Sensitivity of optimum solutions to problem parameters

Derivation of the sensitivity equations that yield the sensitivity derivatives directly, which avoids the costly and inaccurate perturb-and-reoptimize approach, is discussed and solvability of the equations is examined. The equations apply to optimum solutions obtained by direct search methods as well as those generated by procedures of the sequential unconstrained minimization technique class. Applications are discussed for the use of the sensitivity derivatives in extrapolation of the optimal objective function and design variable values for incremented parameters, optimization with multiple objectives, and decomposition of large optimization problems

Application of Genetic Algorithm in Multi-objective Optimization of an Indeterminate Structure with Discontinuous Space for Support Locations

In this thesis, an indeterminate structure was developed with multiple competing objectives including the equalization of the load distribution among the supports while maximizing the stability of the structure. Two different coding algorithms named “Continuous Method” and “Discretized Method” were used to solve the optimal support locations using Genetic Algorithms (GAs). In continuous method, a continuous solution space was considered to find optimal support locations. The failure of this method to stick to the acceptable optimal solution led towards the development of the second method. The latter approach divided the solution space into rectangular grids, and GAs acted on the index number of the nodal points to converge to the optimality. The average value of the objective function in the discretized method was found to be 0.147 which was almost onethird of that obtained by the continuous method. The comparison based on individual components of the objective function also proved that the proposed method outperformed the continuous method. The discretized method also showed faster convergence to the optima. Three circular discontinuities were added to the structure to make it more realistic and three different penalty functions named flat, linear and non-linear penalty were used to handle the constraints. The performance of the two methods was observed with the penalty functions while increasing the radius of the circles by 25% and 50% which showed no significant difference. Later, the discretized method was coded to eliminate the discontinuous area from the solution space which made the application of the penalty functions redundant. A paired t-test (α=5%) showed no statistical difference between these two methods. Finally, to make the proposed method compatible with irregular shaped discontinuous areas, “FEA Integrated Coded Discretized Method (FEAICDM)” was developed. The manual elimination of the infeasible areas from the candidate surface was replaced by the nodal points of the mesh generated by Solid Works. A paired t-test (α=5%) showed no statistical difference between these two methods. Though FEAICDM was applied only to a class of problem, it can be concluded that FEAICDM is more robust and efficient than the continuous method for a class of constrained optimization problem