Leveraging Special-Purpose Hardware for Local Search Heuristics

Xiaoyuan Liu, Hayato Ushijima-Mwesigwa, Avradip Mandal, Sarvagya Upadhyay, Ilya Safro, Arnab Roy

As we approach the physical limits predicted by Moore's law, a variety of specialized hardware is emerging to tackle specialized tasks in different domains. Within combinatorial optimization, adiabatic quantum computers, CMOS annealers, and optical parametric oscillators are few of the emerging specialized hardware technology aimed at solving optimization problems. In terms of mathematical framework, the Ising optimization model unifies all of these emerging special-purpose hardware. In other words, they are all designed to solve optimization problems expressed in the Ising model or equivalently as a quadratic unconstrained binary optimization model. Due to variety of constraints specific to each type of hardware, they usually suffer from a major challenge: the number of variables that the hardware can manage to solve is very limited. Given that large-scale practical problems, including problems in operations research, combinatorial scientific computing, data science and network science require significantly more variables to model than these devices provide, we are likely to witness that cloud-based deployments of these devices will be available for parallel and shared access. Thus hybrid techniques in combination with both hardware and software must be developed to utilize these technologies. Local search meta-heuristics is one of the approaches to tackle large scale problems. However, a general optimization step within local search is not traditionally formulated in the Ising form. In this work, we propose a new meta-heuristic to model local search in the Ising form for the special-purpose hardware devices. As such, we demonstrate that our method takes the limitations of the Ising model and current hardware into account, utilizes a given hardware more efficiently compared to previous approaches, while also producing high quality solutions compared to other well-known meta-heuristics.

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