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Summary Truss optimization is a complex structural problem that involves geometric and mechanical constraints. In the present study, constrained mean-variance mapping optimization (MVMO) algorithms have been introduced for solving truss optimization problems. Single-solution and population-based variants of MVMO are coupled with an adaptive exterior penalty scheme to handle geometric and mechanical constraints. These tools are explained and tuned for weight minimization of trusses with 10 to 200 members and up to 1,200 nonlinear constraints. The results are compared with those obtained from the literature and classical genetic algorithm. The results show that a MVMO algorithm has a rapid rate of convergence and its final solution can obviously outperform those of other algorithms described in the literature. The observed results suggest that a constrained MVMO is an attractive tool for engineering-based optimization, particularly for computationally expensive problems in which the rate of convergence and global convergence are important.