Survey of Mathematical Methods for Multi-Objective Decision Support

This submission proposes a systematic survey of mathematical methods used to support decisions with multiple, often conflicting, objectives. The survey will cover foundational and contemporary approaches, including weighted aggregation methods, lexicographic and goal-programming formulations, epsilon-constraint methods, utility/value-function approaches, outranking methods, Pareto-based evolutionary multi-objective optimization, and robust/stochastic multi-objective formulations. The goal is not only to list methods, but to map where each method performs well, where it fails, and which assumptions are required for valid use. Scope includes both methodological papers and application-oriented studies where methods are implemented and evaluated. The review will organize evidence by decision context (for example: resource allocation, scheduling, infrastructure planning, policy design), data regime (deterministic vs uncertain), and stakeholder structure (single decision-maker vs group decision-making). Each method family will be summarized in a standardized template: mathematical formulation, required inputs, computational complexity profile, strengths, limitations, typical failure modes, and interpretability of outputs. Constraints include heterogeneity in evaluation metrics across studies, inconsistent reporting standards, and domain-specific benchmarks that may limit direct comparability. To address this, the survey will define a normalization scheme for reported outcomes and a qualitative evidence grading rubric for methodological claims. Success criteria are: (1) reproducible screening and selection process, (2) consistent cross-method comparison framework, (3) clear guidance on method selection by use case, and (4) a documented gap analysis identifying underexplored research directions. Deliverables will include a full survey manuscript, comparative summary tables, a method-selection decision map, and a machine-readable extraction sheet of reviewed studies and key attributes. The final output is intended to be directly usable by both researchers planning new algorithmic work and practitioners choosing decision-support techniques under real constraints.