Integer Program Combination Optimization - Problem Set 1 Solutions

University:
Massachusetts Institute of Technology
Course:
15.501/516 | Accounting
Academic year:

2023
Views:

377

Pages:

6
Author:

Myles Abbott

Iпteger Prograп1miпg & ComЬiпatorial Optiп1izatioп Solutioпs to Рr0Ые п1 Set 1 For this and all subsequent assigшnents, unless otherwise specified, Е denotes а suitaЬly sшall real nuшber where Е > О and М denotes а suitaЬly large real nuшber where М Е IR:++ · 1. BW 1.7 Data Mining (а) А possiЬle linear prograшшing forшulation is: шш s.t. l'c с' �i с' �i с < > Е i = 1, ... ,m 1 + Ма;, (1 + с)- M(l - а;), i = 1, ... ,m осп (Ъ) А possiЫe integer prograшming formulation is: ш шш 2)zf + z;) i=l s.t. с' ;юi с' ;юi l z' l z' l z' ,2 �; ,2 �; z'2 а·' z'� z'? ' Ь 1 ,Ь 2 ,с < 1+ Ма; > (1 +с)- M(l - а;) > (у; - b�:z,;) - Ма; > -(у; - b�:z,;) - Ма; < M(l - а;) > (у; - ь;"';) - M(l - а;) > -(у; - ь;-,;) - M(l - а;) < Mai Е Е {0,1} IR+ Е ш:п щ = О implies c'xi ::; 1, z[ 2: IYi - Ь� 2\1, zi2 = О. ai = 1 i1nplies c'xi � (1 + е) > 1, zi1 = О, zl IYi - ::, i = 1,... ,m i = 1,... ,m i = 1,... ,m i = 1,... ,m i = 1,... ,m i = 1, ... ,m i = 1, ... ,m i = 1, ... ,m i = 1, ... ,m i = 1, ... ,m ь;-,J Note; Constraints zi1 :::; M(l - ai) and zf :::; Mai are redundant frшп the foппulation point of view, but шау еnаЫе the рrоЫеш to Ье solved faster. 1