The performance of multi-objective evolutionary algorithms deteriorates appreciably in solving many-objective optimization problems which encompass more than three objectives. One of the known rationales is the loss of selection pressure which leads to the selected parents not generating promising offspring towards Pareto-optimal front with diversity. Estimation of distribution algorithms sample new solutions with a probabilistic model built from the statistics extracting over the existing solutions so as to mitigate the adverse impact of genetic operators. In this paper, an improved regularity-based estimation of distribution algorithm is proposed to effectively tackle unconstrained many-objective optimization problems. In the proposed algorithm, \emph{diversity repairing mechanism} is utilized to mend the areas where need non-dominated solutions with a closer proximity to the Pareto-optimal front. Then \emph{favorable solutions} are generated by the model built from the regularity of the solutions surrounding a group of representatives. These two steps collectively enhance the selection pressure which gives rise to the superior convergence of the proposed algorithm. In addition, dimension reduction technique is employed in the decision space to speed up the estimation search of the proposed algorithm. Finally, by assigning the Pareto-optimal solutions to the uniformly distributed reference vectors, a set of solutions with excellent diversity and convergence is obtained. To measure the performance, NSGA-III, GrEA, MOEA/D, HypE, MBN-EDA, and RM-MEDA are selected to perform comparison experiments over DTLZ and DTLZ$^-$ test suites with $3$-, $5$-, $8$-, $10$-, and $15$-objective. Experimental results quantified by the selected performance metrics reveal that the proposed algorithm shows considerable competitiveness in addressing unconstrained many-objective optimization problems.