Evolutionary algorithms have proven to be highly effective in continuous optimization, especially when numerous fitness function evaluations (FFEs) are possible. In certain cases, however, an expensive optimization approach (i.e. with relatively low number of FFEs) must be taken, and such a setting is considered in this work. The paper introduces an extension to the well-known LSHADE algorithm in the form of a pre-screening mechanism (psLSHADE). The proposed pre-screening relies on the three following components: a specific initial sampling procedure, an archive of samples, and a global linear meta-model of a fitness function that consists of 6 independent transformations of variables. The pre-screening mechanism preliminary assesses the trial vectors and designates the best one of them for further evaluation with the fitness function. The performance of psLSHADE is evaluated using the CEC2021 benchmark in an expensive scenario with an optimization budget of 10^2-10^4 FFEs per dimension. We compare psLSHADE with the baseline LSHADE method and the MadDE algorithm. The results indicate that with restricted optimization budgets psLSHADE visibly outperforms both competitive algorithms. In addition, the use of the pre-screening mechanism results in faster population convergence of psLSHADE compared to LSHADE.