This study proposes a multiobjective variant of the phase-wise teaching learning–based optimization algorithm, namely Non-dominated Sorting phase-wise Teaching Learning–Based Optimization (NSpTLBO), for solving the multiobjective job shop scheduling problems with unrelated parallel machines. The proposed technique is integrated with a no-wait time heuristic mechanism that reschedules the jobs assigned to the machines so as to minimize the constraint violation. Such an approach is implemented to facilitate the determination of feasible solutions in the earlier iterations of the metaheuristic technique. The efficacy of the proposed multiobjective technique is tested on job shop scheduling problems having jobs with release and due time. The performance of the proposed NSpTLBO and the hybrid NSpTLBO heuristic mechanism is compared against five multiobjective metaheuristic and hybrid metaheuristic-heuristic techniques. Based on the hypervolume and coverage metric, the performance of NSpTLBO with the heuristic mechanism is observed to be competitive compared with other algorithms as well as with its stand-alone version. This study has found the presence of the heuristic mechanism to be beneficial to all the multiobjective metaheuristic techniques in determining better-converged and diversified solutions against their stand-alone algorithms as hybrid techniques have provided a better hypervolume ratio than their stand-alone counterpart.