The traditional recommendation algorithms pay too much attention to the precision of recommendation， which leads to the high recommendation rate of popular items. At the same time， the unpopular items are not paid attention to for a long time. This is a classic long-tail problem. In response to this problem， a Multi-objective Dimension Optimization recommendation Model （MDOM）， named Adaptive Group Reranking recommendation Model （AGRM） was proposed， with the construction of two-dimensional weighted similarity based on Euclidean distance and the incorporation of adaptive group reranking. Firstly， a two-dimensional weighted similarity measure was constructed using Euclidean distance， the replacement ratio was set dynamically according to the individual’s historical behavior records， and the long-tail recommendation problem was solved by using the multi-objective optimization algorithm integrated with group. Secondly， two concise objective functions were designed， and the complexity of the objective functions was reduced by taking popularity and long-tail attention into account. Thirdly， based on the two-dimensional weighted similarity measure， a user subset was selected as the "best recommended user group"， and the Pareto optimal solution was calculated. Experimental results on MovieLens 1M and Yahoo datasets show that the coverage of AGRM is the best， with an average increase of 4.11 percentage points and 25.38 percentage points respectively compared to that of Item-based Collaborative Filtering （ItemCF） algorithm， and an average increase of 8.38 percentage points and 33.19 percentage points respectively compared to that of Deep Variational Autoencoder with Shallow Parallel Path for Top-N Recommendation （VASP） model. On Yahoo dataset， the average popularity of AGRM recommendation is the lowest， indicating that AGRM can recommend more long-tail items.