Multi-objective scheduling problems with sequence-dependent setup times (SDST) arise in several real-world production environments and are characterized by conflicting performance criteria, complex interdependencies among decisions and a combinatorial search space that grows rapidly with problem size. These characteristics make the design of effective decision-support tools particularly challenging, especially when decision-maker preferences are not additive and cannot be easily captured by conventional scalarization approaches. This paper proposes NEAR (the Non-dominated Evolutionary Algorithm with preference Relations), a novel multi-objective optimization (MOO) algorithm that integrates Choquet Integral-based preference aggregation into the MOO process. The method enables the incorporation of non-additive preference structures, allowing the modeling of interactions among objectives and supporting preference-guided solution selection and variation. NEAR is applied to the single-machine scheduling problem with SDST, considering the simultaneous minimization of total weighted tardiness , maximum tardiness and makespan . In addition to preference-guided environmental selection, NEAR introduces a Choquet-based crossover mechanism that exploits aggregated preference information during offspring generation. An extensive computational study, including sensitivity analysis with respect to different fuzzy-measure configurations and comparisons with representative multi-objective evolutionary algorithms (including preference-based, indicator-based and decomposition-based methods), demonstrates the robustness and competitiveness of the proposed approach. Statistical analysis confirms that NEAR achieves consistent convergence performance while maintaining satisfactory diversity under varying preference structures.
Andreas C. Nearchou (Thu,) studied this question.