intlp - EE236A(Fall 2007-08 Lecture 17 Integer linear...

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Unformatted text preview: EE236A (Fall 2007-08) Lecture 17 Integer linear programming • integer linear programming, 0-1 linear programming • a few basic facts • branch-and-bound 17–1 Definition integer linear program (ILP) minimize c T x subject to Ax ≤ b, Gx = d x ∈ Z n c mixed integer linear program: only some of the variables are integer 0-1 (Boolean) linear program variables take values or 1 Integer linear programming 17–2 Example: facility location problem • n potential facility locations, m clients • c i , i = 1 , . . . , n : cost of opening a facility at location i • d ij , i = 1 . . . , m , j = 1 , . . . , n : cost of serving client i from location j determine optimal location: minimize ∑ n j =1 c j y j + ∑ m i =1 ∑ n j =1 d ij x ij subject to ∑ n j =1 x ij = 1 , i = 1 , . . . , m x ij ≤ y j , i = 1 , . . . , m, j = 1 , . . . , n x ij , y j ∈ { , 1 } • y j = 1 if location j is selected • x ij = 1 if location j serves client i a 0-1 LP Integer linear programming 17–3 Linear programming relaxation the LP obtained by deleting the constraints x ∈ Z n (or x ∈ {...
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intlp - EE236A(Fall 2007-08 Lecture 17 Integer linear...

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