Expensive Constrained Optimization Algorithm Assisted By A Re-constructed Constraint

In real-world applications,some optimization problems need to conduct computation simulations such as finite element analysis and computational fluid dynamics,or experiments to obtain the values of objectives or constraints.It means that the evaluation of a candidate solution will cost much time.These problems are referred to as expensive constrained optimization problems.Evolutionary optimization algorithms need a lot of function evaluations before locating close to the optimal solution,limiting its application in solving expensive constrained optimization problems.It is an effective way to solve expensive constrained optimization problems by calculating the objective or constrained values using surrogate models instead of the expensive objective or constrained functions.However,when the constrained optimization problem has multiple constrained functions,an error of any model may result in the inability to find a feasible solution.Therefore,this thesis proposes a strategy to re-construct the original constraint function,converting multiple constraint functions to a single constraint function.After that,a surrogate model is trained for the re-constructed function to assist the method in searching for the optimal feasible solution.The main work of this thesis is given as follows:An expensive constrained optimization algorithm based on the reconstructed constraint is proposed.The establishment of multiple models will lead to an increase in computational complexity and error accumulation.Thus,a method is proposed to re-construct a constrained function on the original constraints in this paper.Multiple constrained functions are transferred to a constrained function in the proposed method,and a surrogate model is trained for the re-constructed constrained function.After that,a new infill criterion is proposed according to the adopted surrogate model and the evolutionary algorithm,which is expected to get an optimal feasible solution in a limited computational budget.The experimental results on CEC2006 benchmark problems and black box functions show that the algorithm is effective and competitive for solving expensive constrained optimization problems.An improved expensive constrained optimization algorithm assisted by a surrogate model for re-constructed constraint is proposed.There will be a large number of infeasible solutions in the initial population,which will result in a slow convergence speed.Thus,in order to improve the efficiency of the method,an improved particle swarm optimization algorithm is proposed to search for the optimal solution of a surrogate model for the re-constructed constraint.When a solution is approximated to be feasible,it will be adopted to be a solution of the population for the optimization of the constrained problems.After that,the expensive constrained optimization algorithm based on the re-constructed constraint will be used to search for the optimal feasible solution for the expensive constrained optimization problems.The experimental results on CEC2017 benchmark problems show that the proposed method can achieve better results than canonical algorithms in a limited computational budget.