In recent years, robots have been widely used in assembly systems called robotic assembly lines, where a set of tasks have to be assigned to stations, and each station needs to select one of the different robots to process the assigned tasks. Our focus is on U-shaped layouts because they are widely employed in many industries due to their efficiency and flexibility compared to straight assembly lines. These lines offer more choices to group operations. A worker can be assigned to multiple stations at the entrance and the exit sides. Moreover, it has been shown experimentally that labor productivity can increase significantly in U-shaped lines. However, in many realistic situations, robots may be unavailable during the scheduling horizon for different reasons, such as breakdowns. This research deals with line balancing under uncertainty. It presents robust optimization models for balancing, sequencing, and robot assignment of U-shaped assembly lines with considering sequencing-dependent setup times, failure robots, and preventive maintenance. The nature of this problem is NP-hard with two objective functions; a multi-objective harmony search is suggested to solve it. The parameters of the proposed algorithm were analyzed using the Taguchi method, and their results were compared with the non-dominated sorting genetic algorithm-II (NSGA-II).
