A Non-dominated Sorting Differential Evolution Algorithm Assisted With Dynamic Surrogate Models

Many real-world computationally expensive constrained optimization problems usually involve the use of simulations. These simulations are often computationally expensive, increasing the difficulty of solving real-world optimization problems. Constrained optimization evolutionary algorithm(COEA) can search for optimal solutions without considering the specific characteristics, but it cannot directly solve expensive optimization problems because of slow speed of convergence and a large number of function evaluations. Surrogate models acting as well-established techniques have found widespread use to solve expensive optimization problems, but the solve efficiency are usually low. For reducing the computation cost and ensuring the efficiency, this paper studies on surrogate model assisted evolutionary algorithms(SAEAs). The main contents are given as follows:(1) A solution framework of computationally expensive constrained optimization problems was proposed. It uses COEA to mimic the natural process of evolution by the survival of the fittest and in virtue of surrogate models to compute approximations for the outcome of the computationally expensive non-linear real function.(2) In the aspect of optimization method, a non-dominated sorting differential evolution algorithm was proposed. It is inspired from the dynamic hybrid framework algorithm(Dy HF) and improved the global and local search model. By introducing a new search mechanism and bringing in fast non-domination rank and the elitism operator, the convergence was sped up while the diversity of the population was maintained. The results of comparing with Dy HF through test functions, the algorithm's convergence speed and precision was verified.(3) A non-dominated sorting differential evolution algorithm assisted with dynamic surrogate models was proposed. This method made training data selection strategy and individuals replacement of surrogate model and database management strategy, thus guide the population converge to the exact optimal solution. It had successfully solved different types of testing problems and gas pressure vessel design optimization, and demonstrates its ability to solve computationally expensive constrained optimization problems.