Development of optimization methods to solve computationally expensive problems


Evolutionary algorithms (EAs) are population based heuristic optimization methods used to solve single and multi-objective optimization problems. They can simultaneously search multiple regions to find global optimum solutions. As EAs do not require gradient information for the search, they can be applied to optimization problems involving functions of real, integer, or discrete variables. One of the drawbacks of EAs is that they require evaluations of numerous candidate solutions for convergence. Most real life engineering design optimization problems involve highly nonlinear objective and constraint functions arising out of computationally expensive simulations. For such problems, the computation cost of optimization using EAs can become quite prohibitive. This has stimulated the research into improving the efficiency of EAs reported herein. In this thesis, two major improvements are suggested for EAs. The first improvement is the use of spatial surrogate models to replace the expensive simulations for the evaluation of candidate solutions, and other is a novel constraint handling technique. These modifications to EAs are tested on a number of numerical benchmarks and engineering examples using a fixed number of evaluations and the results are compared with basic EA. addition, the spatial surrogates are used in the truss design application. A generic framework for using spatial surrogate modeling, is proposed. Multiple types of surrogate models are used for better approximation performance and a prediction accuracy based validation is used to ensure that the approximations do not misguide the evolutionary search. Two EAs are proposed using spatial surrogate models for evaluation and evolution. For numerical benchmarks, the spatial surrogate assisted EAs obtain significantly better (even orders of magnitude better) results than EA and on an average 5-20% improvements in the objective value are observed for engineering examples. Most EAs use constraint handling schemes that prefer feasible solutions over infeasible solutions. In the proposed infeasibility driven evolutionary algorithm (IDEA), a few infeasible solutions are maintained in the population to augment the evolutionary search through the infeasible regions along with the feasible regions to accelerate convergence. The studies on single and multi-objective test problems demonstrate the faster convergence of IDEA over EA. In addition, the infeasible solutions in the population can be used for trade-off studies. Finally, discrete structures optimization (DSO) algorithm is proposed for sizing and topology optimization of trusses. In DSO, topology optimization and sizing optimization are separated to speed up the search for the optimum design. The optimum topology is identified using strain energy based material removal procedure. The topology optimization process correctly identifies the optimum topology for 2-D and 3-D trusses using less than 200 function evaluations. The sizing optimization is performed later to find the optimum cross-sectional areas of structural elements. In surrogate assisted DSO (SDSO), spatial surrogates are used to accelerate the sizing optimization. The truss designs obtained using SDSO are very close (within 7% of the weight) to the best reported in the literature using only a fraction of the function evaluations (less than 7%).