Research On Evolutionary Optimization Algorithms For Expensive Complex Multi-Objective Problems

There are some optimization problems in science,engineering,and life that need to optimize multiple conflict objective functions simultaneously.Furthermore,no explicit mathematical models are available for the objective functions,and the computational costs are expensive to evaluate the objective functions.Thus,it is impossible to use evolutionary optimization algorithms directly for solving this kind of problem.Surrogate-assisted evolutionary algorithms are approaches commonly used for solving computationally expensive problems.However,more data are required to train a surrogate model when the dimension of the decision space increases,which will be difficult to train proper surrogate models to guide the search of optimization.On the other hand,an approximation error of any surrogate model for the objective function will mislead the search direction and result in an improper infill sampling when the number of objectives increases.According to the analysis results of evolutionary Bayesian multi-objective optimization and surrogate-assisted evolutionary multi-objective optimization,we carry out research into the evolutionary multi-objective algorithms for solving problems with many objective functions,with large-scale decision variables and with computationally expensive objective functions.The main parts include:1.The performances of evolutionary Bayesian optimization algorithm and surrogate-assisted evolutionary algorithm are compared for solving expensive multi-objective optimization problems.The experimental results show that the surrogate-assisted evolutionary algorithm can obtain better performance for solving expensive multi-objective optimization problems within limited computational resources.2.For expensive many-objective optimization problems,the environmental selection and reproduction strategies are studied at first for solving computational cheap multi-objective problems.Then,two infill sampling techniques are proposed for surrogate-assisted expensive multi-objective optimization algorithms.One infill sampling strategy is based on the overall performance and overall uncertainty of a solution with approximated objective values,and the other infill criterion is based on the acquisition function of the surrogate model for the performance indicator.The experimental results on expensive multi-objective problems with up to ten objectives and practical applications show that surrogateassisted evolutionary optimization algorithms with the proposed infill criteria are effective for solving expensive high-dimensional multi-objective optimization problems.3.For the expensive multi-objective problems with high-dimensional decision space,an evolutionary optimization algorithm with multiple surrogate models is proposed at first to solve the high-dimensional expensive singleobjective problems.A new approach for calculating the approximation uncertainty is proposed.A solution with the minimum uncertainty will be selected from the population of a global search,and a solution with a minimum approximated objective value will be chosen from the population of a local search for an expensive objective evaluation,respectively.The experimental results on optimization problems with 10-,20-,30-,and 50-dimensional decision variables show the efficiency of the proposed method.After that,a large-scale multiobjective optimization algorithm assisted by directed sampling is proposed for computational cheap large-scale multi-objective problems.The trade-off of convergence and diversity is balanced by generating guiding solutions along with two search directions and a complementary environmental selection strategy to achieve a good set of optimal solutions.The experimental results on multiobjective optimization problems with up to 5000 decision variables show that the proposed algorithm is effective for large-scale multi-objective problems.Finally,for those large-scale problems with expensive objective functions,a surrogate model is trained for each objective,and a set of optimal solutions will be searched based on the surrogate models by the large-scale multi-objective optimization algorithm assisted by directed sampling.Then a surrogate model is trained for the approximation uncertainty,and individuals are selected to be expensively evaluated by different infill sampling strategies based on the distribution of the candidate population.The experimental results on 100-dimensional multiobjective optimization problems show that the proposed algorithm is efficient for solving expensive large-scale multi-objective problems.