The focus of this paper is on the parallel multi-start and island models of meta-heuristics within the context of multiobjective optimization on the computational grid. The combination of these two models often provides very effective parallel algorithms. However, experiments on large-size problem instances are often stopped before the convergence of these algorithms is achieved. The full exploitation of the cooperation needs a large amount of computational resources and the management of the fault tolerance issue. In this paper, we propose a grid-based fault-tolerant approach for these models and their implementation on the XtremWeb grid middleware. The approach has been experimented on the bi-objective Flow-Shop problem on a computational grid which is a multi-domain education network composed of 321 heterogeneous Linux PCs. The preliminary results, obtained after an execution time of several days, demonstrate that the use of grid computing allows to fully exploit effectively and efficiently the two parallel models and their combination for solving challenging optimization problems. An improvement of the effectiveness by over 60% compared to a serial meta-heuristic is obtained with a computational grid.