Download e-book for iPad: Constraint Integer Programming by TobiasAchterberg

By TobiasAchterberg

ISBN-10: 3899638921

ISBN-13: 9783899638929

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Additional info for Constraint Integer Programming

Sample text

Djrk → {0, 1}, ÓÒ×ØÖ ÒØ Ê¸ i = 1, . . , k¸ Û ÒØ ÖÚ Ð ÓÑ i = 1, . . , k º Ò× Ì Ò ÓÒ Ö Ð¹Ú ÐÙ × Ô ÖØ Ó Ú Ö ÓÒ×ØÖ xj1 , . . , xjk ¸ Djri = [lji , uji ]¸ lji , uji ∈ ÒØ × Ø × Ø ÓÒ ÔÖÓ Ð Ñ ËÈ = (C, D) Û Ø ∈ ʸ ÓÖ Dji = {lji , . . , uji }¸ lji , uji ∈ ¸ Ð × Dji = [lji , uji ]¸ lji , uji Ò¸ C × ÐÐ ÓÙÒ ÓÒ× ×Ø ÒØ ∀i ∈ {1, . . , k} ∀xji ∈ {lji , uji } ∃x⋆ ∈ Djr1 × . . × Djrk : x⋆ji = xji ∧ C(x⋆ ) = 1. ËÈ Û Ø ÓÑ ÓÒ×ØÖ ÆÓØ Ø ÓÒ× ×Ø ÒØ Ø ÒØ× Ò ÓÒ Ö Ð¹Ú ÐÙ ÓÙÒ ÓÒ× ×Ø ÒØ Ò× × ÐÐ ÓÙÒ ÓÒ× ×Ø Ò
Ý × Û ËÈ Ò Û Ø ÓÒ× ×Ø Òغ ÇÒ Ø ÓØ ÓÒ× ×Ø Òظ ÓÐÐÓÛ Ò × Ø Ü ÑÔÐ ¾º º Ä Ø ÐÐ Ó Ö ÓÒ×ØÖ Ò ¸Ø Ö Ø ÒØ× Ö Ü ÑÔÐ Ö Ú Ö Ð × Ø× ÓÒ×ØÖ Ò ÒØ× Ú Ö Ö Ð × Û Ø ÓÙÒ Ò ÒØ ÖÚ Ð ÓÒ× ×Ø Ò
Ý Ö ÓÙÒ Ò ÓÒ Ö Ð¹Ú ÐÙ ÓÒ× ×Ø ÒØ Ú ÖÝ ÒØ ÖÚ Ð Ú Ö ËÈ× Ø ÒØ ÖÚ Ð ÓÒ× ×Ø Òغ Ø Ð × × Ö ÓÙÒ ÒÓØ ÒØ ÖÚ Ð ÐÐÙ×ØÖ Ø × C : [0, 1] × [0, 1] × [0, 1] → {0, 1} Ø Ð Ò Ö ÓÒ×ØÖ ÒØ C(x) = 1 ⇔ 2x1 + 2x2 + 2x3 = 3.

Uji }¸ lji , uji ∈ ¸ Ð × Dji = [lji , uji ]¸ lji , uji Ò¸ C × ÐÐ ÓÙÒ ÓÒ× ×Ø ÒØ ∀i ∈ {1, . . , k} ∀xji ∈ {lji , uji } ∃x⋆ ∈ Djr1 × . . × Djrk : x⋆ji = xji ∧ C(x⋆ ) = 1. ËÈ Û Ø ÓÑ ÓÒ×ØÖ ÆÓØ Ø ÓÒ× ×Ø ÒØ Ø ÒØ× Ò ÓÒ Ö Ð¹Ú ÐÙ ÓÙÒ ÓÒ× ×Ø ÒØ Ò× × ÐÐ ÓÙÒ ÓÒ× ×Ø Ò
Ý × Û ËÈ Ò Û Ø ÓÒ× ×Ø Òغ ÇÒ Ø ÓØ ÓÒ× ×Ø Òظ ÓÐÐÓÛ Ò × Ø Ü ÑÔÐ ¾º º Ä Ø ÐÐ Ó Ö ÓÒ×ØÖ Ò ¸Ø Ö Ø ÒØ× Ö Ü ÑÔÐ Ö Ú Ö Ð × Ø× ÓÒ×ØÖ Ò ÒØ× Ú Ö Ö Ð × Û Ø ÓÙÒ Ò ÒØ ÖÚ Ð ÓÒ× ×Ø Ò
Ý Ö ÓÙÒ Ò ÓÒ Ö Ð¹Ú ÐÙ ÓÒ× ×Ø ÒØ Ú ÖÝ ÒØ ÖÚ Ð Ú Ö ËÈ× Ø ÒØ ÖÚ Ð ÓÒ× ×Ø Òغ Ø Ð × × Ö ÓÙÒ ÒÓØ ÒØ ÖÚ Ð ÐÐÙ×ØÖ Ø × C : [0, 1] × [0, 1] × [0, 1] → {0, 1} Ø Ð Ò Ö ÓÒ×ØÖ ÒØ C(x) = 1 ⇔ 2x1 + 2x2 + 2x3 = 3.

Djk : x⋆ji = xji ∧ C(x⋆ ) = 1. ÝÔ Ö¹ Ö ÓÒ× ×Ø ÒØ ËÈ × ÐÐ ÀÝÔ Ö¹ Ö ÓÒ× ×Ø Ò
Ý × Ø ×Ô Ø ØÓ Ø × Ò Ð ÒÚÓÐÚ ÙÖØ ÓÑ Ò ÒØ× Ò Ú Ô ÖØ Ò ØÓ ÒØÖÓ Ù ×ØÖÓÒ ÁØ Ü
ÐÙ ÓÒÐÝ ×ÓÐÙØ ÓÒ Ö ÓÒ Ø ÓÖ Ø Ö ØÓ ÓÑ Ú ÒØ× Ö ÝÔ Ö¹ Ö ÓÒ× ×Ø Òغ ÐÓ Ð ÓÒ× ×Ø Ò
Ý ÒÓØ ÓÒ Û Ø ÓÖ ÓÒ×ØÖ × Ø × Ò× Ó Ø × Ú Ö ÒØ Cº C ÁÒ ÓØ Ð × Ö ¹ Ú ÐÙ Ò Ö ÛÓÖ ×¸ ÒÓ Ý ÓÒ× ÝÔ Ö¹ Ö ÓÒ× ×Ø Ò
Ý ÓÖ ÓÑ Ò× Ó Ø Ö Ò ÓÑ Ò× D ⊆ ʸ Òغ ÝÔ Ö¹ Ö ÓÒ× ×Ø Ò
ݺ ËÙ ÄÈ Ö Ð Ü Ø ÓÒ Ó ÓÒØ ÒÙÓÙ× ÒØ ÖÚ Ð× Û Ø ÓÙØ ÓÐÐÓÛ Ò ÓÙÒ × Ó Ø Ú Ò ÓÒ×ØÖ Ú Ö ÓÒ×ØÖ Ú ÓÖ ÒÚÓÐÚ Ø ÓÒ ÐÐݸ Ø Ð Û Ø Ó Ø ÖÓÑ Ø ÓÐ × Ò ÓÖ Ð Û Ø Ð Ø ×ÓÐÙØ ÓÒ Û ÖÓÑ Ø Ú ÖÝ Ø Ñ ¹
ÓÒ×ÙÑ Ò º Ù×Ù ÐÐÝ Ö ×Ø ÔÓ×× Ñ Ò × Ø Ñ× ØÓ ÐÐ Ú ÐÙ × ÔÖÓ Ö Ñ Ò ÓÒÐÝ Ø× ÓÒ×ØÖ Ø Ù ÐÐݺ Ð ÓÖ Ø Ñ Û × ØÓ Ö ÑÓÚ Òغ Ò× Ô ÖØ Ô Ø × Ò Ö Ú ÐÙ × Ò ÓÒ×ØÖ Ø ÓÒ×ØÖ ÐÐ Ó Ö Ð Ü ÒØ ÖÚ Ð Ú Ö× ÓÒ× Ó ÓÑ Ò× Ð × Ø ÓÒ ÒØ Ó ÒÓØ Ù×Ù ÐÐÝ × Ð ÓÖ Ø Ñ× Ò ÓÒ×ØÖ ÓР׺ Ì Ø Ö ÒØ ÒØ ÓÖ ¸ Û ÝÔ Ö¹ Ö ÓÒ× ×Ø Ò
ݸ Û Ö Û ÐÐ ¾¾ Ð ÓÖ Ø Ñ× Ò Ø ÓÒ ¾º ´ ÒØ ÖÚ Ð ÓÒ× ×Ø Ò
ݵº Ò Ö ØÖ ÖÝ ÓÒ×ØÖ ÒØ C ∈ C ÓÒ Ú Ö Ð × xj1 , .

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Constraint Integer Programming by TobiasAchterberg


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