Evolutionary Algorithms For Global Optimization Problems

Evolutionary algorithms are new kinds of modern optimization algorithms that are inspired by principle of nature evolution. As new kinds of random search algorithms, they have some advantages over the traditional optimization algorithms, and are of the great importance and a wide range of applications. The traditional optimization algorithms usually have strict limitations on the functions such as requirement of their differentiability. Unfortunately, these functions usually are not differentiable. Evolutionary algorithms do not require the differentiability of the functions and have parallel property. Therefore, they are often be used to solve some complex, large scale, nonlinear and non-differentiable optimization problems.Firstly, a novel evolutionary algorithm is proposed for unconstrained optimization problems. In order to generate high quality initial population, the uniform design is used. Then a novel crossover operator is designed based on uniform design, and a new mutation operator is designed based on imagined force-attraction which defines a direction of mutation. When individuals search along the direction with mutation probability, the better individuals may be found. The new mutation operator not only overcomes the blindness of the random search, but also keeps the quality of global search. As a result, the proposed evolutionary algorithm can find optimum quickly and decreases the cost of computation.Secondly, based on the idea of mutation operator for unconstrained optimization problems, a new mutation operator is designed for constrained optimization problems. In the algorithm, the direction of total force is computed first, then it is used as a search direction with some probability. The mutation operator can deal with the constraints effectively. Meanwhile, in order to discard some infeasible individuals, a new fitness function is given based on objective function and the degree of constraint violations.Thirdly, for constrained optimization problems, a new PSO algorithm with two particle swarms is presented. The first one is for minimizing the objective function and the other for minimizing the constraint violations.Finally, the simulation results show the efficiency of the proposed algorithms.