  Tuning searches are pivotal in High-Performance Computing (HPC), addressing
complex optimization challenges in computational applications. The complexity
arises not only from finely tuning parameters within routines but also
potential interdependencies among them, rendering traditional optimization
methods inefficient. Instead of scrutinizing interdependencies among parameters
and routines, practitioners often face the dilemma of conducting independent
tuning searches for each routine, thereby overlooking interdependence, or
pursuing a more resource-intensive joint search for all routines. This decision
is driven by the consideration that some interdependence analysis and
high-dimensional decomposition techniques in literature may be prohibitively
expensive in HPC tuning searches. Our methodology adapts and refines these
methods to ensure computational feasibility while maximizing performance gains
in real-world scenarios. Our methodology leverages a cost-effective
interdependence analysis to decide whether to merge several tuning searches
into a joint search or conduct orthogonal searches. Tested on synthetic
functions with varying levels of parameter interdependence, our methodology
efficiently explores the search space. In comparison to
Bayesian-optimization-based full independent or fully joint searches, our
methodology suggested an optimized breakdown of independent and merged searches
that led to final configurations up to 8% more accurate, reducing the search
time by up to 95%. When applied to GPU-offloaded Real-Time Time-Dependent
Density Functional Theory (RT-TDDFT), an application in computational materials
science that challenges modern HPC autotuners, our methodology achieved an
effective tuning search. Its adaptability and efficiency extend beyond
RT-TDDFT, making it valuable for related applications in HPC.
