Design And Application Of Decomposition-based Evolutionary Algorithm For Expensive Multi-objective Optimization Problem With Learning Guidance

Expensive multi-objective problem is a hotspot as well as a difficulty of real projects in recent years.Compared with multi-objective optimization problem,such problem usually has complex mechanism model,and each accurate evaluation of its objective function has to spend high costs of time and economic.With the gradual development of the computational Intelligence,the evolutionary algorithm has been widely used to solve the multi-objective optimization problems for its superior robustness and global character.However,in the process of its evolution,it has to do plenty of evaluation with fitness functions to get better results,which greatly limits the evolutionary technology to deal with expensive multi-objective problem.A mainstream method is to use the computationally cheap surrogate model instead of the real evaluation model to reduce the evaluation times of expensive functions,so as to estimate the individual fitness in the evolutionary algorithm at a lower cost and guide the evolutionary direction of the algorithm.Because the surrogate model is essentially a supervised machine learning model,this kind of method is also called learning-guided evolutionary algorithms.But unfortunately,most of the existing learning-guided evolutionary algorithms can only deal with the optimization problem of 1-3 objectives,and it is difficult to effectively extend to the computationally expensive many-objective optimization problem,so there are still much room for improvement and perfection.In fact,the key to solving expensive multi-objective optimization problem lies in the design of multi-objective evolutionary algorithm framework,the construction of surrogate model and the selection of infilling solutions.In view of this,we first consider to make full use of the advantages of decomposition-based evolutionary algorithms,and proposed a general framework termed as a cone decomposition evolutionary algorithm based on a dual set of reference vectors.And on this basis,in order to overcome the shortcomings of the single-surrogate model,a random forest-guided cone decomposition evolutionary algorithm with a dual set of reference vectors is designed to solve expensive multi-objective optimization problems,especially for the computationally expensive many-objective optimization problem.The main contributions and innovations of this thesis are summarized as follows:(1)On the basis of the cone decomposition evolutionary algorithm,a dual set of reference vectors are used to cooperate with each other to guide the search of the evolutionary algorithm,and proposes a framework of cone decomposition evolutionary algorithm based on a dual set of reference vectors,in which the two sets of reference vectors are constructed with the ideal point and the nadir point as the coordinate origin respectively.In this algorithm,the general cone decomposition strategy is used to decompose the multi-objective optimization problem into a series of cone sub-problems,and then the solutions in the two sets of reference vectors are associated to the most suitable cone sub-problems according to the KD tree-assisted global association mechanism.A group of populations are maintained on each set of reference vectors in each generation of evolution,so the individual cone update mechanism can be used to update the current population on two sets of reference vector for new individuals generated by cross-mutation.Finally,based on the SEnergy metric,the most suitable one of the above two potential populations is selected as the parent population for the next generation of evolution.By using this method,the flexibility of the algorithm in dealing with irregular PFs can be effectively increased,so that the algorithm can deal with more types of frontier problems.(2)On the basis of the above decomposition-based evolutionary algorithm framework,by borrowing the idea of ensemble learning,a random forest-guided cone decomposition evolutionary algorithm is further proposed for solving expensive multi-objective optimization problem.In this algorithm,the multi-objective optimization problem is decomposed into a series of single-objective optimization sub-problems according to two sets of reference vectors,and then the algorithm of CDEA-DR is used to solve these sub-problems.In the specific process of evolution,a random forest is constructed to predict the fitness of each point in the search space so as to guide the evolutionary trend of the algorithm.At the same time,a novel selection criteria of infilling solutions based on a dual set of reference vectors is used to select the promising sampling solutions,and then evaluated them by using the real functions for random forest updating,so as to iterate until the maximum number of real evaluation is satisfied.With the application of random forest learning method,the number of real evaluation is reduced from million to hundred,as well as save time greatly.In addition,the local search technology is also added to improve the quality of infilling solutions,which is helpful to increase the prediction accuracy of the model and maintain the stability of the whole population.(3)Experiments on two series of test instances(DTLZ and WFG)as well as two practical engineering problems,are conducted to test the comprehensive performance of the proposed algorithm framework and a random forest-assisted cone decomposition evolutionary algorithm,respectively.In addition,it is compared with the state-of-art algorithms in the field to verify the effectiveness of the proposed algorithm in dealing with expensive multi-objective optimization problems.The comprehensive experiments on standard test instances and practical engineering problems indicate that,the decomposition-based evolutionary algorithm RFCDEA-DR designed in this thesis can effectively overcome the limitations of multi-objective evolutionary algorithms in dealing with computationally expensive many-objective optimization problems,and greatly reduce the evaluation times of expensive objective functions while maintaining the characteristics of evolutionary algorithms.Compared with the current mainstream surrogate-assisted evolutionary algorithms,it can not only obtain a solution set with better quality as a whole,but also optimize the results that approximate the pareto front in finite function evaluations,which effectively reduces the engineering time and economic cost,greatly expands the scope of application of decomposition-based multi-objective evolutionary algorithms,and has a broad development space and application prospects.