Evolutionary Algorithms For Two Types Of Constrained Optimization Problems

Constrained optimization problems are common optimization models in the fields of engineering and economic management.According to the number of objective functions,constraint optimization models mainly involve single-objective optimization problems and multi-objective optimization problems.The computational difficulty of constrained optimization problems lies in two aspects.Firstly,the functions involved often contain a large number of extreme points and may be non-differentiable.Secondly,the constraint field may be small and feasible solutions are not easy to find.At present,designing effective algorithms for constrained optimization problems has always been a key area of optimization algorithm research.In this thesis,for single-objecitve and multi-objective constrained optimization problems,the related evolutionary algorithms are designed by using heuristic information and constraint handling techniquesFor single-objective constrained optimization problems,based on the problem information and population distribution,a genetic algorithm using a bidirectional information search scheme is presented.Firstly,heuristic information is used to generate at least one feasible individual in the population.Secondly,for each parent individual,both a feasible solution and an individual with a good objective function value are selected in terms of probability distributions.And then the offspring is generated by the vector sum of these three points.Finally,simulation experiments and comparison results show that the proposed evolutionary algorithm is feasible and effective.For multi-objective constrained optimization problems,a new evolutionary algorithm is designed.Firstly,a constraint handling method based on the dichotomy method is proposed.Secondly,in view of the diversity and convergence of nondominated solutions,a local search based on a surrogate optimization model is proposed to facilitate the algorithm to find more high-quality solutions.Finally,the improved individuals by the constraint handling procedure and those by the surrogate optimization model are archived externally,and non-dominated sorting is performed periodically to obtain pareto-solutions.Simulation experiments demonstrate the effectiveness of the algorithm.