表題番号：2003A-952
日付：2004/03/31
研究課題メタ制御型ボルツマンマシーンによる混合整数二次計画問題の解法
| 研究者所属（当時） | 資格 | 氏名 | |
|---|---|---|---|
| （代表者） | 大学院情報生産システム研究科 | 教授 | 和多田 淳三 |
- 研究成果概要
- In 1952, H. Markowitz proposed a method to allocate an amount of funds to plural stocks for investment. The method was named a portfolio selection problem. Based on time-series data of return rate, it theoretically decides the best investing rate to each of stocks, which minimizes the risk, i.e. the variance of the profits in keeping the least expected return rate that a decision maker desires. It is characteristic that the model can reduce the risk by means of allocating the amount of funds to many stocks. The model is excellently concise for real problems. Since then, researches have been pursued on various aspects of the model, such as realizing efficient calculation.
J. Watada et al employed Hopfield and Boltzmann machines into a model to solve the portfolio selection problem. The Hopfield machine is an interconnected neural network proposed by J. J. Hopfield in 1982. The Boltzmann machine is a neural network proposed by G. E. Hinton in 1984. The Boltzmann Machine is a model that is implemented with probabilistic behavior in order to improve a Hopfield Neural Network, which easily terminates at a local minimum of an energy function. This model deletes the units of lower layer, which are not selected in the Meta-controlling layer in its execution. Then the lower layer is restructured using the selected units. Because of this feature, a Meta-controlled Boltzmann machine converges more efficiently than a conventional Boltzmann machine. This is an efficient method for solving a portfolio selection problem by transforming its objective function into the energy function since the Hopfield and Boltzmann Machines converge at the minimum point of the energy function.
We evaluated the inner behaviors of this model so that we can apply this model to such a wider range of problems as optimization problems and quadratic mixed integer programming problems. In this paper, we evaluated the performace of the inner behaviors of this model in applying to portfolio selection problem and also compared the performance between our model and comercial package LINGO. This comparison showed that our model can solve such problems in drastic short time.