Multi-objective Evolutionary Algorithms Based On A Space-gridding Scheme

In engineering optimization or scientific research, multi-objective optimizationproblems are always considered. Different from single objective optimization, inmulti-objective optimization problems, the objectives often conflict with each otherand there is no solution at which all the objectives are optimal. So, to find a solutionset of well distributed and close-to-Pareto-optimal solutions is important formulti-objective optimization. In recent years, with the rapid development ofevolutionary algorithms, the evolutionary algorithm for multi-objective optimizationproblems has become a hot research topic. Based on a space-gridding technology, thethesis presents two types of evolutionary algorithms for solving multi-objectiveoptimization problems as follows:For unconstrained multi-objective optimization problems, first of all, theobjective space is divided into grids and all points are put into these grids. All pointsin a grid are deleted if the grid is dominated by others according to the vertexcoordinates of grids, which can decrease the computation amount of the algorithm.Secondly, in order to find a well spread set of solutions, the minimum value of eachobjective is chosen as a parent individual in crossover operation. Finally, we computethe distance between adjacent individuals at each objective component. A smallerdistance means the individual is located at dense part of solutions, whereas a largerdistance value implies the point is located at sparse part of solutions. When thenon-dominant set is updated, the points with smaller distance value will be deleted.Experimental results show that these technologies can improve the efficiency of thealgorithm.For constrained multi-objective optimization problems, firstly, the decision spaceis divided into grids and a feasible ratio is defined for each grid. The crossover and mutation operations are executed according to this ratio, which can generate as morefeasible individuals as possible. Then, the objective space is also divided into grids tofind non-dominated solutions, and the procedure can reduce the computation time.Experimental results show that these technologies based on space-gridding canimprove the efficiency of the algorithm.