Previous researchers have made impressive strides in developing algorithms and solution methodologies to address multi-objective optimization (MOO) problems in industrial engineering and associated fields. One traditional approach is to determine a Pareto optimal set that represents the trade-off between objectives. However, this approach could result in an extremely large set of solutions, making it difficult for the decision maker to identify the most promising solutions from the Pareto front. To deal with this issue, later contributors proposed alternative approaches that can autonomously draw up a shortlist of Pareto optimal solutions so that the results are more comprehensible to the decision maker. These alternative approaches are referred to as the pruning method in this review. The selection of the representative solutions in the pruning method is based on a predefined instruction, and its resolution process is mostly independent of the decision maker. To systematize studies on this aspect, we first provide the definitions of the pruning method and related terms; then, we establish a new classification of MOO methods to distinguish the pruning method from the a priori, a posteriori, and interactive methods. To facilitate readers in identifying a method that suits their interests, we further classify the pruning method by the instruction on how the representative solutions are selected, namely into the preference-based, diversity-based, efficiency-based, and problem specific methods. Ultimately, the comparative analysis of the pruning method and other MOO approaches allows us to provide insights into the current trends in the field and offer recommendations on potential research directions.