| Most of the optimization problems encountered in engineering have conflicting objectives. In order to solve these problems, genetic algorithms (GAs) and gradient-based methods are widely used. GAs are relatively easy to implement, because these algorithms only require first-order information of the objectives and constraints. On the other hand, GAs do not have a standard termination condition and therefore they may not converge to the exact solutions. Gradient-based methods, on the other hand, are based on first- and higher-order information of the objectives and constraints. These algorithms converge faster to the exact solutions in solving single-objective optimization problems, but are inefficient for multi-objective optimization problems (MOOPs) and unable to solve those with non-convex objective spaces.;The work in this dissertation focuses on developing a hybrid strategy for solving MOOPs based on feasible sequential quadratic programming (FSQP) and nondominated sorting genetic algorithm II (NSGA-II). The hybrid algorithms developed in this dissertation are tested using benchmark problems and evaluated based on solution distribution, solution accuracy, and execution time. Based on these performance factors, the best hybrid strategy is determined and found to be generally efficient with good solution distributions in most of the cases studied. The best hybrid algorithm is applied to the design of a crushing tube and is shown to have relatively well-distributed solutions and good efficiency compared to solutions obtained by NSGA-II and FSQP alone. |
