E. Valiante

Haesol Im, Fabian Böhm, Giacomo Pedretti et al.

The Boolean satisfiability (SAT) problem is a computationally challenging decision problem central to many industrial applications. For SAT problems in cryptanalysis, circuit design, and telecommunication, solutions can often be found more efficiently by representing them with a combination of exclusive OR (XOR) and conjunctive normal form (CNF) clauses. We propose a hardware accelerator architecture that natively embeds and solves such hybrid XOR--CNF problems using in-memory computing hardware. To achieve this, we introduce an algorithm and demonstrate, both experimentally and through simulations, how it can be efficiently implemented with memristor crossbar arrays. Compared to the conventional approaches that translate XOR--CNF problems to pure CNF problems, our simulations show that the accelerator improves computation speed, energy efficiency, and chip area utilization of in-memory accelerators by $\sim$10$\times$ for a set of hard cryptographic benchmarking problems. Moreover, the accelerator achieves a $\sim$10$\times$ speedup and a $\sim$1000$\times$ gain in energy efficiency over state-of-the-art SAT solvers running on CPUs.

Haesol Im, Chan-Woo Yang, Moslem Noori et al.

Research into the development of special-purpose computing architectures designed to solve quadratic unconstrained binary optimization (QUBO) problems has flourished in recent years. It has been demonstrated in the literature that such special-purpose solvers can outperform traditional complementary metal--oxide--semiconductor architectures by orders of magnitude with respect to timing metrics on synthetic problems. However, they face challenges with constrained problems such as the quadratic assignment problem (QAP), where mapping to binary formulations such as QUBO introduces overhead and limits parallelism. In-memory computing (IMC) devices, such as memristor-based analog Ising machines, offer significant speed-ups and efficiency gains over traditional CPU-based solvers, particularly for solving combinatorial optimization problems. In this work, we present a novel hardware-aware QAP optimization framework designed for IMC hardware. By co-designing the local search heuristic with the underlying hardware, we exploit the intrinsic massive parallelism that allows for computing of full neighbourhoods simultaneously to make update decisions. We ensure binary solutions remain feasible by selecting local moves that lead to neighbouring feasible solutions, leveraging feasible-space search heuristics and the underlying structure of a given problem. Our approach is compatible with both digital computers and analog hardware. We demonstrate its effectiveness in CPU implementations by comparing it with state-of-the-art heuristics for solving the QAP.

Moslem Noori, Elisabetta Valiante, Thomas Van Vaerenbergh et al.

A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the problem. However, the accuracy of the estimated performance metrics depends on the number of runs and should be studied using statistical tools. We present a statistical analysis of the common metrics, and develop guidelines for experiment design to measure the optimizer's performance using these metrics to a high level of confidence and accuracy. To this end, we first discuss the confidence interval of the metrics and how they are related to the number of runs of an experiment. We then derive a lower bound on the number of repeats in order to guarantee achieving a given accuracy in the metrics. Using this bound, we propose an algorithm to adaptively adjust the number of repeats needed to ensure the accuracy of the evaluated metric. Our simulation results demonstrate the utility of our analysis and how it allows us to conduct reliable benchmarking as well as hyperparameter tuning and prevent us from drawing premature conclusions regarding the performance of stochastic optimizers.