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<html xmlns:o="urn:schemas-microsoft-com:office:office"xmlns:w="urn:schemas-microsoft-com:office:word"xmlns="http://www.w3.org/TR/REC-html40"><head><meta http-equiv=Content-Type content="text/html; charset=GB2312"><meta name=ProgId content=Word.Document><meta name=Generator content="Microsoft Word 9"><meta name=Originator content="Microsoft Word 9"><link rel=File-List href="./No55.files/filelist.xml"><title> 分枝定界</title><!--[if gte mso 9]><xml> <o:DocumentProperties> <o:Author>lixuewu</o:Author> <o:LastAuthor>a</o:LastAuthor> <o:Revision>2</o:Revision> <o:TotalTime>1</o:TotalTime> <o:Created>1996-12-31T16:41:00Z</o:Created> <o:LastSaved>1996-12-31T16:41:00Z</o:LastSaved> <o:Pages>16</o:Pages> <o:Words>3695</o:Words> <o:Characters>21065</o:Characters> <o:Company>dksl</o:Company> <o:Lines>175</o:Lines> <o:Paragraphs>42</o:Paragraphs> <o:CharactersWithSpaces>25869</o:CharactersWithSpaces> <o:Version>9.2812</o:Version> </o:DocumentProperties></xml><![endif]--><!--[if gte mso 9]><xml> <w:WordDocument> <w:PunctuationKerning/> <w:DrawingGridHorizontalSpacing>5.25 磅</w:DrawingGridHorizontalSpacing> <w:DrawingGridVerticalSpacing>7.8 磅</w:DrawingGridVerticalSpacing> <w:DisplayHorizontalDrawingGridEvery>0</w:DisplayHorizontalDrawingGridEvery> <w:DisplayVerticalDrawingGridEvery>2</w:DisplayVerticalDrawingGridEvery> <w:Compatibility> <w:SpaceForUL/> <w:BalanceSingleByteDoubleByteWidth/> <w:DoNotLeaveBackslashAlone/> <w:ULTrailSpace/> <w:DoNotExpandShiftReturn/> <w:AdjustLineHeightInTable/> <w:UseFELayout/> </w:Compatibility> </w:WordDocument></xml><![endif]--><style><!-- /* Font Definitions */@font-face {font-family:宋体; panose-1:2 1 6 0 3 1 1 1 1 1; mso-font-alt:SimSun; mso-font-charset:134; mso-generic-font-family:auto; mso-font-pitch:variable; mso-font-signature:3 135135232 16 0 262145 0;}@font-face {font-family:仿宋_GB2312; panose-1:2 1 6 9 3 1 1 1 1 1; mso-font-charset:134; mso-generic-font-family:modern; mso-font-pitch:fixed; mso-font-signature:1 135135232 16 0 262144 0;}@font-face {font-family:"\@仿宋_GB2312"; panose-1:2 1 6 9 3 1 1 1 1 1; mso-font-charset:134; mso-generic-font-family:modern; mso-font-pitch:fixed; mso-font-signature:1 135135232 16 0 262144 0;}@font-face {font-family:"\@宋体"; panose-1:2 1 6 0 3 1 1 1 1 1; mso-font-charset:134; mso-generic-font-family:auto; mso-font-pitch:variable; mso-font-signature:1 135135232 16 0 262144 0;} /* Style Definitions */p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; text-align:justify; text-justify:inter-ideograph; mso-pagination:none; font-size:10.5pt; mso-bidi-font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:宋体; mso-font-kerning:1.0pt;}p.MsoFooter, li.MsoFooter, div.MsoFooter {margin:0cm; margin-bottom:.0001pt; mso-pagination:none; tab-stops:center 207.65pt right 415.3pt; layout-grid-mode:char; font-size:9.0pt; font-family:"Times New Roman"; mso-fareast-font-family:宋体; mso-font-kerning:1.0pt;} /* Page Definitions */@page {mso-page-border-surround-header:no; mso-page-border-surround-footer:no; mso-gutter-position:top;}@page Section1 {size:515.95pt 728.6pt; margin:72.0pt 2.0cm 65.2pt 2.0cm; mso-header-margin:36.0pt; mso-footer-margin:36.0pt; mso-even-footer:url("./No55.files/header.htm") ef1; mso-footer:url("./No55.files/header.htm") f1; mso-paper-source:0;}div.Section1 {page:Section1;}--></style></head><body lang=ZH-CN style='tab-interval:21.0pt;text-justify-trim:punctuation' bgcolor="#e8ffe8"><div class=Section1><p class=MsoNormal align=left style='text-align:left;text-indent:96.0pt;mso-char-indent-count:6.0;mso-char-indent-size:16.0pt;mso-layout-grid-align:none;text-autospace:none'><span style='font-size:16.0pt;font-family:仿宋_GB2312;color:blue;mso-font-kerning:0pt'>第<span lang=EN-US> 5 章 分枝定界<o:p></o:p></span></span></p><p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:none;text-autospace:none'><span lang=EN-US style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p><p class=MsoNormal align=left style='text-align:left;text-indent:20.0pt;mso-char-indent-count:2.0;mso-char-indent-size:10.0pt;mso-layout-grid-align:none;text-autospace:none'><span style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>任何美好的事情都有结束的时候。现在我们学习的是本书的最后一章。幸运的是，本章用到的大部分概念在前面各章中已作了介绍。类似于回溯法，分枝定界法在搜索解空间时，也经常使用树形结构来组织解空间（常用的树结构是第</span><spanlang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>1 6</span><span style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>章所介绍的子集树和排列树）。然而与回溯法不同的是，回溯算法使用深度优先方法搜索树结构，而分枝定界一般用宽度优先或最小耗费方法来搜索这些树。本章与第</span><spanlang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>1 6</span><span style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>章所考察的应用完全相同，因此，可以很容易比较回溯法与分枝定界法的异同。相对而言，分枝定界算法的解空间比回溯法大得多，因此当内存容量有限时，回溯法成功的可能性更大。<spanlang=EN-US><o:p></o:p></span></span></p><p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:none;text-autospace:none'><span lang=EN-US style='font-size:12.0pt;font-family:Arial;mso-fareast-font-family:仿宋_GB2312;color:blue;mso-font-kerning:0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p><p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:none;text-autospace:none'><span lang=EN-US style='font-size:12.0pt;font-family:Arial;mso-fareast-font-family:仿宋_GB2312;color:blue;mso-font-kerning:0pt'>5.1 </span><spanstyle='font-size:12.0pt;font-family:仿宋_GB2312;color:blue;mso-font-kerning:0pt'>算法思想<spanlang=EN-US><o:p></o:p></span></span></p><p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:none;text-autospace:none'><span lang=EN-US style='font-size:12.0pt;font-family:仿宋_GB2312;color:blue;mso-font-kerning:0pt'><![if !supportEmptyParas]> <![endif]><o:p></o:p></span></p><p class=MsoNormal align=left style='text-align:left;text-indent:20.0pt;mso-char-indent-count:2.0;mso-char-indent-size:10.0pt;mso-layout-grid-align:none;text-autospace:none'><span style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>分枝定界（</span><span lang=EN-USstyle='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>branch and bound</span><span style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>）是另一种系统地搜索解空间的方法，它与回溯法的主要区别在于对</span><spanlang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>E</span><span lang=EN-US style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>-节点的扩充方式。每个活节点有且仅有一次机会变成</span><spanlang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>E</span><span lang=EN-US style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>-节点。当一个节点变为</span><spanlang=EN-US style='font-size:10.0pt;mso-fareast-font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>E</span><span lang=EN-US style='font-size:10.0pt;font-family:仿宋_GB2312;color:black;mso-font-kerning:0pt'>-节点时，则生成从该节点移动一步即可到达的所有新节点。在生成的节点中，抛弃那些不可能导出（最优）可行解的节点，其余节点加入活节点表，然后从表中选择一个节点作为下一个</span><span⌨️ 快捷键说明
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