A novel problem dealing with design of reconfigurable automated machining lines is considered. Such lines are composed of workstations disposed sequentially. Each workstation needs the most suitable equipment. Each available piece of equipment is characterized by its cost, can perform a set of operations and requires skills of a given level for its maintenance. A multiobjective approach is proposed to assign tasks, choose and allocate pieces of equipment to workstations taking into account all the problem parameters and constraints. The techniques developed are based on a genetic algorithm of type NSGA-II. The NSGA-II suggested is also combined with a local search. These two genetic algorithms (with and without local search) are tested for several line examples and for two versions of the considered problem: bi-objective and four-objective cases. The results of numerical tests are reported. What is the most interesting is that the assessment of these algorithms is accomplished by using three measuring criteria: the direct measures of gaps, the measures proposed by Zitzler and Thiele in 1999 and the distances suggested by Riise in 2002.