Genetic Algorithms For Solving Global Optimization Problems

Optimization problem widely exists in engineering and application of business，and it is very important to design efficient and feasible algorithms for solving theproblem. By simulating natural evolution, genetic algorithm with global search abilityhas been proposed, and there is no requirement on differentiability and continuity offunctions involved. Genetic algorithm is robust and has strong global search ability.In this thesis, genetic algorithms are investigated for dealing with constrained andunconstrained optimization problems, respectively, the main results are as follows：Considering that the optimal solutions to constrained optimization problems maybe located at the boundary of the feasible region, we propose a new genetic algorithmbased on hybrid genetic operator. Firstly, in this algorithm, the crossover process isexecuted separately according to feasible and infeasible individuals. For feasibleindividuals, the best individual is taken as the other parent individual for the crossoveroperation; for infeasible individuals, according to the degree of constraint violation,we choose infeasible individuals and any feasible individual as parents for crossover.Secondly, in order to make infeasible solutions move to feasible region and feasiblesolutions move to the boundary of the feasible region, we introduce a hybrid mutationoperator based on boundary mutation and Gaussian mutation. Numerical experimentand comparison results show that the algorithm is efficient.For unconstrained optimization problems, a genetic algorithm based oninformation of better points is presented. First, for a crossover parent individual, anytwo individuals better than the crossover individual are chosen. Then, based onreflection, extension and contraction of the simplex method, crossover offspring isgenerated as well as possible. The numerical experiment results show the approach isefficient.