Single-objective And Multi-objective Optimization Evolutionary Algorithms

In many fields of science and technology, economics and management, etc., there are a lot of problems to can be converted into the kind of mathematical model about certain function optimization. Evolutionary algorithms are one of the effective algorithms for hard optimization, global optimization and multiobjective optimization problems, which are attached more and more importance to. This paper studies evolutionary algorithms for single objective optimization, multiobjective optimization and lexicographically stratified multiobjective optimization and proposes novel evolutionary algorithms.To aim at the shortcoming that evolutionary algorithms spend large amount of computation and is weak at local search, a mathematical experiment method—the uniform design is combined into the evolutionary algorithm operator. The novel evolutionary operator has the local search property similar to that in traditional optimization techniques and explores the search space effectively. The numerical experiments show the effectiveness of the novel algorithm with its less computation, higher convergent speed for a group of benchmark problems.To multiobjective optimization problems, a new fitness function is constructed by maximization of the weighted normalized objectives. The way defining weights is much different from the general ways. Not only the weights defined are not limited between zero and one, but also their sum is not required to be one. The weight vectors are carefully and reasonably designed via generalized sphere coordinate transformation and uniform design. As result, the population can keep the diversity, and the uniform search may be easy. The most important characterization of the proposed algorithm is that it can always find enough uniformly solutions distributed on Pareto frontier no matter whether the Pareto frontier is convex or not. A comparison of numerous preferable evolutionary techniques shows that the proposed algorithm is effective.A novel evolutionary algorithm is proposed to handling constrained optimization problems. By treating the constraints as objectives, the proposed algorithm...