Global Optimization by Quantum Dynamics with Energy Dissipation

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  • Itami Teturo
    Faculty of Mechanics and Robotics, Hiroshima International University

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  • エネルギー散逸を許す実時間量子ダイナミクスによる大域最適化
  • エネルギー サンイツ オ ユルス ジツジカン リョウシ ダイナミクス ニ ヨル タイイキ サイテキ カ

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Abstract

Both reduction in computational load and setting parameters with ease are necessary in calculation of global optimization. For this we propose a new quantum mechanical method of the problem. Global optimization is achieved by a quantum particle with energy dissipation due to frictional force. Canonical quantization is applied to a system that consists of one mass point under friction proportional to its velocity. Realistic motion of a particle is abstracted from a resultant quantum system according to a causal interpretation. By simulation of the quantum particle motion under potential functions V(x) with local minima and one global minimum, it is clarified that the particle with its initial position at the local minimum at rest necessarily arrives at the global minimum. Only one particle is needed in the new algorithm. When we clarify mathematical structure of our algorithm, difficulties found in quantum annealing or conventional method for global optimization will thereby be solved in the new method.

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