| Multi-objective optimization problems with multiple conflicting targets are widely existed in multiple research fields and engineering practices.Using the idea of divide and conquer,MOEA/D,an evolutionary algorithm based on decomposition,decomposes a complex multi-objective optimization problem into multiple single-objective optimization problems and then processes them at the same time.MOEA/D has become the mainstream algorithm to solve multi-objective optimization problems due to its low computational complexity.However,as the number of targets increases,in order to better approach the global Pareto Front(PF),the population size required by the algorithm needs to increase exponentially,and the computing resource consumption increases.The preferred multi-objective evolutionary algorithm based on decomposition reduces the search range of the algorithm by introducing the preference information from the decision-maker,which not only alleviates the population size limitation when solving the high-dimensional problem,but also provides the preferred solution which is easier to be adopted by the decision maker.Therefore,the preferred multi-objective evolutionary algorithm based on decomposition is favored by more and more researchers.However,the existing preference algorithm based on decomposition has some defects in the decomposition method and does not support the interaction between decision maker and algorithm.Moreover,the convergence rate of the algorithm is slow due to the limitation of the population generation method when solving the complex practical problems such as reservoir flood control operation.This paper starts from the improvement of decomposition method and the application to practical problems,as follows:(1)Aiming at the problems of the existing preference algorithms,this paper proposes an interactive multi-objective optimization algorithm based on preference,called i-MOEA/D.Firstly,this paper theoretically analyzes the problem that the decomposition method of 45 degree projection direction may cause the preference region to deviate from the preference point when solving complex problems,and studies a decomposition method that can correct the position of the preference region by weighting the nearest neighbor points.Secondly,combined with the interactive idea that allows decision makers to change preference points,an improved interactive decomposition strategy is proposed.Based on the MOEA/D algorithm,the i-MOEA/D algorithm is formed.Finally,the effectiveness of the improved decomposition strategy is verified by comparing with the algorithm using the existing decomposition method on the PF complex test problem,and the advantages of i-MOEA/D algorithm are verified by comparing with the other three representative preference algorithms on the low-dimensional and high-dimensional test problem.(2)Aiming at flood control operation of reservoirs,this paper proposes a data-driven interactive reservoir flood control operation algorithm,called DD-MOEA/D.Firstly,this paper theoretically analyzes the problem that the initial population obtained by the common random initialization method is far from the final Pareto frontier,which leads to the slow convergence rate of the algorithm and the limitation that the common population renewal method cannot respond to the change of preference points quickly when the interaction occurs.Secondly,based on the characteristics of reservoir flood control operation,a population generation method based on similar flood information and preference points is proposed.On the basis of i-MOEA/D,the data-driven population initialization method is used to generate the initial population,and at each interaction,the adaptive selection is introduced to the data-driven population to form the DD-MOEA/D algorithm.Finally,the effectiveness and stability of DD-MOEA/D algorithm are proved by comparing with i-MOEA/D algorithm on the flood control operation of six floods in Ankang Reservoir of Shaanxi province. |
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