Author:
Cen Yunuo,Das Debasis,Fong Xuanyao
Abstract
AbstractSimulated annealing (SA) attracts more attention among classical heuristic algorithms because many combinatorial optimization problems can be easily recast as the ground state search problem of the Ising Hamiltonian. However, for practical implementation, the annealing process cannot be arbitrarily slow and hence, it may deviate from the expected stationary Boltzmann distribution and become trapped in a local energy minimum. To overcome this problem, this paper proposes a heuristic search algorithm by expanding search space from a Markov chain to a recursive depth limited tree based on SA, where the parent and child nodes represent the current and future spin states. At each iteration, the algorithm selects the best near-optimal solution within the feasible search space by exploring along the tree in the sense of “look ahead”. Furthermore, motivated by the coherent Ising machine (CIM), the discrete representation of spin states is relaxed to a continuous representation with a regularization term, which enables the use of the reduced dynamics of the oscillators to explore the surrounding neighborhood of the selected tree nodes. We tested our algorithm on a representative NP-hard problem (MAX-CUT) to illustrate the effectiveness of the proposed algorithm compared to semi-definite programming (SDP), SA, and simulated CIM. Our results show that with the primal heuristics SA and CIM, our high-level tree search strategy is able to provide solutions within fewer epochs for Ising formulated combinatorial optimization problems.
Funder
National Research Foundation Singapore
Agency for Science, Technology and Research
Publisher
Springer Science and Business Media LLC
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献