When Do Low-Dimensional Probes Help Multiobjective Optimization?

Large-scale multiobjective optimization must explore hundreds or thousands of decision variables under limited evaluation budgets, making broad coverage of the decision space impractical. Low-dimensional probes address this challenge by concentrating evaluations on structured candidate families. Yet terminal performance alone cannot reveal why probing helps. Gains may come from representation, additional queries, or candidate retention, and conflating these effects can misattribute improvements and obscure both the underlying bottleneck and how probing should be improved. We study these effects through a controlled shared-scalar probe embedded in a fixed multiobjective search backbone. Our analysis identifies when a single scalar block is sufficient, separates finite-grid error from a representation-induced floor, and shows that identical nondominated decision sets need not imply identical population states. Under a fixed budget, additional probe queries can improve the evaluated candidate pool but reduce evaluations available for downstream search. We further separate losses from withholding evaluated candidates and finite-population selection, while matched-budget and matched-query comparisons distinguish query value from retention value. Across 64 benchmark configurations, additional-query value varies substantially with problem structure. Targeted controls further support retaining paid alternatives more consistently than the tested adaptive placement strategy.