In this paper a new estimation of distribution algorithm Sim- EDA is presented. This algorithm combines a multipopulation approach with distribution modelling. The proposed approach is to tackle sev- eral similar instances of the same optimization problem at once. Each subpopulation is assigned to a different instance and a migration mech- anism is used for transferring information between the subpopulations. The migration process can be performed using one of the proposed strate- gies: two based on similarity between problem instances and one which migrates specimens between subpopulations with uniform probability. Similarity of problem instances is expressed numerically and the value of the similarity function is used for determining how likely a specimen is to migrate between two populations. The Sim-EDA algorithm is a general framework which can be used with various EDAs. The presented algorithm has been tested on several instances of the Max-Cut and TSP problems using three different migration strategies and without migration. The results obtained in the experiments confirm, that the performance of the algorithm is improved when information is transferred between subpopulations assigned to similar instances of the problem. The migration strategy which transfers specimens between the most similar problem instances consistently produces better results than the algorithm without migration.