This paper presents a multi-objective swarm optimization algorithm for scheduling experiments across the Grid. In a sense, MOABC (Multi-Objective Artificial Bee Colony) is implemented to optimize the scheduling of an experiment with dependent jobs respect to the minimization of its execution time and cost. The main advantage in this approach is that it provides decision support for the final user. The user chooses among a range of alternatives with the best execution time and cost, considering these values with the same importance. The obtained results show, not just that the MOABC algorithm is reliable taking into account the standard deviation, but also that its results dominate the results obtained by other grid schedulers. In this research, the well-known DBC (Deadline Budget Constraint) algorithm from Nimrod-G and the WMS (Workload Management System) scheduler from the middleware gLite (Lightweight Middleware for Grid Computing) are compared with the proposed algorithm.