Design of statistical quality control procedures using genetic algorithms

A new adaptive restart rule for Genetic Algorithms (GAs) is considered. The rule is based on the Schnabel Census method, originally developed for statistical estimation of a size of animal population. In this paper, the Schnabel Census method is applied as a heuristic to estimate the number of different solutions that may be visited with positive probability, given the current distribution of offspring. The rule consists in restarting a GA as soon as the maximum likelihood estimate reaches the number of different solutions observed at the recent iterations. We demonstrate how the new restart rule can be applied in a GA with steady-state replacement scheme, using three different combinatorial optimization problems as examples. Computational experiments on well-known benchmarks show a statistically significant advantage of the GAs with the new restarting rule over the original versions of GAs. The new restart rule also tends to be superior to the well-known rule, which restarts an algorithm when the current iteration number is twice the number of iterations till the current best incumbent was found.

Numerous agentic workflows are based on a generator-verifier loop: a generator proposes candidates, a cheap verifier scores them, and the workflow terminates when a proposal is verified as good enough. The verifier typically proxies a more costly ground-truth oracle, and as the generator searches adaptively against it, false acceptances may accumulate. Proposals can pass the proxy but fail under the costlier ground-truth check. We study when to stop these loops while controlling the false discovery rate of the accepted proposals. Our construction introduces tools of independent interest in distribution-free statistical testing and conformal risk control, including analysis of $e$-values constructed through index betting and a novel conformal risk control procedure for non-monotone losses. We validate the approach in synthetic settings and on a protein-design benchmark.

Pharmaceutical process characterization is central to Quality by Design because it defines how variations in process parameters affect the ability to meet product quality specifications, thereby supporting proven acceptable ranges and robust manufacturing. In practice, however, characterization still relies largely on factorial design of experiments (DOE) approaches, which are inefficient for resolving multivariate pass/fail boundaries in higher-dimensional spaces. While Bayesian optimization has transformed process optimization, adaptive methods for multi-objective process characterization remain lacking. Here, we introduce JAREX (Joint Acceptable Region EXploration), a Bayesian active-learning acquisition function for multi-objective process characterization. JAREX formulates characterization as a joint boundary-learning problem and adaptively selects experiments to recover the joint pass region defined by simultaneous satisfaction of threshold criteria across multiple objectives. JAREX combines an optimistic joint-feasibility mask with a multi-objective extension of randomized straddle, focusing sampling on the joint edge of failure. Our benchmark study suggests that JAREX provides more accurate and sample-efficient recovery of the joint pass region than factorial DOE, space-filling designs, and greedy objective-wise strategies over the full experimental budget range. For batched experimentation, it reduces the number of iterative process characterization experiments by more than half while preserving high accuracy for the boundary-identification task. Implemented in the open-source obsidian package, JAREX provides a modular framework for adaptive, data-efficient multi-objective algorithmic process characterization, supporting sample-efficient range finding in high-dimensional spaces.