Several Intelligent Algorithms For Constrained Optimization Problems

Intelligent computing originated from natural (biological) rules, also known as "soft computing", is a kind of computational algorithms simulating these rules for solving practical problems efficiently. Its related concepts are easy to understand and it is usually convenient to execute. Moreover, it is usually efficient because a population of individuals cooperate to complete the task. Due to the advantages of its simplicity, flexibility and robustness, intelligent computing has become a hot research area and has been widely used in many fields such as computer science, telecommunication network, knowledge discovery, robots and so on.Most real-world optimization problems involve constraints. It is necessary for us to deal with constraints firstly when we are faced with a constrained optimization problem. The methods based on penalty are one of the most common approaches to deal with constrained optimization problems. In spite of their simplicity they have several drawbacks in which the main one is the difficulty to tune the penalty parameters. A careful tuning scheme is required to the penalty parameters that can accurately estimate the degree of penalization so that the approach can get a proper balance between the feasible solutions and infeasible solutions and become more efficient.In order to solve constrained optimization problems effectively, evolutionary algorithms and particle swarm optimization algorithms are applied to deal with them. Starting from the framework that the constrained optimization algorithm = constraint processing technology + intelligent algorithms, some improved approaches on both basic aspects: constraint handling technology and intelligent algorithms, have been proposed. The main contributions of this thesis can be summarized as follows:1. Penalty function method is one of the most widely used methods for constrained optimization problems in evolutionary algorithms. It makes the search approach to the feasible region gradually by the way to punish the infeasible solutions. The penalty functions are usually defined as the sum of the objective function and the penalty terms. This kind of the methods are of two main drawbacks. Firstly, it is difficult to control penalty parameters. Secondly, when the difference between the objective function value and the constrained function value is great, the algorithm can not effectively distinguish feasible solutions from infeasible ones, and thus can not handle the constraints effectively. To overcome the shortcomings, two satisfaction degree functions defined by the objective function and the constraints function are designed, respectively. A new penalty function is constructed by these two satisfaction degree functions. Moreover, an adaptive penalty parameter is designed, which is varying with the quality of the population and the number of the generations. As a result, the penalty parameter can be easily controlled. Based on these, a new penalty function optimization model is proposed. Furthermore, a new crossover operator and a new mutation operator are designed. Finally, a new evolutionary algorithm for constrained optimization problems is proposed.2 Firstly, in order to make use of the information of the infeasible solutions near the feasible region, a self-adaptively extended-feasible region is constructed. This region includes not only all feasible solutions, but also some infeasible solutions near the boundary of the feasible region. Furthermore, in order to design a universal and fair solution quality measure for different constrained optimization problem, a new fitness function based on stochastic ranking is constructed. Finally, a new crossover operator, which is the improvement of the arithmetic crossover operator, is proposed. It can produce individuals with better diversity than the arithmetic crossover operator can.3 Firstly, a new penalty function which has no parameter and can effectively handle constraints is proposed, then a hybrid fitness function defined by the penalty function and objective function is designed. The new fitness function not only can distinguish feasible individuals from infeasible ones, but also can evaluate both feasible and infeasible individuals reasonably. Moreover, a new crossover operator based on simplex scheme and a PSO mutation operator are also proposed. These new operators can exploit the search space more efficiently, and can provide potential search direction. As a result, the better individuals can often be generated.4 Particle swarm algorithm is efficient to solve optimization problems. However, for constrained optimization problems, it usually cause premature and can trap into a local optimum easily. To overcome this shortcoming, a bi-particle swarm algorithm for constrained optimization problems is proposed. Firstly, In order to use the information of the good infeasible solutions (i.e. with low constrained violation and good objective function value), a dynamic extended optimization region (deleting poor feasible solutions and adding good infeasible solutions in feasible region) is designed which can search from both the feasible region and the infeasible region. Secondly, two search directions are designed for feasible and infeasible solutions, respectively. They are efficient to exploit the search space and increase diversity of the population.