求解器中的线性优化二元约束公式
Linear optimization binary constraints formulation in Solver
我正在研究这个投资问题陈述并且在制定约束方程时遇到困难。
"设 x1、x2、x3 和 x4 表示
经纪人选择投资或不投资投资选项 1、2、3、4 的二元变量。假设经纪人有以下约束：
*if x3 + x4 ge 1 Then x1 + x2 = 1 and if x3 + x4 = 0 then x1 + x2 ge 0*
如何组合上述约束条件？
我会让你做最后的检查，但基本上这应该是这样的：
"The constraints is if X3 + X4 ge 1 Then x1 + X2 = 1."
这相当于：
(x3 or x4) implies ((x1 and not x2) or (not x1 and x2))
- (x3 or x4) captures the >= 1
- x1 + x2 = 1 is an XOR and captured by ((x1 and not x2) or (not x1 and x2))
- DNF of XOR
让我们问一下 WolframAlpha to do boolean minimization: Computation -> 我们对 CNF!
感兴趣
- The CNF produced is ready to be mapped to ILP as it's a conjunction of ORs
- Each OR is a term of it's literals summing up to >= 1:
(1 - x1) + (1 - x2) + (1 - x3) >= 1
(1 - x1) + (1 - x2) + (1 - x4) >= 1
x1 + x2 + (1 - x3) >= 1
x1 + x2 + (1 - x4) >= 1
这应该是一个相当紧凑/强大的公式！
我建议用 Truth Table 仔细检查它。
我正在研究这个投资问题陈述并且在制定约束方程时遇到困难。
"设 x1、x2、x3 和 x4 表示 经纪人选择投资或不投资投资选项 1、2、3、4 的二元变量。假设经纪人有以下约束：
*if x3 + x4 ge 1 Then x1 + x2 = 1 and if x3 + x4 = 0 then x1 + x2 ge 0*
如何组合上述约束条件？
我会让你做最后的检查，但基本上这应该是这样的：
"The constraints is if X3 + X4 ge 1 Then x1 + X2 = 1."
这相当于：
(x3 or x4) implies ((x1 and not x2) or (not x1 and x2))
- (x3 or x4) captures the >= 1
- x1 + x2 = 1 is an XOR and captured by ((x1 and not x2) or (not x1 and x2))
- DNF of XOR
让我们问一下 WolframAlpha to do boolean minimization: Computation -> 我们对 CNF!
感兴趣- The CNF produced is ready to be mapped to ILP as it's a conjunction of ORs
- Each OR is a term of it's literals summing up to >= 1:
(1 - x1) + (1 - x2) + (1 - x3) >= 1
(1 - x1) + (1 - x2) + (1 - x4) >= 1
x1 + x2 + (1 - x3) >= 1
x1 + x2 + (1 - x4) >= 1
这应该是一个相当紧凑/强大的公式！
我建议用 Truth Table 仔细检查它。