C.40:5.18 - Compare an operation after its allowed refinement

A stipulated development exercise has two executable changing operations, T for local tuning and G for changing a grouping. Each trial starts from comparable material with quality 10 and receives the same two-unit refinement allowance. All intermediate constructions in this initial case remain admissible. Higher final quality is preferred, and the trials’ gains use the same comparison scale.

Choosing only from immediate quality would discard G before its useful continuation. Complete the agreed trials, retain their operation and refinement conditions, and initialize the two mean gains at 2 and 6. Under :4.11’s one-quarter uniform exploration rule, the next eligible proposal uses G with probability 3/4 + (1/4)(1/2) = 7/8 and T with probability 1/8. The choice still needs the actual random draw and execution; the probabilities are not produced candidates.

Suppose another comparable completed G trial returns gain -2. Its mean becomes (6 - 2)/2 = 2, tied with T. With the stipulated tie rule favoring T, the next probabilities reverse. Retain the individual outcomes: the mean alone conceals G’s variable result and supplies no guarantee of a further gain. If the receiving requirement had already been satisfied by T at 12, the extra search might have been unnecessary.

If G instead denotes a group of two executable changes, the group choice still needs a member selection. With uniform choice inside G at the initial means, each member receives probability (7/8)(1/2) = 7/16; T receives 1/8. A completed member trial updates the group’s mean while retaining which member ran. This shares sparse experience but can hide a useful difference between members. Split the comparison when that difference can change the next choice and enough examination is affordable; renaming two changes as a group did not make their effects equal.

Now a changed construction rule makes G’s intermediate grouping inadmissible. Remove G from the eligible operations until a permitted version exists; a later score of 16 cannot waive that condition. If instead the available refinement time changes, the old final-gain comparison answers the old allowance. Obtain the affected comparison or retain its uncertainty before using it to allocate the next work. These are different returns from merely preferring the currently larger mean.