The training objective for Evo-GDPO is formalized as a PPO-style clipped surrogate objective driven by the decoupled, batch-normalized aggregated advantage $\widehat{A}_i^\Sigma$ and regularized by token-level KL divergence:

$\mathcal{L}_{\text{III}}^{\text{Evo-GDPO}}(\theta) = - \mathbb{E} \left[ \frac{1}{G} \sum_{i=1}^G \frac{1}{|\mathbf{h}_i|} \sum_{j=1}^{|\mathbf{h}_i|} \min \left( \rho_{i,j}(\theta) \widehat{A}_i^\Sigma, \text{clip}(\rho_{i,j}(\theta), 1 - \epsilon_{\text{clip}}, 1 + \epsilon_{\text{clip}}) \widehat{A}_i^\Sigma \right) \right] + \beta_{\text{KL}} \mathbb{E} [ \text{KL}(p_\theta \parallel p_{\text{ref}}) ]$

where the importance weight ratio is defined by:

$\rho_{i,j}(\theta) = \frac{p_\theta(y_{i,j} \mid y_{i,<j}, \mathbf{c}_{\tau,n})}{p_{\theta_{\text{old}}}(y_{i,j} \mid y_{i,<j}, \mathbf{c}_{\tau,n})}$

Here, $|\mathbf{h}_i|$ denotes the harness token length, $\epsilon_{\text{clip}} > 0$ is the clipping boundary, and $p_{\text{ref}}$ is the frozen Stage-II repair checkpoint. Unlike standard GRPO objectives that reward candidates solely based on relative within-group ranking, Evo-GDPO explicitly rewards candidates for overtaking historical archive incumbents and achieving greater efficiency under reward parity.