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A tree search algorithm towards solving Ising formulated combinatorial optimization problems.

Yunuo Cen1, Debasis Das1, Xuanyao Fong2

  • 1Department of Electrical and Computer Engineering, National University of Singapore, Singapore, 117583, Singapore.

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Summary
This summary is machine-generated.

This study introduces a novel tree-based heuristic search algorithm for combinatorial optimization problems. It enhances simulated annealing (SA) and coherent Ising machines (CIM) to find better solutions faster for Ising Hamiltonian problems.

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Area of Science:

  • Computational physics
  • Combinatorial optimization
  • Heuristic algorithms

Background:

  • Simulated annealing (SA) is a popular heuristic for optimization but can get stuck in local minima.
  • Practical SA implementations face limitations due to annealing speed, deviating from Boltzmann distribution.
  • Ising Hamiltonian problems are common in combinatorial optimization, requiring efficient solution methods.

Purpose of the Study:

  • To propose a novel heuristic search algorithm that overcomes limitations of traditional simulated annealing.
  • To improve the efficiency and effectiveness of finding solutions for Ising Hamiltonian-based combinatorial optimization problems.
  • To integrate concepts from coherent Ising machines (CIM) for enhanced search capabilities.

Main Methods:

  • Developed a recursive depth-limited tree search algorithm expanding on SA.
  • Incorporated a "look ahead" strategy to explore future spin states.
  • Relaxed discrete spin states to continuous representation with regularization, inspired by CIM.
  • Utilized oscillator dynamics for neighborhood exploration around selected tree nodes.

Main Results:

  • The proposed algorithm demonstrated effectiveness on the MAX-CUT problem, an NP-hard problem.
  • Achieved comparable or better performance than semi-definite programming (SDP), SA, and simulated CIM.
  • Provided solutions within fewer epochs for Ising-formulated combinatorial optimization problems.

Conclusions:

  • The high-level tree search strategy effectively enhances primal heuristics like SA and CIM.
  • The algorithm offers a promising approach for solving complex combinatorial optimization problems.
  • Continuous state representation and oscillator dynamics contribute to improved search efficiency.