The Grid Mechanism For Multi-Objective Evolutionary Algorithm

Multi-objective optimization which is solved by evolutionary algorithms is the principle research area in optimization method. Most real-world problems have two or more conflicting objectives. Different from the single objective optimization problems which have the only optimum solution, the optimum solutions of multi-objective optimization problems are a group of trade-off solutions, namely Pareto optimum solutions set. Multi-objective evolutionary algorithm is a kind of random search algorithm which simulates the nature selection and evolution. It specializes in solving highly sophisticated and nonlinear multi-objective optimization problems. It appeals many researchers so that it develops rapidly. However, a great amount of evolutionary algorithms did not consider the used information such as the information of population, the proceeding of evolutionary and the spread of elitist when dealing with the MOPs as well as CMOPs. In addition, the presence algorithms did not regard the impacts of evolutionary on the global knowledge. Actually, it has an important impact on the population and that population does more progress in the proceeding of evolutionary in a unique position. On the other hand the adaptive grid algorithm have difficult in the cell size of each dimension for the size is fixed, and then the amount of the grid is also fixed. In generally, the individuals occupied a small number of the grid, so the distribution is affected. The research work in this paper focus on the grid mechanism for multi-objective evolutionary algorithm and the contribution of this work contains the following two folds:First, a constrained multi-objective evolutionary algorithm base on grid incentives (denoted as C-GIEA) is proposed. Most of the constrained multi-objective evolutionary algorithms do not consider the exchange of information among the population resulting in a lack of guidance search. C-GIEA makes use of grids which record a variety of information and constraint, and then guiding the evolution of population. On one hand, the population is made to the better approximation of the search area, and ultimately closes to the optimal solution according to its strong search capability in the constraints of space; on the other hand, the information of grid is adjusted by the one of population. Therefore, the population and that information can learn from each other and co-evolution. Conversely, the population is promoted and leaded. From an extensive comparative study with two states-of-the-art algorithms, the experiments indicate that the proposed algorithm provides good performance in terms of convergence, spread and distribution.Second, a novel multi-objective evolutionary based on Hybrid Adaptive Grid Algorithm (denoted as HAGA) is presented. The number of bisections of the space in the adaptive grid algorithm is difficult to be established. If the number is not chosen appropriately, it will make a poor convergence and a bad diversity of solutions set. HAGA is made up of a local search operator and a pruning operator, and then combined with differential evolution operator. To the contrary, they help the grid algorithm to find much better solutions. The main idea of the proposed method is that the search space is divided into a number of cell grids by dividing the each objective equally. An individual is deleted randomly from the gird which includes the most number of individuals. And then the local search operator, a pruning operator and differential evolution operator is used according the conditions. Therefore, on one hand it improves the convergence of the algorithm; on the other hand it can improve the spread and the distribution of the solutions set. From an extensive comparative study with three states-of-the-art algorithms on twenty-one test problems, it is observed that the proposed algorithm outperforms the other three algorithms as regards convergence and comprehensive performance.