Research On Diversity Maintenance Strategy Of Evolutionary Multi-objective Optimization And Application

There exist some multi-objective optimization problems (MOPs) in science and engineering, and these problems usually consist of several conflicting objectives that must be satisfied simultaneously. Only one optimal solution can be found in the classical multi-objective optimization algorithms by weighting method and most of these algorithms require some prior knowledge such as suitable weights.Evolutionary multi-objective optimization algorithms based on Pareto-optimal can find a set of solutions in a single run, and are less susceptible to the shape or continuity of the Pareto front. Therefore, evolutionary multi-objective optimization has become an important alternative approach to solve MOP. Due to the limitation of population size, evolutionary multi-objective optimization algorithms only can achieve a set of finite discrete solutions. So how to guarantee the distance between the approximation and the true Pareto set as possible as small and the spread of the Pareto solutions as possible as uniformly are the two key indexes of evolutionary multi-objective optimization algorithm; Maintaining the population diversity can not only help to find the promising optimal solutions, but make the discrete solutions spread uniformly. Therefore, the research of diversity maintenance strategy becomes one of the most important points of evolutionary multi-objective optimization algorithm. This dissertation mainly focuses on the study of population diversity maintenance and performance assessment of evolutionary multi-objective optimization algorithm and the balance between the convergence and the diversity, the major contributions of this dissertation are as follows:The evolutionary multi-objective optimization algorithms need to maintain the population diversity and to speedup the convergence. To achieve the balance between population and the algorithm convergence, a new evolutionary multi-objective optimization scheme based on hierarchical clustering model is proposed. In the scheme, the whole population is divided into multiple sub-populations according to the individual's fitness rank, moreover, individuals of different levels evolve independently, which prevent promising low-fitness individuals from eliminating in competition with individuals of higher-fitness at the beginning of evolutionary process. Individual migration strategies are constructed in the algorithm to carry out the interaction between sub-populations, which can allow individuals exchange at some migration rate to exchange promising genes. The evolutionary multi-objective optimization algorithm based on the hierarchical clustering model can maintain the diversity of population and avoid the premature solutions. The numerical experiments on benchmark test functions show that the proposed scheme can achieve the balance between the exploration and exploitation capability.Most of the conventional evolutionary multi-objective optimization algorithms employ single diversity maintenance strategy, which can't adapt the diversity maintenance strategies to the different approximate Pareto front. Due to the randomness of EA, the search process usually presents oscillation, even degeneration phenomenon at some extent. In order to address the above issues, this dissertation proposes an adaptive diversity maintenance strategy, which including staged diversity preservation strategy, interpolation- extrapolation strategy and hybrid diversity maintenance strategy based on exploitation.·The staged diversity maintenance strategy is used to exploration (global search) at the beginning of evolutionary process to find non-dominated solutions of a broader space and to exploitation (local search) at the end of evolutionary process to find as many non-dominated solutions of the approximate Pareto front as possible. When there exist the following two situations:approximate Pareto front disconnects or the non-dominated solutions concentrate in some regions, the interpolation- extrapolation strategy is used to improve the search capabilities and to find more non-dominated solutions in those regions. The hybrid diversity maintenance strategy based on exploitation employs an external archive to maintain and update the non-dominated solutions to mitigate the randomness of crossover and mutation operations of the evolutionary operators to some extent.This dissertation designs the metrics of convergence and diversity to measure and assess the convergence of evolutionary multi-objective optimization algorithm and the diversity of population. The inverted generation distance (IGD) can measure the convergence of algorithm and the diversity of population, which is also used to design the adaptive iteration termination criterion. The variance of population and informational entropy are used to assess the population diversity.To validate the effectiveness of the proposed scheme and strategy, this dissertation establishes a wireless sensor network node deployment model of minimizing the cost and maximizing network coverage. The proposed scheme and adaptive diversity maintenance strategy are used to solve the above problem. Numerical experiments demonstrate that the solutions set which distributed uniformly on the whole Pareto optimal front can fit the preference of decision makers and meet the requirement of problems.