A New Multi-objective Optimization Genetic Algorithm

In order to solve multi-objective optimization problem in the real-life, according to the existing theory and algorithms, a new multi-objective genetic algorithms was presented. Based on the original genetic algorithm, to improve genetic operators, Pareto rank methods used to determine the individual fitness, the smaller the rank the greater the probability of the individual being selected, I define a function which is the inverse function of Pareto rank. According to roulette selection method, using arithmetic crossover and non-uniform mutation operator, in the computing process, increased a memory to store the current population of Pareto optimal solution, the new individuals was joined the temporary memory , compared with the current individual of memory, from the temporary memory, the individual which is worse than the new entrants'individual will be deleted. In the temporary memory, the solution of the individual is always optimal. To improve the local search capability of the algorithm, the artist applies a golden section search in the search process of the algorithm to improve the convergence speed. Golden section search is the classic one-dimensional search method, in order to use its good search capabilities; the artist extends it to the n-dimension of space, and gives the specific steps of the algorithm. According to the numerical examples, the artist tests the effectiveness of the algorithm; any of the algorithms are not omnipotent, which of all have the area, through a counter-example to illustrate the given new multi-objective genetic algorithm is no exception. Professor Wolpert and Macready presented a free search and optimization of free lunch theorem (No Free Lunch Theorem). According to the theorem , to support this view in the paper. The algorithm improved the speed of certain types of problem solving, while the other will inevitably reduce the settlement rate of a class of problems.