Symbolic algorithms for integer programming : from logic specification to solvers 整数プログラミングの記号アルゴリズム : 論理仕様から解決系へ
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著者
書誌事項
- タイトル
-
Symbolic algorithms for integer programming : from logic specification to solvers
- タイトル別名
-
整数プログラミングの記号アルゴリズム : 論理仕様から解決系へ
- 著者名
-
李, 強
- 著者別名
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リ, キョウ
- 学位授与大学
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筑波大学
- 取得学位
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博士 (工学)
- 学位授与番号
-
甲第2130号
- 学位授与年月日
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1999-03-25
注記・抄録
博士論文
Integer programming (IP) is an important mathematical optimization technique that attempts to find an optimal solution under constraints so that the objective value is minimal or maximal. Optimisation problems that can be solved with IP are important in operations research and computer science, such as the knapsack problem, the traveling salesman problem, ...
1998
目次
- Contents / (0005.jp2)
- 1 Introduction / p1 (0006.jp2)
- 2 Preliminaries / p9 (0010.jp2)
- 2.1 Introduction / p9 (0010.jp2)
- 2.2 Integer programming:problem definition / p9 (0010.jp2)
- 2.3 Polynomial theory / p16 (0014.jp2)
- 3 Modelling Integer Programming with Logic / p21 (0016.jp2)
- 3.1 Introduction / p21 (0016.jp2)
- 3.2 Review of logical modelling frameworks for IP / p22 (0017.jp2)
- 3.3 Modelling language L⁺ / p22 (0017.jp2)
- 3.4 Algorithm for transformation on L⁺ / p24 (0018.jp2)
- 3.5 Implementation in Mathematica / p34 (0023.jp2)
- 4 Gröbner bases for Integer Programming / p37 (0024.jp2)
- 4.1 Introduction / p37 (0024.jp2)
- 4.2 Gröbner bases / p37 (0024.jp2)
- 4.3 Buchberger algorithm / p38 (0025.jp2)
- 4.4 Gröbner bases as test sets in IP / p40 (0026.jp2)
- 5 Minimised Geometric Buchberger Algorithm(MGBA) / p47 (0029.jp2)
- 5.1 Introduction / p47 (0029.jp2)
- 5.2 Strategy 1:indirect encoding / p49 (0030.jp2)
- 5.3 Strategy 2:direct encoding / p53 (0032.jp2)
- 5.4 Truncated Gröbner bases / p57 (0034.jp2)
- 5.5 Minimised Geometric Buchberger Algorithm / p59 (0035.jp2)
- 5.6 Implementation, Experiment and Comparison / p66 (0039.jp2)
- 5.7 Concluding remarks / p68 (0040.jp2)
- 6 Applying MGBA to Stochastic Integer Programming / p69 (0040.jp2)
- 6.1 Introduction / p69 (0040.jp2)
- 6.2 Chance constrained IP problem / p69 (0040.jp2)
- 6.3 Test set for chance constrained IP / p72 (0042.jp2)
- 6.4 Algorithm for chance constrained IP / p74 (0043.jp2)
- 6.5 Application / p79 (0045.jp2)
- 7 Conclusion / p87 (0049.jp2)
- 7.1 Contributions / p87 (0049.jp2)
- 7.2 Future work / p88 (0050.jp2)
- Appendix A / p89 (0050.jp2)
- Bibliography / p95 (0053.jp2)
- Index / p103 (0057.jp2)
- List of Notations / p105 (0058.jp2)
