| In the real world,there are a large number of expensive and constrained black-box optimization problems,which have three major difficulties: the problems have no gradient information,the constraints are difficult to deal with,and the real data of function evaluations are expensive.Data-driven evolutionary constraint optimization adopts evolutionary algorithms,constraint handling techniques and surrogate models to deal with those difficulties and has become the main method to solve such problems.Existing data-driven evolutionary constrained optimization methods have achieved certain performance in solving expensive constrained black-box optimization problems,but they still encounter many challenges in solving such problems.Especially in the case of a small amount of real data,the algorithm needs to quickly complete the optimization under the limited amount of data,which puts forward higher requirements for the convergence ability of the optimization algorithms,the application of constraint handling techniques and the prediction accuracy of the surrogate models.This paper focuses on the evolutionary constraint optimization algorithms driven by small data and proposes evolutionary optimization algorithms for several types of different problems.The main work is as follows:1.In expensive constrained continuous optimization problems,because of the small amount of real data that can be used,it is necessary to accelerate the convergence of the optimization algorithm.The local search has the characteristics of fast convergence speed but easy to fall into the local optimal solution,while the global search has good diversity,but the convergence speed is slow.In order to combine the advantages of both,a restart strategy is proposed to coordinate the two search methods.The global search explores in the global search space and the local search exploits promising local areas.In order to avoid the local search falling into the local optimal solution,when the local search lags behind the global search or the convergence is stagnant,the restart strategy is used to restart the local search.The experimental results show that the restart strategy can effectively speed up the convergence of the algorithm and avoid the algorithm from falling into the local optimal solution.2.In the combinatorial optimization problem with expensive constraints,the combinatorial optimization space has neighborhood similarity,but the crossover and mutation operators in the genetic algorithm are not good at utilizing the neighborhood information,so it is not suited for searching the combinatorial optimization space.The variable neighborhood search algorithm can use the neighborhood to search,but the computational cost is high and the diversity is not good.In order to make the optimization algorithm take into account the global parallel search ability of the evolutionary algorithm and the local exploitation ability of the neighborhood search algorithm,a competitive neighborhood search algorithm is proposed.The competitive neighborhood search operator performs random search for individuals in multiple neighborhoods of an individual at the same time and individuals in multiple neighborhoods compete,which improves the search efficiency of individual neighborhoods.At the same time,each individual in the population uses the competitive neighborhood search operator to search,which ensures the global search ability and parallel ability of the competitive neighborhood search algorithm.The experimental results show that the competitive neighborhood search algorithm can significantly improve the search efficiency and has excellent performance on the test problems.3.In the expensive constrained self-organizing swarm optimization problem,there are different fidelity simulations in the swarm simulation.The low-fidelity simulation is fast,but the simulation fidelity is low,and the high-fidelity simulation has higher fidelity but is more time-consuming.To make full use of different fidelity simulations,a multi-fidelity collaborative strategy is proposed.The multi-fidelity collaborative strategy first selects some promising individuals from the population for low-fidelity simulation,and then selects the best individuals from the individuals evaluated by lowfidelity simulation for further evaluation using high-fidelity simulation.On the one hand,the sampling individuals are screened with the help of low-fidelity simulation,and on the other hand,the waste of evaluation resources caused by random use of highfidelity simulation is avoided.The experimental results show that the multi-fidelity collaborative strategy takes into account the simulation of different levels and achieves good optimization results under different swarm sizes and different constraints. |
