🤖 AI Summary
This work addresses the challenge of efficiently determining whether permutation optimization is worthwhile—and which search strategy to employ—in scenarios where system components are fixed but their ordering significantly impacts performance. The authors propose PRISM, a novel protocol that introduces fitness landscape diagnostics into permutation optimization for the first time. By leveraging low-cost first-order autocorrelation and fitness-distance correlation analyses, PRISM predicts search behavior prior to optimization, thereby guiding the selection of appropriate search strategies, operators, and simplification schemes. Empirical validation across diverse tasks—including neural architecture design, scientific machine learning, and large-model instruction sequencing—demonstrates that PRISM accurately forecasts optimization outcomes and confirms the complementary nature of permutation and content optimization.
📝 Abstract
Permutation optimization arises whenever the components of a system are fixed but their ordering affects performance. We introduce PRISM, a predictive protocol for permutation optimization that measures a fitness landscape before selecting a search strategy. PRISM uses inexpensive landscape diagnostics, including one-step move autocorrelation and fitness-distance correlation, to predict useful mutation operators, identify when structured search is likely to outperform random sampling, and detect regimes in which search provides little advantage. Across synthetic permutation landscapes, neural architecture benchmarks, scientific machine learning pipelines, and large-language-model instruction ordering, the protocol makes testable predictions about search behavior before optimization begins. Exhaustive instruction-ordering experiments reveal substantial performance variation induced solely by permutation, while cross-model experiments show that useful ordering structure can transfer across model families and task difficulty. Additional experiments demonstrate that instruction ordering remains consequential after prompt wording is optimized, indicating that content optimization and ordering optimization are complementary. The results position PRISM not as a universally superior optimizer, but as a framework for determining when permutation search is useful, which representation and operator should be used, and when simpler alternatives are preferable.