Research On Multi-Objective Evolutionary Algorithm And Its Applications In Reservoir Optimization

Multi-Objective Optimization Problems(MOOPs)are different from previous optimization problems that only contain single objective.The solutions for a multi-objective problem represent the trade-offs between the objectives instead of the single best value,which makes it difficult for traditional techniques to achieve better results in solving these problems such as mathematical programming and gradient descent.For the multi-objective optimization problem,especially the multi-objective optimal scheduling problem of the reservoir,the Swarm Intelligence(SI)based optimization algorithm can obtain a good compromise solution through a single run without a priori information.However,limited by its relatively simple sorting and screening mechanism,it is difficult for these algorithms to achieve better results when dealing with problems with complex pareto fronts.In addition,with the continuous updating of technical equipment and the improvement of demand,the scale of optimization problems in reality is also constantly increasing,which makes the number of objective in real problems no longer limited to two or three.Such problems are called many objective optimization problems(MaOPs).For the many objective optimization problem,with the number of objective increasing sharply,almost all solutions in a population become non-dominated with one another and the conflict between convergence and diversity becomes aggravated with the increasing number of objectives in MaOPs,which makes the previous multi-objective evolutionary algorithms(MOEAs)deteriorate dramatically.Therefore,in consideration of the theoretical research on multi-objective optimization and many objective optimization as well as its application to the multi-objective optimization scheduling problem in actual reservoirs,this paper has completed the work recognized by domestic and foreign peers through the relevant analysis and exploration,which are shown as follows:(1)Swarm intelligence based multi-objective evolutionary algorithms focus on the construction of biological behavior and lack the efficient mechanism to assist the operation of other main process,which limits the improvement of the overall performance of the algorithm.In order to improve the performance and adaptability of the algorithm in dealing with different types of optimization problems,an opposition-based multi-objective moth-flame algorithm is proposed.The algorithm is initialized by using opposition-based learning,which replaces the randomization process of the traditional algorithm,thus the proposed algorithm can obtain a more suitable starting candidate region without prior knowledge.In addition,the algorithm maintains the external archive by introducing an indicator-based strategy,thereby effectively improves the quality of the solution obtained by the algorithm.Moreover,the algorithms are also verified through a series of experimental comparisons.The experimental results show that the proposed algorithm has better performance and adaptability on some multi-objective optimization problems with different pareto fronts.(2)The traditional multi-objective evolutionary algorithm is limited by its relatively simple design mechanism.The selection mechanism used tends to focus on one aspect of convergence or diversity,which make it difficult for these algorithms to balance convergence and diversity well.In view of this,a grid sorting strategy based multi-objective whale algorithm is proposed.Based on the grid coordinates,the grid sorting strategy in the proposed algorithm makes full use of character that grid which can represent the convergence and diversity simultaneously by calculating the dominant relation of the individuals on the grid and the distribution of the surrounding individuals.By adopting the above mechanism to evaluate and select the individuals,the performance of the proposed algorithm has been improved effectively.In addition,the proposed algorithm has been verified through a series of experiments and related indicators.The experimental analysis is also carried out on aspects of convergence and diversity.The results show that the algorithm can better balance convergence and diversity and tends to perform well with different types of multi-objective optimization problems.(3)In view of the fact that it is difficult for traditional multi-objective algorithms to achieve good results in many objective optimization problems,especially when balancing the convergence of the algorithm and the diversity of the solutions,a many objective evolutionary algorithm with adaptive clustering is proposed to effectively deal with the many objective optimization problems.The algorithm uses an adaptive clustering strategy based on the reference vector to partition the population.This strategy comprehensively considers the angle and distance between the individual and reference vectors through an adaptive function,thus to efficiently cluster the population into multiple sub-populations with the aims of reducing the complexity of subsequent calculations.In addition,for each sub-population,this algorithm proposes a hybrid distance-based selection strategy to select the individuals effectively in the view of the convergence and diversity,thus improving the performance of the algorithm in dealing with many objective optimization problems.In addition,the algorithm is compared with a series of current many objective evolutionary algorithms on the standard test problems.The experimental results show that the proposed algorithm has advantages and potential over the previous algorithms in dealing with many objective optimization problems.(4)Aiming at the present situation that most of the current multi-objective evolutionary algorithms focus on the construction of algorithm mechanism and lack of theoretical analysis,the convergence of multi-objective evolutionary algorithms in the stagnant state is analyzed by combining with the theory of random process.Although there are many algorithms have been designed for multi-objective optimization problem,there are still few theoretical analysis on the convergence of the algorithm.In view of this,this paper analyzes the convergence of the proposed multi-objective evolutionary algorithm in this thesis and proves it at the theoretical level.In addition,this thesis also makes a preliminary analysis and discussion on the convergence proof of the many-objective evolutionary algorithm,and discusses the existing problems and limitations,which lays a foundation for the subsequent theoretical proof in the future.(5)Taking the actual river basin as the research object,the multi-objective reservoir optimization models which meet different requirements are designed.According to the different demand of models and the complexity of the problem,the many objective evolutionary algorithm proposed in this paper is used to solve the problem respectively.Most of the previous reservoir optimization models are designed using a single objective or bi-objective with a large number of complex constraints which are transformed from the other objectives.Although the above methods reduce the complexity of the problem.However,the gaps between the theoretical and practical are increasing.Moreover,it is difficult to satisfy the actual demand for reservoir optimization.In view of this,this paper takes the Lushui river basin in Jiangxi province as the research object,and designs an optimization model to meet the comprehensive needs according to different demands.The many objective evolutionary algorithm designed in this paper is also adopted for optimization of the proposed model.Through the calculation and analysis of the actual optimization problem,the performance and potential of the proposed algorithm in dealing with real multi-objective optimization problems are verified.Furthermore,these results also provide new ideas and methods for reservoir optimization scheduling.