| Evolutionary algorithms are very widely used optimization methods that are based on Darwinian principles. They maintain a population of candidate solutions that are usually initialized randomly. In each generation, they use two variational operations, recombination and mutation to produce new solutions from old ones. In accordance with the precept of survival of the fittest, the worst individuals are culled from the population, while the better ones are allowed to survive to get included in the next generation. Evolutionary algorithms are highly effective in exploring the search space for good optima. In order to add an exploitative behavior, the Nelder-Mead simplex approach is often incorporated within the evolutionary search. This hybrid strategy provides faster convergence towards optimal solutions. As the Nelder-Mead simplex algorithm is intrinsically a single objective scheme, this hybridization has so far not been extended to multi-objective evolutionary algorithms.;This thesis proposes a method to add the Nelder-Mead simplex local search procedure to multi-objective evolutionary algorithms. In order to do so the concept of fuzzy dominance, an extension of the traditional concept of Pareto dominance, has been suggested. Using fuzzy dominance, it is possible to assign scalar fitness values to individual solutions within a given population. Within each generation of the proposed algorithm, the fuzzy dominances of the individuals are first computed. A part of the population is selected for further improvement based on fuzzy dominance, through the Nelder-Mead simplex algorithm, while the remaining ones undergo recombination and mutation in the usual manner.;The proposed algorithm is compared with two standard evolutionary multi-objective optimization algorithms, NSGA-II and SPEA-2, on several benchmark problems, and on gene differential equation modeling problem. Simulation results show that it performs significantly better than both NSGA-II and SPEA-2. The algorithm is then applied to a large-scale problem involving the estimation of a total of 31 parameter of a gene network model for A. thaliana flowering time control, with five objectives to be optimized. Using the set of evolved parameters, the model simulations were able to closely follow the available gene expression data. |
