A parallel program, when running, can be conceived as a set of parallel components (tasks) which can be executed according to some precedence relationship. In this case efficient scheduling of tasks permits to take full advantage of the computational power provided by a multiprocessor or a multicomputer system. This involves the assignment of partially ordered tasks onto the system architecture processing components. This paper shows the problem of allocating a number of non-identical tasks in a multiprocessor or multicomputer system. The model assumes that the system consists of a number of identical processors and only one task may execute on a processor at a time. All schedules and tasks are non-preemptive. The well-known Graham’s [8] list scheduling algorithm (LSA) is contrasted with an evolutionary approach using a proposed indirect-decode representation.