Laplacian Ranking ( LaRa ): A Convex Graph‐Regularized Model for Multi‐Criteria Ranking

Abstract

ABSTRACT Laplacian Ranking (LaRa) is a graph‐regularized multi‐criteria decision analysis method that incorporates relational geometry among alternatives into ranking while preserving convexity, interpretability and deterministic reproducibility. LaRa combines quantile normalization, metric‐weighted distances, a sparse similarity graph, a reference‐oriented prior and an optional quadratic pairwise target‐gap term. Its base score is the unique minimizer of a strictly convex quadratic objective, obtained by solving a symmetric positive definite linear system, with an optional deterministic dominance‐repair step. We evaluate LaRa on seven literature‐grounded real‐data problems spanning materials, manufacturing equipment, industrial robotics, renewable‐energy siting, and energy‐technology selection, together with a controlled synthetic pharmaceutical‐style benchmark. Five cross‐domain cases use one common fixed configuration and sensitivity grid rather than dataset‐specific tuning. Results show that the graph contribution is regime‐dependent. It is ordinally inert for cryogenic materials and clean‐energy technologies, measurable but non‐disruptive for flywheel selection, improves concordance with published rankings for CNC machine tools, arc‐welding robots and Colombian solar‐PV siting, and reduces concordance for gear‐material selection, which is retained as an explicit failure boundary. On the fixed synthetic benchmark, the high‐smoothing configuration attains Kendall's and Spearman's , reduces mean absolute rank error from 0.556 for TOPSIS to 0.111, and exactly recovers the Top‐3 set. These findings position LaRa as a relational refinement of pointwise MCDA whose usefulness depends on whether neighbourhood geometry is substantively meaningful and empirically supported. Accordingly, graph smoothing should be activated as a conditional modelling component and accompanied by sensitivity analysis rather than assumed beneficial in practical MCDA applications.