PRISM: A Predictive Protocol for Permutation Optimization via Landscape Diagnostics
Blessings Mambwe
cs.LG, cs.AI, math.OC
Submitted: 2026-08-08
Updated: 2026-08-11
Comments: Preprint. Includes theoretical analysis, exhaustive permutation-landscape experiments, LLM instruction-ordering experiments, scientific machine learning pipeline studies, and neural architecture search benchmarks. Code and reproducibility artifacts available
Code: https://github.com/bleymambwe/PRISM
License: http://creativecommons.org/licenses/by/4.0/
The gist: Permutation optimization arises whenever the components of a system are fixed but their ordering affects performance.
Terminology
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.
Sources
- On Fitness Landscape Analysis of Permutation Problems: From Distance Metrics to Mutation Operator Selection
- Lost in the Prompt Order: Revealing the Limitations of Causal Attention in Language Models
- Chain-of-Thought Prompting Elicits Reasoning in Large Language Models
- Self-Consistency Improves Chain of Thought Reasoning in Language Models
- Large Language Models Are Human-Level Prompt Engineers
- Large Language Models as Optimizers
- DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines
- Training Verifiers to Solve Math Word Problems
- Measuring Mathematical Problem Solving With the MATH Dataset
- NAS-Bench-201: Extending the Scope of Reproducible Neural Architecture Search
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