The problem of finding an AND/OR precedence-constraint assembly schedule using optimization neural computation is presented. The precedence relationships of assembly operation result from the geometric constraints of subtasks. Because of the existence of geometric constraints among assembly subtasks, the assembly operation involves AND/OR precedence relationships; that is, the order of assembly crucially determines whether the desired task can be achieved. A feasible assembly schedule is a schedule that satisfies these AND/OR precedence constraints. It has been shown that all the feasible assembly schedules can be generated by transforming geometric constraints of subtasks to the pattern-matching operation. Using the question-answer pattern and pattern-matching operation, the assembly scheduling problem can be transformed into an AND/OR precedence-constrained traveling salesman problem (TSP). Two precedence-constrained TSPs, cost-constrained TSP (CCTSP) and state-constrained TSP (SCTSP), are discussed. The CCTSP artificially sets the cost of the prohibited moves to a very large value which ensures that the constraints are satisfied, while the SCTSP restricts the movement of next assembly subtasks. The advantage of the SCTSP over CCTSP in the generation of the assembly schedule will be illustrated. A novel method proposed here is to obtain the best AND/OR precedence-constraint assembly schedule using neural network computation. The geometric constraints of an assembled object are transformed into the elements of the connection matrix which specifies the connection strength among neurons. A modified Hopfield network is used to tackle the AND/OR precedence-constraints assembly scheduling problem. Multirobot assembly sequences generation is also discussed. The designed algorithm can accommodate various constraints and applications. Detailed algorithms, examples and experiments are presented. © 1992 Chapman & Hall.