| 講演概要 | ： |
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本発表では, 非線形制御ポリシーを用いて多期間にわたる動的な資産配分を決定する最適化問題を |
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定式化し, 問題求解のための計算手法を提案する. |
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ここで, 制御ポリシーとは投資対象資産の過去の収益の関数である. |
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カーネル法を利用することで, 非線形関数の中から最適な制御ポリシーを選択する問題は |
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凸2次最適化問題として定式化される. |
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さらに, L1-ノルムを用いた正則化を利用することで問題を線形最適化問題に帰着する. |
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計算実験では, 投資対象資産の収益率のシナリオを1期間自己回帰モデルによって生成し, |
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先行研究の手法と比較して我々の提案する投資戦略は良好な運用成績を得られることを示す.
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| 講演概要 | ： |
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In this paper, we deal with the node capacitated in-tree packing problem. The input consists of |
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a directed graph, a root node, a node capacity function and edge consumption functions for heads and tails. |
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The problem is to find a subset of rooted spanning in-trees and their packing numbers, where the packing |
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number of an in-tree is the number of times it is packed, so as to maximize the sum of packing numbers |
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under the constraint that the total consumption of the packed in-trees at each node does not exceed the |
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capacity of the node. This problem is known to be NP-hard. |
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Previously, we proposed a two-phase heuristic algorithm for this problem. The algorithm generates |
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promising candidate in-trees to be packed in the first phase and computes the packing number of each in-tree |
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in the second phase. In this paper, we improve the first phase algorithm by using Lagrangian relaxation |
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instead of LP (linear programming) relaxation. |
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We conducted computational experiments on graphs used in related papers and on randomly generated |
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instances. The results indicate that our new algorithm generates in-trees faster than our previous algorithm |
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and obtains better solutions than existing algorithms without generating many in-trees.
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