Evolutionary Algorithms For Unconstrained Global Optimization Problems With Continuous Variables

During the past three decades, unconstrained optimization problems have been intensively studied in various areas, such as in science, engineering and business, etc. Designing effective unconstrained optimization algorithms has received considerable attention from researchers. Evolutionary algorithm (EA) is a kind of global random search methods based on biological evolution mechanisms. In the existing optimization algorithms, EA has become an acknowledged approach to solve the optimization problems regarding its potential to solve complex global optimization problems.The main goal of the thesis is to discuss the unconstrained optimization problem with continuous variables and find the effective evolutionary algorithms for it. At first, origination and development of the global optimization problem are introduced. Then, the four branches of EA, convergence theory of EA, criterions for EA, existing works and some difficulties in EA are described.In Chapter 3, a crossover operator based on a descent scale function is designed, which keeps global search ability when looking for descent directions. To realize this purpose, the initial population is generated by combining determinate factors with random ones. To improve the performance of the algorithm, a mutation operator which increases the convergence-speed and avoids being trapped in the local optima is given. Then, an evolutionary algorithm based on all these techniques is proposed, and its global convergence is proved in detail. Finally, the experiments results indicate that the proposed algorithm is fast and efficient for all the test functions.In Chapter 4, the descent directions are determined by the relationship between the best individual and remaining ones in the population at first. To improve the search ability of the non-uniform mutation operator in the late stage of the evolution, an improved non-uniform mutation operator is designed by balancing the ability of global search and local exploration. Based on these, a novel algorithm with high searching speed is proposed and its global convergence is proved. At last, we executed proposed algorithm on 27 global optimization benchmark problems. The experiment results indicate that this mutation operator works better than the previous non-uniform mutation operator and the proposed algorithm can obtain better and more robust ones than the compared algorithms.