Abstract: The combinatorial optimization problem (COP), which aims to find the optimal solution in discrete space, is fundamental in various fields. Unfortunately, many COPs are NP-complete, and require much more time to solve as the problem scale increases. Troubled by this, researchers may prefer fast methods even if they are not exact, so approximation algorithms, heuristic algorithms, and machine learning have been proposed. Some works proposed chaotic simulated annealing (CSA) based on the Hopfield neural network and did a good job. However, CSA is not something that current general-purpose processors can handle easily, and there is no special hardware for it. To efficiently perform CSA, we propose a software and hardware co-design. In software, we quantize the weight and output using appropriate bit widths, and then modify the calculations that are not suitable for hardware implementation. In hardware, we design a specialized processing-in-memory hardware architecture named COPPER based on the memristor. COPPER is capable of efficiently running the modified quantized CSA algorithm and supporting the pipeline further acceleration. The results show that COPPER can perform CSA remarkably well in both speed and energy.

Key words: Combinatorial optimization; Chaotic simulated annealing; Processing-in-memory

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