A constrained multi-objective coevolutionary algorithm with adaptive operator selection for efficient test scheduling in interposer-based 2.5D ICs

Interposer-based 2.5-dimensional integrated circuits (2.5D ICs) have emerged as a promising solution to address wire delay and power consumption challenges in modern semiconductor design. However, the increasing complexity and density of 2.5D ICs introduces critical test scheduling challenges, where existing methods fail to effectively optimize hardware cost and test time while satisfying strict power and duration constraints. To overcome these limitations, this paper models the test scheduling problem in 2.5D ICs as a constrained multi-objective optimization problem (CMOP) and proposes a constrained multi-objective coevolutionary algorithm (termed AOSCEA) with adaptive operator selection. The algorithm introduces a two-chromosome-based encoding method paired with a matching-level-based decoding strategy to effectively map the discrete scheduling problem to continuous evolutionary algorithm frameworks, enabling efficient exploration of the search space. A coevolutionary mechanism is incorporated into the algorithm with two populations: a main population that solves the CMOP and an auxiliary population that ignores constraints to enhance exploration. Additionally, targeting to enhance the versatility of the algorithm across different test scheduling problems, AOSCEA employs two deep Q-networks to adaptively select genetic operators and constraint handling techniques for the main population during the optimization process. Extensive experiments on various test scheduling instances in 2.5D ICs with different scales demonstrate that AOSCEA outperforms several state-of-the-art algorithms in terms of solution quality, convergence speed, and robustness.