TITLE:
Stochastic Process Optimization Technique
AUTHORS:
Hiroaki Yoshida, Katsuhito Yamaguchi, Yoshio Ishikawa
KEYWORDS:
Optimization, Stochastic Process, Path Integral, Expected Value, Quantum Mechanics
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.19,
November
10,
2014
ABSTRACT: The conventional optimization methods were generally based on a deterministic approach, since their purpose is to find out an accurate solution. However, when the solution space is extremely narrowed as a result of setting many inequality constraints, an ingenious scheme based on experience may be needed. Similarly, parameters must be adjusted with solution search algorithms when nonlinearity of the problem is strong, because the risk of falling into local solution is high. Thus, we here propose a new method in which the optimization problem is replaced with stochastic process based on path integral techniques used in quantum mechanics and an approximate value of optimal solution is calculated as an expected value instead of accurate value. It was checked through some optimization problems that this method using stochastic process is effective. We call this new optimization method “stochastic process optimization technique (SPOT)”. It is expected that this method will enable efficient optimization by avoiding the above difficulties. In this report, a new optimization method based on a stochastic process is formulated, and several calculation examples are shown to prove its effectiveness as a method to obtain approximate solution for optimization problems.