חשבון פעולות לאופטימיזציה באוכלוסייה: סיכון מודולרי והבטחות סופיות

תקציר מקורי באנגליתarXiv:2606.14289v3 Announce Type: replace-cross Abstract: Population-based optimizers combine update rules such as mutation, selection, and recombination. When one rule changes, it is often unclear which convergence guarantees survive or how the new combination should be assessed. We develop an operator calculus: an operator is a population-update rule, and the calculus specifies how separately checked effects can be combined. Under explicit regularity and small-step conditions, the leading changes caused by the updates add, yielding reusable building blocks for convergence analysis. The framework distinguishes finding and retaining a good solution, reducing the population's mean objective, and concentrating candidates near an optimizer, and identifies the extra approximation conditions ne