Application Research Of Co-evolutionary Genetic Algorithm Based On Multi-objective Optimization Area

Multi-objective optimization problem has always been an important research subject in fields of science and engineering. Evolutionary algorithms have the advantage of solving multi-objective optimization problem, because they do not need much information about the optimization problem before the optimization process, and they can search multiple solutions of optimization problem simultaneously, moreover, they have the ability of dealing with large space problems, for these reasons, genetic algorithms can overcome the drawbacks of traditional optimization methods. Since then genetic algorithms have been widely used to solve multi-objective optimization problems, and many classical multi-objective evolutionary algorithms have appeared, however, genetic algorithms need not only fast convergence but also population diversity, which composes a conflict of genetic algorithms. The co-evolutionary mechanism emphasizes the interaction between populations and environment, and it involves the role of competition and cooperation between evolutionary populations, so it could not only improve population diversity but also speed up convergence rate, therefore, co-evolutionary genetic algorithms are more consistent with the general laws of natural evolution than traditional genetic algorithms, and they have become the trend of solving multi-objective optimization problems.To further improve the convergence speed and population diversity of co-evolutionary genetic algorithms, this paper proposes a new algorithm to solve multi-objective optimization problems, and the main contents are as follows:(1) The paper proposes a co-evolutionary genetic algorithm based on multi-level search area. As the basis of multi-objective evolutionary algorithms, the current simple objective co-evolutionary algorithms still have slow convergence rate and high computational complexity. The co-evolutionary genetic algorithm based on multi-level search area proposes a search mode of dividing search area, apply intensive search to high probability regions, and apply sparse search to low probability regions, so the algorithm helps further improve the performance of co-evolutionary genetic algorithms. It puts forward a standard to measure evolutionary stagnate; When all the populations tend to evolutionary stagnate, the whole search space is divided into three levels via clustering, including: key area,secondary area and periphery area, which can help search the global optimal solution; Search area of different levels is subject to different search intensity, at the same time, the algorithm enhances search in key area, while it weakens search in periphery area. Through dividing search area, simulation results indicate that the algorithm speeds up the convergence rate and reduces the complexity of the algorithm, so the algorithm is an effective method for solving optimization problems.(2) The paper proposes a staged multi-objective co-evolutionary algorithm. At present, multi-objective evolutionary algorithms with high convergence performance always have low distribution performance, and multi-objective evolutionary algorithms with high distribution performance always have low convergence performance, therefore, multi-objective evolutionary algorithms need to further improve the performance of convergence and distribution. The staged multi-objective co-evolutionary algorithm has two stages, population evolutionary stage focuses on improving the convergence performance, and excellent individuals're-evolutionary stage focuses on improving the distribution performance, the convergence performance and distribution performance both are improved simultaneously; In the stage of population evolution, it uses the frame of culture algorithm for reference, and each population selects outstanding individuals from population space to join belief space, then it extracts knowledge to guide the population's evolutionary process; At the same time, each population learns the best population's culture, and vulnerable populations are annexed in the evolutionary process; In the stage of re-evolution of excellent individuals, make all populations'belief space join general belief space, and make individuals mutate in their neighborhood in order to explore more excellent individuals and enrich population diversity. Through dividing evolutionary stage, simulation results indicate that the algorithm significantly improves in terms of the performance of convergence and distribution compared to NSGAⅡ.(3)Apply the staged multi-objective co-evolutionary algorithm to solving multi-objective 0/1 knapsack problem and Portfolio optimization problem. Multi-objective 0/1 knapsack problem and Portfolio optimization problem both are multi-objective optimization problem in real life, and they are practical problems of everyday life, but traditional optimization methods still can't satisfy people's needs. In the application test, make the staged multi-objective co-evolutionary algorithm compare to classical multi-objective evolutionary algorithm (NSGAⅡ). Simulation results indicate that the staged multi-objective co-evolutionary algorithm has better performance of convergence and distribution than NSGAⅡ, and it is able to provide excellent solutions for decision makers, which verifies the efficiency of the algorithm. KEYWORDS: co-evolution; multi-objective optimization; genetic algorithm; multi-objective...