High-dimensional Multi-objective Evolutionary Algorithm And Application Based On Simplified Hypervolume

Multi-objective optimization problems(MOPs)have been used in many real-world applications.In the last few decades,large number of multi-objective evolutionary algorithms(MOEAs)have been proposed.However,these MOEAs encounter challenges when solving MOPs with more than three objectives which can also be recognized as many-objective optimization problems(MaOPs).In various evolutionary algorithms,indicator-based evolutionary algorithms have demonstrated good performance for solving many-objective optimization problems.This kind of algorithms combine indicator with evolutionary algorithms to enhance the selection pressure,and guide the evolutionary process toward the true Pareto optimal front(PF).However,the indicator needs prohibitively expensive computational effort,and the computational complexity of these indicator-based evolutionary algorithms grows exponentially with the increasing number of objectives.To simplify the calculation of hypervolume indicator,this thesis proposes a simplified hypervolume calculation method to roughly estimate the convergence and diversity of solutions,the major contributions of this thesis can be summarized as follows:1.A simplified hypervolume calculation method is proposed to roughly evaluate the convergence and diversity of solutions.The main idea is to use the nearest neighbor solutions to calculate the hypervolume value,not only investigates the sparseness of the space around the solution,but also estimates the convergence according to the relative position between the solution and the neighbor solutions.2.The selection operator and update strategy based on the simplified hypervolume is proposed.To enhance the quality of offspring,the selection operator evaluates the convergence and diversity of parents according to the simplified hypervolume,and choose parents with good convergence and diversity to produce better offspring.To balance the convergence and diversity of external population,the update strategy stores solutions with good convergence and diversity according to the simplified hypervolume and nondomination.3.A new evolutionary algorithm using the new selection operator and update strategy is proposed to prove the performance of the simplified hypervolume.Then,the simplified hypervolume-based evolutionary algorithm for many-objective optimization(SHEA)is compared with four state-of-the-art algorithms on fifteen test functions of CEC2018 competition on many-objective optimization,and the experimental results prove the feasibility of SHEA.4.The proposed simplified hypervolume-based evolutionary algorithm for manyobjective optimization is applied to unmanned aerial vehicle(UAV)path planning.First,a digital map is established according to the original forms and mountains in the flight environment.Then,the constraints and cost functions are set considering the threats during the flight of UAV and the performance requirements.Finally,this multi-constrained many-objective optimization problem is solved by the proposed algorithm.And the experimental results are compared with some MOEAs to prove the better convergence and diversity of the result sets obtained from SHEA.