Papers

K.Hotta and J.Kawahara
``Evaluation of Political Redistricting in Japan by Optimization and Enumeration''
(2023). [Eprint Repository:Optimization Online]
堀田敬介
``国政選挙の議席配分と最適区割2020'' [japanese]
(Apportionment and optimal districting for 2020 national elections)
統計数理研究所 共同研究リポート 461「最適化：モデリングとアルゴリズム 34」 (2023) ??-??. [PDF]
堀田敬介
``衆議院小選挙区の都道府県内較差'' [japanese]
(Vote disparity among districts in each prefecture)
経営論集 Vol.7, No.3 (2021) 1-15. [PDF]
堀田敬介, 根本俊男, 和田淳一郎
``参議院最適合区について'' [japanese]
(Optimal Combined Districts in the House of Councilors)
選挙研究; Japanese Journal of Electoral Studies , 35-2 (2019) 86-102.
堀田敬介
``選挙区画定問題の解法'' [japanese]
(How to solve the electoral districting problem)
経営論集 Vol.5, No.6 (2019) 1-24. [PDF]
堀田敬介
``指定都市議会議員選挙における投票価値の平等'' [japanese]
(Equality of vote value of the elections for city assembly members in the ordinance-designated cities)
経営論集 Vol.5, No.3 (2019) 1-20. [PDF]
堀田敬介
``数理最適化を利用した大学生の外食利用と栄養バランスに関する論考'' [japanese]
(A research on out-of-home dining and nutrient intake balance of university students using mathematical optimization)
湘南フォーラム Vol.22 (2018) 99-116. [PDF]
(Shonan Forum: Journal of the Shonan Research Institute)
堀田敬介
``複数人選出選挙制度の較差是正のための最適化と限界値分析'' [japanese]
(Optimization for the multi-member constituency system)
Transactions of the Operations Research Society of Japan, 60 (2017) 74-99. [PDF]
J. Kawahara, T. Horiyama, K. Hotta and S. Minato
``Generating All Patterns of Graph Partitions within a Disparity Bound''
In Proceedings of the 11th International Conference and Workshops on Algorithms and Computation (WALCOM 2017) Vol. 10167 (2017) 119-131. [PDF]
堀田敬介
``衆議院議員小選挙区制最適区割 2016'' [japanese]
(Optimal division for the single-member constituency system of the House of Representatives 2016)
経営論集 Vol.3, No.1 (2017) 1-19[,付録22-114]. [PDF]
(Journal of Public and Private Management)
K. Hotta
``Optimal division of the electoral districts for the single-member constituency system''
technical paper (2016). [PDF]
小河智哉, 堀田敬介
``文教大学湘南校舎における科目時間割配置の支援'' [japanese]
(Providing support in solving course timetabling problem at Bunkyo university)
湘南フォーラム Vol.20 (2016) 21-46. [PDF]
(Shonan Forum: Journal of the Shonan Research Institute)
堀田敬介
``最適化技術のクラス編成問題への適用'' [japanese]
(The use of an optimization technique to solve student sectioning problems)
経営論集 Vol.2, No.1 (2016) 1-18. [PDF] [BURS Repository]
(Journal of Public and Private Management)
堀田敬介
``区割画定作業支援のための選挙区割の特徴化'' [japanese]
(Characterization of constituency for decision support)
Transactions of the Operations Research Society of Japan , 59 (2016) 60-85. [PDF]
堀田敬介
``合区および総定数変化に対する議席配分最適化'' [japanese]
(Optimization for the apportionment problem with straddling some prefectures and changing the number of the members)
選挙研究; Japanese Journal of Electoral Studies , 31-2 (2015) 123-141.
堀田敬介
``合県モデルと区割人口頑健性による選挙制度の評価と提言'' [japanese]
(...)
RIMS 研究集会報告集 No.1879 (2014) 79-90. [PDF]
堀田敬介
``予備登録制度の実態調査と制度改善に向けて'' [japanese]
(Actual condition survey of the preliminary registry system and an idea of the improvement)
湘南フォーラム Vol.17 (2013) 153-172. [PDF]
(Shonan Forum: Journal of the Shonan Research Institute)
堀田敬介
``選挙区割の最適化と列挙索引化'' [japanese]
(...)
オペレーションズ・リサーチ 57(11) (2012) 623-628. [PDF]
堀田敬介
``衆議院議員小選挙区制最適区割2011'' [japanese]
(An optimal districts for the single-seat constituency system of the House of Representatives 2011)
情報研究 47 (2012) 43-83. [PDF]
堀田敬介
``最適化を利用したピアノの実用的な指使いに関する考察'' [japanese]
(...)
統計数理研究所 共同研究リポート 267「最適化：モデリングとアルゴリズム 24」 (2011) 120-127.
堀田敬介
``成績を考慮したゼミ配属法の比較と提案'' [japanese]
(A quantitive comparison of the methods considering academic results for class assignment problems)
情報研究 44 (2011) 59-73. [PDF]
堀田敬介
``市区郡分割を考慮した選挙区画定問題の最適化モデル'' [japanese]
(A mathematical model with adjusting the population of the divided city for the redistricting problem)
情報研究 43 (2010) 41-60. [PDF]
根本俊男，堀田敬介
``平成大合併を経た衆議院小選挙区制区割環境の変化と一票の重みの格差'' [japanese]
(The effect of the Heisei-era mergers on the limits of the reduction in population disparity between single-member election districts in Japan)
Transactions of the Operations Research Society of Japan , 53 (2010) 90-113. [PDF]
根本俊男，堀田敬介
``一票の重みの格差から観た小選挙区数'' [japanese]
(The effect of the number of single-member election districts on the reduction in population disparity in Japan)
選挙研究; Japanese Journal of Electoral Studies 21 (2006) 169-181.
堀田敬介
``学生満足度の観点によるゼミ配属法の定量的比較'' [japanese]
(A quantitive comparison among seminar assignment methods with a view to enhancing student satisfaction)
情報研究 35 (2006) 367-378. [PDF]
K. Hotta
``A complexity analysis of a smoothing method for P*(k)-LCP''
情報研究 33 (2005) 403-411. [PDF]
根本俊男，堀田敬介
``公平な小選挙区制のための数理モデル'' [japanese]
(...)
システム/制御/情報 49(3) (2005) 78-83. [info]
根本俊男，堀田敬介
``衆議院小選挙区制における一票の重みの格差の限界とその考察'' [japanese]
(On the Limits of the Reduction in Population Disparity Between Single-Member Election Districts in Japan)
選挙研究; Japanese Journal of Electoral Studies 20 (2005) 136-147.
根本俊男，堀田敬介
``区割画定問題のモデル化と最適区割の導出'' [japanese]
(...)
オペレーションズ・リサーチ 48(4) (2003) 50-56. [PDF]
根本俊男，堀田敬介
``選挙区最適区割問題のモデリングと厳密解導出'' [japanese]
(Political Redistricting in Japan)
日本OR学会 第15回RAMPシンポジウム論文集 (2003) 104-117. [PDF]
K. Hotta and A. Yoshise
``A Complexity Bound of a Predictor-Corrector Smoothing Method Using CHKS-functions for Monotone LCP,''
Computational Optimization and Applications 22 (2002) 351-367.
[cf.->DPS.873 (2000)]
K. Hotta and A. Yoshise
``A Complexity Analysis of a Smoothing Method Using CHKS-Function for Monotone Linear Complementarity Problems and Its Numerical Experiences,''
統計数理研究所 共同研究リポート 125「最適化：モデリングとアルゴリズム 13」 (2000) 139-151.
K. Hotta M. Inaba and A. Yoshise
``A Complexity Analysis of a Smoothing Method Using CHKS-functions for Monotone Linear Complementarity Problems,''
Computational Optimization and Applications 17 (2000) 183-201.
[cf.->DPS.807 (1998)]
K. Hotta and A. Yoshise
``Global convergence of a class of non-interior point algorithms using Chen-Harker-Kanzow-Smale functions for nonlinear complementarity problems,''
Mathematical Programming 86 (1999) 105-133.
K. Hotta and A. Yoshise
``On the Complexity of Non-Interior-Point Methods for Monotone Linear Complementarity Problems,''
統計数理研究所 共同研究リポート 113「最適化：モデリングとアルゴリズム 12」 (1998) 209-223.
K. Hotta and A. Yoshise
``A Class of Non-Interior Continuation Methods and Its Numerical Experiences,''
統計数理研究所 共同研究リポート 104「最適化：モデリングとアルゴリズム 11」 (1997) 265-279.
堀田敬介，吉瀬章子
``線形相補性問題に対する内点法のスケーリングに関する一考察,'' [japanese]
統計数理研究所 共同研究レポート 84「最適化：モデリングとアルゴリズム 8」 (1996) 109-118.

Presentations

市野達也,川原純,湊真一,堀田敬介, ``MDD を用いた変更の少ない選挙区割の列挙''
Date: 日本OR学会 春季研究発表会, March 8, 2023
Abstract: [PDF](日本OR学会：春季研究発表会アブストラクト集)

市野達也,川原純,湊真一,堀田敬介, ``多分決定グラフを用いた変更の少ない選挙区割の列挙''
Date: 2022年度「組合せ遷移」学生シンポジウム, Feburuary 20, 2023
Place: 東北大学
開催概要, プログラム

堀田敬介,川原純, ``最適化と解列挙による2022選挙区勧告案の検証評価''
Date: 日本OR学会 秋季研究発表会, September 14, 2022
Place: 朱鷺メッセ 新潟コンベンションセンター, 新潟
Abstract: [PDF](日本OR学会：秋季研究発表会アブストラクト集), pptx: [PDF]

堀田敬介, ``国政選挙の議席配分と最適区割2020''
Date: 研究集会「最適化：モデリングとアルゴリズム」, March 23, 2022
Place: 政策研究大学院大学, 東京
pptx: [PDF]

堀田敬介, ``都道府県議会の選挙区画定''
Date: 日本OR学会 秋季研究発表会, September 12, 2019
Place: 東広島芸術文化ホールくらら, 広島
Abstract: [PDF](日本OR学会：秋季研究発表会アブストラクト集), pptx: [PDF]

堀田敬介, ``都道府県議会の選挙区割''
Date: 日本選挙学会 研究会, July 14, 2019
Place: 東北大学 川内キャンパス, 宮城
Abstract: [PDF]

堀田敬介, ``複数議員選出選挙制度の最適化モデルによる都道府県議会の格差評価''
Date: 評価のOR, July 28, 2018
Place: 筑波大学 東京キャンパス, 東京
Abstract:

1つの選挙区から複数議員を選出する選挙区制度（中・大選挙区制）について，法律上の規則を守り選挙区を作成することを考える．このモデルは一人選出選挙区制度（小選挙区制）のモデルより自然に導かれるが，最適解導出には前処理で用いる第2妥当選挙区（根本・堀田2003）列挙が鍵となる．このモデルを用い，47ある都道府県議会のそれぞれについて，目的関数を一票の最大較差最小化として最適区割を導出し，現行区割と比較分析し，評価をする． 　国政選挙の較差が改善へと向かう中で（衆議院小選挙区制の最大較差2倍未満，都道府県毎の最大化較差も全て2倍未満），都道府県議会の最大較差は，過半数の都道府県で2倍を超える．そのうち2.5倍以上3倍未満が5県，3倍以上4倍未満が5道県，5倍以上が1都である．一方，1.5倍未満を2県が達成している．果たして地方議会の最大較差が大きくなってしまうのは制度上仕方のないことなのか，その妥当性と共に，最適区割による限界値分析で明らかにする．

K. Hotta, T. Nemoto and J. Wada, ``Optimal division for the multi-member constituency system''
Date: ISMP 2018(23rd), July 2, 2018
Place: University of Bordeaux, Bordeaux, France
Abstract:

We propose the optimization technique to solve the multi-member constituency system with an appropriate objective function. This is an extended model of the single-seat constituency system. We can solve this model using some idea of the preprocessing and MIP solver. Let us introduce two case studies to use this technique. One is the electoral redistricting problems of the Prefectural assembly in Japan. There are 47 prefectures in Japan. Each prefecture has a parliament. In many prefectures, the maximum disparity of one vote is more than three times. The purpose of the problem is to show the minimum disparity ratio between values of votes in different constituencies of each prefecture. The other is the apportionment problem of the electoral system in the House of Councillors in Japan. In that system, 73 members are apportioned to 47 constituencies in proportion to the population. However, since the ratio of the maximum population to the minimum population is more than 20 times, the disparity was nearly 5 times. Therefore, several constituencies are grouped together recently. We clarify the relationship between that and the disparity. We show several results with some objective function using Social Welfare Function.

堀田敬介, 根本俊男, 和田淳一郎 ``参議院選挙合区に対する数理的考察''
Date: ワークショップ　離散構造とアルゴリズム, January 26, 2018
Place: 京都大学, 京都
Abstract: [PDF]

堀田敬介, 根本俊男, 和田淳一郎 ``参議院最適合区について''
Date: 公共選択学会 大会, November 18, 2017
Place: 関西学院大学, 兵庫
Abstract: [PDF]

J. Kawahara, T. Horiyama, K. Hotta and S. Minato, ``Enumeration algorithms for political districting''
Date: IFCS 2017(15th), August 8, 2017
Place: Tokai University, Tokyo, Japan
Abstract:

The most important thing of the political districting problem in Japan is to reduce the vote-value disparity. For given m seats and the graph, the problem is to make the m-connected components. The objective is to reduce the ratio between the maximum population and the minimum among components. The optimization technique is useful to achieve the purpose. In 465 members of the House of Representatives, 289 members are elected by the single-seat constituency system. At first, 289 members should be apportioned to 47 prefectures (Japan has 47 prefectures) in proportion to the population by optimization to reduce the disparity, and then the optimal districts can be obtained in each prefecture. All problems can be solved exactly, not approximately, by optimization. The optimal solutions give us the limit of the disparity between values of votes in different constituencies. All problems can also be enumerated quickly by frontier-based search. Thus, we can evaluate each solution by several other features. For example, deviation among constituencies, the robustness for the population movement in the future, similarity between cities which belong to one electoral district, difference from the current electoral district, and so on. They can be used to provide the judgment materials to decide the political redistricting. In this research, we produce the results and the evaluation on the latest data. It is a great support for the decision-making.

K. Hotta, J. Kawahara, T. Horiyama and S. Minato, ``Enumeration and Evaluation for the single-seat constituency system''
Date: IFORS 2017(21th), July 17, 2017
Place: Quebec City Convention Centre, Quebec City, Quebec, Canada
Abstract: [PDF]

堀田敬介, ``都道府県議会の格差是正　〜複数議員選出選挙区に対する最適化〜''
Date: 日本選挙学会 研究会, May 21, 2017
Place: 香川大学, 香川
Abstract: [PDF]

J.Kawahara, T.Horiyama, K.Hotta, S.Minato, ``Generating All Patterns of Graph Partitions within a Disparity Bound''
Date: WALCOM 2017(11th), March 29, 2017
Place: Hsinchu, Taiwan
Abstract: [PDF]

堀田敬介, ``2016年最適区割と一票の較差''
Date: 日本OR学会 2016年度 秋季研究発表会, September 16, 2016
Place: 山形大学, 山形
Abstract: [PDF] <-日本OR学会：秋季研究発表会アブストラクト集

川原 純, 堀山 貴史, 堀田敬介, 湊 真一, ``一票の格差が小さな選挙区割の列挙''
Date: 統計学会, 2016年 統計関連学会連合大会 September 5, 2016
Place: 金沢大学, 石川
Abstract: [PDF]

K.Hotta, ``Optimal division of the electoral districts for the single-member constituency system''
Date: OR 2016, September 1, 2016
Place: Helmut-Schmidt-Universitaet/Univ. der Bundeswehr Hamburg, Hamburg, Germany
Abstract:

Japanese electoral system is now flawed. The vote-value disparity between constituencies for the Diet is large. The Supreme Court of Japan decided that the disparity in the value of votes for the House of Representatives was ``in a state of unconstitutionality’’. Because of this, the Diet also has tried to rectify the zoning of electoral districts to narrow the vote-value gap. Up to now the Diet has reduced the number of seats. The number of members for the single-seat constituency for the House of Representatives is 289 in 2016. It has been 295 from 2013 to 2016, and 300 from 1994 to 2013.
　The planning process for the redistricting of the single-seat constituency in Japan is as follows. First, all seats are apportioned to 47 prefectures in proportion to the population. Then, each electoral district is decided in each prefecture. This research shows the optimal division of the electoral districts, and the limit of the disparity ratio by using 0-1 IP model for the apportionment problem and the 47 redistricting problems, respectively. The population of the 2015 Census is used. The current cities are used as a component comprising electoral district. The optimization model is based on Nemoto&Hotta(2003). The limit of the disparity ratio is 1.653 for the apportionment problem, and 1.962 for the districting problems.

堀田敬介, ``日本の国政選挙制度と一票の較差''
Date: 経営学セミナー, June 29, 2016
Place: 文教大学, 神奈川
Abstract: [PDF]

川原 純, 堀田敬介, 堀山 貴史, 湊 真一, ``種々の評価尺度を用いた選挙区割の比較''
Date: 情報系 WINTER FESTA 〜基礎から変える情報分野〜, Dec 22-23, 2015
Place: 一橋大学, 東京
PPT: HP[PDF]

川原 純, 堀田敬介, 堀山 貴史, 湊 真一, ``$m$連結成分分割の高速列挙法と区割の比較''
Date: 日本OR学会 秋季研究発表会, Sep 10-11, 2015
Place: 九州工業大学, 福岡
PPT: [PDF]

川原 純, 堀山 貴史, 堀田敬介, 湊 真一, ``連結成分重み比順に連結成分分割を列挙する手法''
Date: ERATO湊離散構造処理系プロジェクト・ワークショップ, Jun 11, 2015
Place: 北海道大学, 札幌
PPT: [PDF]

堀田敬介, 川原 純, 堀山 貴史, 湊 真一, ``フロンティア法による連結成分列挙と選挙制度への応用''
Date: 日本選挙学会 研究会, May 17, 2015
Place: 市民会館崇城大学ホール, 熊本
PPT: [PDF]

堀田敬介, ``選挙区割画定支援のための特徴化''
Date: 都市のOR, Aug 22, 2014
Place: 筑波大学, 茨城
PPT: [PDF]

K.Hotta, ``A study of the enumeration of the electoral districts''
Date: IFORS 2014(20th), July 14, 2014
Place: Barcelona International Convention Center, Barcelona, Spain
Abstract:

堀田敬介, ``フロンティア法による 区割の高速列挙と索引化''
Date: 日本選挙学会 研究会, May 18, 2014
Place: 早稲田大学, 東京
PPT: [PDF]

K.Hotta, ``A study of the robustness of the electoral district for the population movement''
Date: Informs Annual Meeting 2013, October 9, 2013
Place: Minneapolis Convention Center & Hilton Mineapolis, Minneapolis, Minnesota, USA
Abstract:

The electoral redistricting problem can be solved by 0-1 IP model and some idea. The optimal district shows the limit of the disparity between values of votes in different constituencies. The gap has been expanding year after year because of the population movement. By the optimization and the enumeration for the problem under the current population and the projected population, the robust district is obtained for the decision support.

堀田敬介, ``合県モデルと区割人口頑健性による選挙制度の評価と提言''
Date: RIMS研究集会｢最適化の基礎理論と応用」, August 29, 2013
Place: 京都大学, 京都
PPT: [PDF]

K.Hotta, ``The Evaluation of the Political Redistricting and the Robustness of the Electoral District for the Population Movement''
Date: Euro/Informs MMXIII, July 1, 2013
Place: SAPIENZA Universita di Roma, Rome, Italy
Abstract:

In Japan, 300 seats of the House of Representatives are elected by the single-seat constituency system. Each electoral district is made by the apportionment to the 47 prefectures and the redistricting in each prefecture. The gap in the value of individual votes is more than 2. The situation was considered to be against a constitutional purpose by the Supreme Court in 2012. In this research, the effect of the relaxation of some constraints to improve the disparity is evaluated. The robustness of the district according to the population movement is also studied.

堀田敬介, ``区割画定における合県の評価と人口頑健性について''
Date: 日本選挙学会 研究会, May 19, 2013
Place: 京都大学, 京都
Abstract: [PDF]
PPT: [PDF]

堀田敬介, ``一票の格差を縮小する選挙制度改革と画定作業支援 ―最適化・列挙の観点から―''
Date: 第11回 産学交流テクニカルフォーラム, Dec.7, 2012
Place: 藤沢産業センター6F・7F, 神奈川
Abstract:

「一票の格差」という言葉をニュース等で耳にしたことはあっても，それを「実感」として知らない人は多く，国政選挙がどのように実施されているかを知る日本人も少ない．衆議院小選挙区がどのように作られており，どんな問題なのか，本質はどこかを周知し，選挙制度改革への提言をする

：
K.Hotta, ``Enumeration and Characterization of the Electoral Districting for the decision support''
Date: ISMP 2012(21th), August 21, 2012
Place: TU Berlin, Berlin, Germany
Abstract:

In Japan, 300 members of the House of Representatives, the Lower House, are elected by the single-seat constituency system. Each electoral district is made by the apportionment to the 47 prefectures and the redistricting in each prefecture. The apportionment gives the lower bound of the gap in the value of individual votes. Because of the density of population in an urban area, the lower bound of the ratio is close to 2 times. As a result, the gap is more than 2 by the redistricting. In Japan, the state of the same condition has been continuing for over ten years. By optimizing both the apportionment problem and the redistricting problems respectively, the limit of the disparity is 1.939 for the population in 2010 and the provinces in 2011. The 0-1 IP model to optimize the redistricting was studied by Nemoto and Hotta in 2003. The optimal district gives the limit of the disparity, but it is not always practical. So, it is better to enumerate some practical district, to point out the similarity to the current district, and to characterize the district candidates. This research provides them for the decision support.

K.Hotta, ``A Study on Quantitative Evaluation of the Model for the Piano Fingering''
Date: Euro XXV, July 10, 2012
Place: Conference Center of Radisson Blu Hotel Lietuva, Vilnius, Lithuania
Abstract:

The fingering problem is to decide the natural fingering for the music score. In the previous research, I studied the fingering of the musical passage with single-note, 3rd or 6th-chord and the chord for both right and left hand respectively, by optimizing them as IP. The passage with single-note is the most difficult because of the flexibility. Then, unnatural fingering was occurred in several passages. In order to improve the model and the cost function, I study the effects of them by measuring the existing qualitative results of the score quantitatively, and seek the better fingering.

堀田敬介, ``なぜ一票の格差はなくならないのか？ ―最適化を用いた国政選挙制度への提言―''
Date: 電子情報通信学会, Mar.20, 2012
Place: 岡山大学, 岡山
Abstract:

PPT: [PDF]
堀田敬介, ``一票の格差の観点からの選挙区割と最適化''
Date: ERATOセミナー, Dec.19, 2011
Place: 北海道大学, 札幌
Abstract:

　現在，衆議院議員は小選挙区制（300人）と比例代表制（180人）で選出されており，衆議院の小選挙区制における 「一票の格差」 は2009年選挙時点で2.31倍である．衆議院小選挙区における 「一票の格差」 とは，300小選挙区の内，最大人口を有する選挙区の人口を最小人口を有する選挙区の人口で除した値のことである．これが2倍を超えるという状態が，日本国憲法第14条 「法の下の平等」 に反するとして選挙の度に訴訟がおこされている．
　　衆議院が小選挙区制を導入したのは1994年であり，1996年10月選挙（2.31倍），2000年5月選挙（2.47倍），2005年9月選挙（2.17倍），2009年8月選挙（2.31倍）の各衆議院選挙において一票の格差の訴訟が起こされた．最高裁判決は1996年，2000年，2005年については 「合憲」 としたが，2009年については小選挙区制になって初めて 「違憲状態」 の判決を出した（ただし，選挙無効請求は棄却）．
　　衆議院小選挙区制の 「一票の格差」 については，その限界がどこにあるのかをルールにそって問題をモデル化し，最適化を利用して導出した根本・堀田による一連の定量分析研究がある．これにより，都道府県毎の現行区割による格差と最適区割による限界格差との差，および全国格差の限界値が初めて明らかとなった．さらに，定数配分・区割画定の方策を変更した場合に格差に与える影響など，様々な状況における結果を示した．
　　ここでは，以上の結果や最新データによる結果を踏まえながら，現行制度の改善すべき点，どのような制度設計が格差を下げるうえで望ましいのか，数理計画手法や最適化がこの問題に対してどのように有効であるのか，などについて述べる．

PPT: [PDF]
K.Hotta, ``A mathematical approach for the piano fingering''
Date: OR 2011, August 31-September 2, 2011
Place: ETH, Zurich, Switzerland
Abstract:

It is important to consider the fingering for playing the piano naturally. The fingering problem for the piano score is to specify the natural and reasonable fingering automatically. There are some previous works; for example, the fingering for a score with at most 10 notes by solving the Dynamic Programming, the fingering for a score with a few notes by the Genetic Algorithm, and the fingering based on the Hidden Markov model. All of them are applied to the right-hand single passage. The model in this research is the 0-1 Integer Programming based on several fingering rules. The IP models are for the right and left hand single passage, the 3rd and 6th sequence, and the chord sequence, respectively. Considering the fingering, there are several rules to be mentioned in common. However, in fact, each different types of note sequence should be treated on the basis of different fingering rules. That required the several types of IP-model. There is no best solution for every pianist. So, in the model, some costs are designed to be capable of reflecting the different personalities. In this research, it is reported that what kind of rule is better or not for each type of sequence. It is not difficult to get the optimal solution to solve the problem based on several settings, but it is difficult to evaluate the solution. A way to do is to show each value of cost of the solution, respectively.

K.Hotta, ``A study of an automatic fingering for the piano score.''
Date: IFORS 2011(19th), July 10-15, 2011
Place: Melbourne Convention&Exhibition Centre, Melbourne, Australia
Abstract:

It is important to consider the fingering for playing the piano naturally. The fingering problem is to specify the natural and reasonable fingering automatically for the piano score. For example, the model of this problem can be formulated as IP based on several rules. In this research, I focused on being able to specify the fingering for the chord sequence.

堀田敬介, ``国政選挙における一票の格差の現状と対策''
Date: 日本選挙学会 研究会, May 15, 2011
Place: 関西学院大学, 兵庫
Abstract: [PDF]
PPT: [PDF]

K.Hotta, ``A mathematical approach to seek the natural and practical piano fingering''
Date: EURO XXIV, July 10-14, 2010
Place: FCUL, Universidade de Lisboa, Lisbon, Portugal
Abstract:

Given a piano score, the piano fingering problem is to decide the natural and reasonable fingering for the piano performance. The problem is not only the allocation of fingers to notes in score, but also some kind of melody analysis of music. Considering several costs based on that, I modeled the problem as {0,1}-IP, and tried to seek the practical fingering. The determination of the fingering is based on a lot of rules, which several piano players and researchers have mentioned. However, some of them seem like a contradiction. I also seek the useful and helpful rules for the fingering.

堀田敬介, ``一票の限界格差にもとづいた選挙制度の分析''
Date: 日本OR学会 「評価のOR」, June 19, 2010
Place: 政策研究大学院大学, 東京
Abstract:

　衆議院議員は小選挙区制（300人）と比例代表制（180人），参議院議員は選挙区制（146人）と比例代表制（96人）で選出される．衆議院の小選挙区制における「一票の格差」は2009年選挙時で2.31倍であり，参議院の選挙区制における格差は2007年選挙時で4.86倍である．2009年衆議院選挙の違憲訴訟は高裁で9例出ているが，違憲4，違憲状態3，合憲2と司法判断は異なった．2007年参議院選挙の違憲訴訟は最高裁が合憲とした．衆議院小選挙区は2011年度に見直しが行われる予定であり，参議院は改革協議会により2011年度中に公職選挙法改正を目指すこととなった．
　　選挙制度は，日本の国政・議会運営をどのように行うべきかという観点から決めるべきだと思うが，これだけ「一票の価値」を皆が気にするのであれば，定量分析の観点から制度の見直しをする必要があるだろう．
　　衆議院小選挙区制については，最適化を利用した根本・堀田による一連の定量分析研究により，一票の格差の限界と選挙制度の不備が明らかにされた．小選挙区以外の制度は，基本的には議員定数配分問題となる．選挙制度改革が行われようとしている今，現行制度が不備な点，格差が広がる要因がどこにあるのかを最適化の定量分析の観点から改めて明らかにし，格差を是正するための選挙制度設計について考察する．

PPT: [PDF]

堀田敬介, ``最適化を利用したピアノの実用的な指使いに関する考察''
Date: 最適化：モデリングとアルゴリズム, March 23, 2010
Place: 統計数理研究所, 東京
Abstract: -
K.Hotta, ``A Study of a Practical Piano Fingering''
Date: INFORMS Annual Meeting 2009, October 11-14, 2009
Place: San Diego Convention Center, San Diego, California, USA
Abstract:

There are some research of piano fingering. But they cannot be widely applied by strong constraints, so they are not useful for piano performance. The purpose of this research is to seek a practical piano fingering using mathematical technique.

堀田敬介, ``選挙区画定問題の最適化モデルに対する市区郡分割の方策と考察''
Date: 日本OR学会 秋季研究発表会, September 9, 2009
Place: 長崎大学, 長崎
Abstract: -

PDF <-日本OR学会：秋季研究発表会アブストラクト集

根本俊男，堀田敬介, ``県境緩和による一票の重みの格差への影響について''
Date: 日本選挙学会 研究会, May 5, 2009
Place: 同志社大学, 京都
Abstract:

衆議院議員選挙の小選挙区制度においては，一票の重みの格差をなるべく小さくすることが求められる．この格差に影響を与える要因の分析については、著者らの一連の研究により定量的に明示されてきた．その結果の一つとして，2005年度の国勢調査による人口データと平成の大合併が一段落した市区群隣接関係のネットワークを用いて計算すると2倍を下回る選挙区の画定が不可能であることがわかっている．
　　市区郡を最小単位として選挙区画定を行うことは，歴史的経緯や行政サービスの観点，および選挙を実際に行う上でもこれからも尊重されるであろう．しかしながら，来る2010年に予定されている区割見直しの際に，現行の区割画定基準を抜本的に変更しない場合，多くの市区郡において行政界を切る選挙区を作らない限り，一票の重みの格差を2倍未満におさめることはできない．そこで，なるべく現行規定を尊重しつつ格差をさげる一つの試みとして都道府県境を緩和することが考えられる．
　　本研究では，格差拡大に影響を与えている都道府県境の一部を必要最小限のみ緩和することによって，どの程度格差縮小に貢献できるかを定量的に示す．

K.Hotta and T.Nemoto, ``Political Redistricting: A Case Study in Japanese Election System''
Date: INFORMS Annual Meeting 2008, October 12-15, 2008
Place: Marriott Wardman Park Hotel & Omni Shoreham Hotel, Washington D.C., USA
Abstract:

In Japan, the population disparity ratio between districts is more than 2 and get worse for years. In past research, we explored numerically the cause of this large disparity and showed the limit of reduction in the disparity ratio, and also showed the difference in the weight of one vote cannot be improved significantly. In this talk, we analyze the effect of some idea by changing the redistricting guidelines in Japan to decrease the disparity below 2 for the next redistricting in 2010.

根本俊男，堀田敬介, ``公正な選挙制度を実現するための定量分析の歩み''
Date: 日本OR学会 SSOR2007, August 29-31, 2007
Place: 伊東ホテル聚楽, 伊東, 静岡
Abstract: -

Poster: [PDF]

K.Hotta and T.Nemoto, ``A Mathematical Analysis of the Division Rules of Cities for Political Redistricting''
Date: INFORMS International, July 8-11, 2007
Place: Wyndham Rio Mar Beach Resort & Spa, Puerto Rico, USA
Abstract:

Using IP, we showed the limit of the vote-value disparity for the redistricting of the House of Representatives in Japan, and analyzed the disparity and the legislative apportionment quantitatively. As a result of this analysis, we found the disparity is heavily dependent on the rules for making divisions of cities. In this research, by changing the numerical value specified in the division rules and using it as a parameter, we analyze what kind of change appears in the marginal gap.

Poster: [PDF]

根本俊男，堀田敬介, ``小選挙区割における市区郡分割方式と一票の重みの格差の関係''
Date: 日本選挙学会 研究会, May 19-20, 2007
Place: 神戸大学, 兵庫
Abstract: -

Poster: [PDF]

根本俊男，堀田敬介, ``オペレーションズ・リサーチから観た小選挙区制''
Date: 日本OR学会 中部支部シンポジウム, September 22, 2006
Place: 静岡大学, 浜松，静岡
Abstract: -
根本俊男，堀田敬介, ``小選挙区制度デザインを支援する定量分析方法''
Date: 日本応用数理学会, September 15-17, 2006
Place: 筑波大学, つくば，茨城
Abstract: -
根本俊男，堀田敬介, ``小選挙区区割画定問題に対する行政区域変化の影響分析''
Date: 日本OR学会 秋季研究発表会, September 11-13, 2006
Place: 愛知大学, 名古屋，愛知
Abstract: -

PDF <-日本OR学会：秋季研究発表会アブストラクト集

K.Hotta and T.Nemoto, ``A Mathematical Analysis of the Political Redistricting Problem in Japan''
Date: ISMP 2006(19th), July 29 - Augst6, 2006
Place: Federal University of Rio de Janeiro, Rio de Janeiro, Brazil
Abstract:

The parliament of Japan is made up of two houses: the House of Representatives and the House of Councilors. The House of Representatives has 480 members. The election system consists of two voting methods. Of the 480 seats, 300 are elected according to the single-seat constituency system.

In Japan, revision of single-seat electoral districts is discussed carefully every 5 years. The aim is to reduce the widening vote-value disparity through redistricting. We formulate this redistricting problem using two types of {0,1}-integer programming: set partition-type and graph partition-type. We solved them and obtained the optimal 300 districts through our own methods. Consequently, we can show the quantitative index for the discussions of electoral redistricting.

根本俊男，堀田敬介, ``平成の大合併が及ぼした一票の重みの格差への影響とその考察''
Date: 日本選挙学会 研究会, May 20-21, 2006
Place: 上智大学, 東京
Abstract: -

Poster: [PDF]

K.Hotta and T.Nemoto, ``Mathematical analysis of the limits of reduction in population disparity between single-member election districts in Japan''
Date: 2nd Pacific Workshop on Discrete Mathematics, December -, 2005
Place: Tokai University Pacific Center, Honolulu, Hawaii
Abstract: [PDF]
K.Hotta and T.Nemoto, ``Districting Problem in Japan: An IP Approach for Graph Partitioning Problem''
Date: SJOM 2005, October 31 - November 2, 2005
Place: -, Singapore
Abstract: -
根本俊男，堀田敬介, ``数理的アプローチによる一票の重みの格差の要因分析''
Date: 日本OR学会 第17回RAMPシンポジウム, October 20-21, 2005
Place: シティ弘前ホテル, 弘前，青森
Abstract: -

Poster: [PDF]

根本俊男，堀田敬介, ``衆議院小選挙区数に着目した一票の重みの格差是正効果''
Date: 日本OR学会 秋季研究発表会, September 14-15, 2005
Place: 神戸学院大学, 神戸，兵庫
Abstract: -

PDF <-日本OR学会：秋季研究発表会アブストラクト集

K.Hotta and T.Nemoto, ``On the limits of reduction in population disparity of the single-seat constituency in Japan''
Date: IFORS 2005(17th), July 11-15, 2005
Place: Hilton Hawaiian Village Beach Resort & Spa, Honolulu, Hawaii, USA
Abstract:

For the single-seat constituencies in Japan, we show that the limit of reduction in the disparity ratio is 1 to 1.750 under the present election law. Furthermore, even if the principle of population proportional apportionment is sacrificed, the ratio is reduced only to 1 to 1.722.

根本俊男，堀田敬介, ``一票の重みの格差から観た最適小選挙区数''
Date: 日本選挙学会 研究会, May 14-15, 2005
Place: 愛知学院大学, 名古屋，愛知
Abstract: -

Poster: [PDF]

根本俊男，堀田敬介, ``小選挙区制における一票の重みの格差の限界''
Date: 日本OR学会 「都市のOR」, November 20-21, 2004
Place: 南山大学, 名古屋，愛知
Abstract: -
根本俊男，堀田敬介, ``グラフ分割問題のモデル化と区割画定問題への応用''
Date: 「半順序集合とアルゴリズム」, August 23-25, 2004
Place: 南山大学, 名古屋，愛知
Abstract: -
根本俊男，堀田敬介, ``衆議院小選挙区における一票の重みの格差の限界とその考察''
Date: 日本選挙学会 研究会, May -, 2004
Place: 中央大学, 東京
Abstract: -

Poster: [PDF]

根本俊男，堀田敬介, ``選挙区最適区割問題のモデリングと厳密解導出''
Date: 日本OR学会 「第15回RAMPシンポジウム」, September -, 2003
Place: 東京工業大学, 東京
Abstract: -
根本俊男，堀田敬介, ``小選挙区制における一票の重みの格差の限界''
Date: 日本OR学会 秋季研究発表会, September -, 2003
Place: 福岡大学, 福岡
Abstract: -

PDF <-日本OR学会：秋季研究発表会アブストラクト集

K.Hotta and T.Nemoto, ``Political Redistricting: A Case Study in Japan''
Date: ISMP 2003(18th), Augst 18-22, 2003
Place: Technical University of Denmark, Copenhagen, Denmark
Abstract:

We consider the political redistricting problem for the 300 single-seat constituencies of the House of Representatives in Japan. This Problem becomes 47 redistricting subproblems because the 300 single-seats are apportioned to 47 prefectures by law. There are two difficulties to solve them in Japan. The first is the scale of subproblems. For example, Tokyo consists of 56 cities and 25 districts. The second is the difference from well-studied countries such as USA. In USA, compactness, geographical criteria, is emphasized, but it is of little significance in Japan. It is important not to divide city into smaller parts due to the law, and to find the optimal solution to make an index against gerrymandering from the point of politics. Accordingly, it is hard to find the exact solution, not an approximate solution, with a conventional method. However, we formulated subproblems as two combinatorial optimization problems, the set partition type and the graph partition type, solved them with some interesting idea, and then obtained the optimal 300 districts for the first time.

根本俊男，堀田敬介, ``数理的に最適な小選挙区区割の導出''
Date: 日本選挙学会 研究会, May 18, 2003
Place: 石川県立社会教育センター, 金沢
Abstract: -

Poster: [PDF]

根本俊男，堀田敬介, ``小選挙区割画定問題に対する数理的アプローチ''
Date: 日本OR学会 「アルゴリズム研究部会」, April -, 2003
Place: 東京大学, 東京
Abstract: -
根本俊男，堀田敬介, ``小選挙区区割り画定問題のモデル化とその周辺''
Date: 日本OR学会 東北支部講演会, March -, 2003
Place: 東北大学, 仙台，宮城
Abstract: -
根本俊男，堀田敬介, ``区割画定問題に対する数理的アプローチ''
Date: 日本OR学会 春季研究発表会, March 27-28, 2002
Place: 富山国際会議場, 富山
Abstract: -

PDF <-日本OR学会：春季研究発表会アブストラクト集

根本俊男，堀田敬介, ``区割画定問題のモデル化''
Date: 統計数理研究所 「最適化：モデリングとアルゴリズム」, March -, 2002
Place:統計数理研究所, 東京
Abstract: -
K.Hotta and A.Yoshise, ``A Predictor-Corrector Smoothing Method Using CHKS-Functions for the LCP''
Date: Optimization Workshop at Tokyo Institute of Technology, June -, 2001
Place:東京工業大学, 東京
Abstract: -
堀田敬介，吉瀬章子, ``単調線形相補正問題に対するプレディクタ・コレクタ型平滑法の計算複雑度解析と計算機実験''
Date: 日本OR学会 秋季研究発表会, September 20-21, 1999
Place:成蹊大学, 東京
Abstract: -

PDF <-日本OR学会：秋季研究発表会アブストラクト集

K.Hotta and A.Yoshise, ``A Complexity Analysis of a Predictor-Corrector Smoothing Method Using CHKS-Functions for Monotone Linear Complementarity Problems''
Date: IFORS 1999(15th), August 16-20, 1999
Place:---, Beijing, China
Abstract: -
堀田敬介, ``単調線形相補正問題に対するCHK関数を用いた平滑法について''
Date: 日本OR学会 数理計画法特設研究部会, March -, 1999
Place:---, 東京
Abstract: -
K.Hotta and A.Yoshise, ``On the Complexity of Non-Interior-Point Methods for Monotone Linear Complementarity Problems''
Date: 日本OR学会 春季研究発表会, May 27, 1998
Place:仙台市青年文化センター, 仙台
Abstract: -

PDF <-日本OR学会：春季研究発表会アブストラクト集

K.Hotta and A.Yoshise, ``Numerical Experiences in a Class of Non-Interior-Point Algorithms Using Chen-Harker-Kanzow Functions''
Date: 日本OR学会 組合せ最適化研究部会, December -, 1996
Place:東京工業大学, 東京
Abstract: -
堀田敬介，吉瀬章子, ``線形相補性問題に対する内点法のスケーリングに関する一考察''
Date: 日本OR学会 組合せ最適化研究部会, May -, 1995
Place:東京商船大学, 東京
Abstract: -

Books

堀田敬介
『経営学部の数学基礎』 (2022)
堀田敬介・久保田幸子
『はじめてのデータベース はじめてのAccess』 創成社 (2013) 創成社download
堀田敬介
『えくせるであそぶ』 創成社 (2005) 創成社download， 主な内容， 関数索引・用語索引， 正誤表(2010/8/7版)
Keisuke Hotta
``Smoothing Methods Using CHKS-Functions for Monotone Complementarity Problems'' Ph.D Thesis, Doctoral Program in Policy and Planning Sciences, University of Tsukuba (2000)

Awards received

2015年度 日本選挙学会賞：優秀論文 (2016.5.14)