Quasi-Monte Carlo Simulation for High-dimensional Systems with Complex Structure

2021 Fiscal Year Final Research Report

• Project/Area Number: 18K04602
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 25010:Social systems engineering-related
• Research Institution: National Graduate Institute for Policy Studies
• Principal Investigator: Morohosi Hozumi 政策研究大学院大学, 政策研究科, 教授 (10272387)
• Project Period (FY): 2018-04-01 – 2022-03-31
• Keywords: シミュレーション分析 / 準乱数 / モンテカルロ法

Outline of Final Research Achievements

This research focused on generating non-uniform random numbers for the simulation analysis of high-dimensional complex systems. Our generation algorithms make use of copula, which is a unified methodology to describe multi-variate probability distributions. The main topics of the study are to develop and implement Monte Carlo and quasi-Monte Carlo algorithms as well as their performance tests of them. The new algorithms show good performance compared to the existing ones. Furthermore, some practical problems are investigated for the application. They are robust optimization of facility location problem and the measure of equity of apportionment problem. Simulation methods are useful for those problems to find new findings and implications.

Free Research Field

社会システム工学

Academic Significance and Societal Importance of the Research Achievements

高次元の非一様な乱数や準乱数の生成は，複雑な確率システム分析のためには必要不可欠な技術であるが．本研究では，一般的な多変量確率分布を統一的に扱う手法である接合関数を取り上げて，パラメトリックとノンパラメトリックの双方の立場から，アルゴリズムを考案した．特にノンパラメトリックな場合は，従来ほとんど研究が行われておらず，効率的なアルゴリズムを考案し性能評価を行ったことは，学術的な意義を持つと考える．またいくつかの応用例においては，シミュレーションを駆使した手法を活用すること自体新しい試みであり，今後も発展が望まれる内容を示すことができた．