every now and then which require the output that equalize several conflicting objectives. In recent years several methods have been developed to find a solution to multiobjective problems. The most efficient method for obtaining a compromise solution is the game theory method, which is based on the Pareto minimum or optimum solution. A thorough methodology is developed, and subsequently applied to three examples problems. The first problem is to design four helical springs which are further used to support a milling machine. The objective is to minimize the weight of the spring, also to minimize the deflection, and to maximize the natural frequency thus making the problem as a multiobjective problem. Further the subjected constraint is the shear stress constraint. After finding the optimized solution of the deterministic problem, the problem is again solved using Stochastic Nonlinear Programming, and after that it is solved using Interval Analysis. Game theory is used individually in all the three cases. The second problem is to design a gear box where the objectives are defined as the weight of the gear box, stress developed in the shaft 1, and the stress developed in shaft 2. It is subjected to nine constraints which are bending stress in teeth, contact stress of teeth, transverse displacement of shafts 1 and 2, and constraints related to the torque. The third problem is to design a power screw and the objective is to minimize the volume of the screw, and to maximize the critical buckling load and thus making it a multiobjective problem. It is subjected to constraints of being screw to be self locking, then the shear stress in screw thread, and the bearing stress in threads. The results of all the three problems that are achieved using Deterministic, Stochastic Nonlinear Programming, and Interval Analysis Method are tabulated, and the value of each objective achieved using these three methods for each problem at a time are compared to find out the most optimized solution.


Interval Analysis; Stochastic Nonlinear Programming; Optimization; Game Theory