Large language models generate candidate programs for automatic heuristic design, while evolutionary search evaluates and selects them to guide further generation. Online post-training uses rewards from candidate evaluations to adapt the generator. Retained programs can also guide later generation as parents. This motivates rewards that reflect their reuse opportunities beyond immediate fitness. We propose Search-value credit (SVC), which constructs response-level rewards from actual admission to the retained set and a short-term parent-exposure proxy. Admission determines reward eligibility; the proxy weights eligible responses by reuse opportunities under existing parent-selection rules. Rewards are computed after candidate evaluation, without evaluating descendants. SVC retains the search and learning procedures of the Co-Evolution of Algorithms and Language Model (CALM) framework. Across four combinatorial optimization tasks with the same base model and response budget, SVC achieves the best mean final search performance on three tasks among six conditions. Under identical prompts and parents on traveling salesman and capacitated vehicle routing tasks, SVC-trained generators yield a higher mean proportion of responses whose programs outperform the best prompting parent than those trained with CALM's native reward. These findings support reward construction using search retention and selection information.

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