When High Reliability Meets Low Cost: Exploring Approximate-TMR via Efficient Multiobjective Optimization Frameworks

In fields where fault tolerance is critical, such as aerospace and autonomous driving, the Triple Modular Redundancy (TMR) is widely utilized due to its high reliability, yet it comes with significant overhead. To mitigate this issue, Approximate TMR (ATMR) has emerged as a promising solution. However, few studies have addressed the multi-objective optimization problem between hardware saving and fault tolerance caused by approximation. This paper presents two pioneering multi-objective optimization frameworks tailored for fault-tolerant circuit design that leverage approximate redundancy to achieve this delicate balance. The first framework, Dynamic Adjustment Multi-Objective Optimization (DA-MOO), proposes a Dynamic Adjustment Optimized NSGA-II (DAON) algorithm utilizing parity expansion and dynamic probability adjustment to generate ATMR solutions. This method surpasses traditional TMR by halving area and power overhead while still achieving over 70% of fault coverage. Considering the computational intensity of DA-MOO, we further propose the Pre-Encoding Multi-Objective Bayesian Optimization (PE-MOBO) framework, achieving a 198x improvement in computational time over traditional methods. In summary, DA-MOO is well-suited for scenarios requiring a premium on reliability alongside cost-efficiency, such as in the commercial aerospace industry, while PE-MOBO is particularly advantageous for applications demanding rapid design cycles, like consumer electronics.