  The compression of deep learning models is of fundamental importance in
deploying such models to edge devices. The selection of compression parameters
can be automated to meet changes in the hardware platform and application using
optimization algorithms. This article introduces a Multi-Objective
Hardware-Aware Quantization (MOHAQ) method, which considers hardware efficiency
and inference error as objectives for mixed-precision quantization. The
proposed method feasibly evaluates candidate solutions in a large search space
by relying on two steps. First, post-training quantization is applied for fast
solution evaluation (inference-only search). Second, we propose the
"beacon-based search" to retrain selected solutions only and use them as
beacons to know the effect of retraining on other solutions. We use a speech
recognition model based on Simple Recurrent Unit (SRU) using the TIMIT dataset
and apply our method to run on SiLago and Bitfusion platforms. We provide
experimental evaluations showing that SRU can be compressed up to 8x by
post-training quantization without any significant error increase. On SiLago,
we found solutions that achieve 97\% and 86\% of the maximum possible speedup
and energy saving, with a minor increase in error. On Bitfusion, beacon-based
search reduced the error gain of inference-only search by up to 4.9 percentage
points.
