The no-wait flow shop extends the classical flow shop by considering a practical constraint (in steel, plastic, and several industries) that operations of each job should be processed continuously on machines. In this paper, we propose to use a multiobjective evolutionary algorithm based on decomposition (MOEA/D) for no-wait flow shop scheduling with minimization of makespan and maximum tardiness as two objectives. First, we propose a crossover operator that inherits gene blocks with smaller machine idle time from parent solutions. Second, we investigate the effects of initial population by using different job ordering rules. Third, we generate ninety problem instances and conduct experiments on these instances. Experimental results confirm that our idle-time-based crossover and multi-rule initialization lead to good solution quality. We make all data of problem instances and sets of solutions publicly accessible to promote future research on this topic.