Correlation between penalty parameter and accuracy in penalty-based QKP solving via simulated annealing

Determine whether a correlation exists between the penalty parameter P and the solution accuracy when applying the classical penalty method to Quadratic Knapsack Problem instances solved with simulated annealing on Ising machines, and, if present, specify the nature of this dependence across instances and penalty magnitudes.

Background

In the benchmark comparing the self-adaptive Ising machine (SAIM) to the classical penalty method for Quadratic Knapsack Problems (QKP), the authors tuned the penalty parameter P by progressively increasing it from an initial value to improve feasibility. They observed that larger P generally increases feasibility, consistent with prior works.

However, despite this tuning effort across multiple instances, the authors report that they did not observe a clear correlation between the chosen penalty magnitude and the achieved solution accuracy under simulated annealing, highlighting an unresolved relationship between penalty scaling and accuracy outcomes for QKP with Ising-based solvers.