逻辑或

形式

$$y=Or(x_1,x_2,..,x_i)=\{\begin{array}{ll}1,& \underset{i}{\bigvee }{x}_i\\ \\ 0,& \mathrm{\neg }\underset{i}{\bigvee }{x}_i\end{array}$$

额外变量

$y^{\prime }\in \{0,1\}$ ：逻辑或值。

导出符号

$$y=y^{\prime }$$

数学模型

$$\begin{array}{rl}s.t.& \{\begin{array}{ll}{y}^{\prime }\ge \frac{x_i}{max(x_i)},& max(x_i)>1\\ \\ y^{\prime }\ge x_i,& else\end{array}\\ \\ & y^{\prime }\le \sum _i{x}_i& \end{array}$$

样例

kotlin

import kotlinx.coroutines.*
import fuookami.ospf.kotlin.utils.math.*
import fuookami.ospf.kotlin.core.frontend.variable.*
import fuookami.ospf.kotlin.core.frontend.expression.polynomial.*
import fuookami.ospf.kotlin.core.frontend.expression.symbol.linear_function.*
import fuookami.ospf.kotlin.core.frontend.inequality.*
import fuookami.ospf.kotlin.core.frontend.model.mechanism.*
import fuookami.ospf.kotlin.core.backend.plugins.scip.*

val x = BinVar("x")
val y = BinVar("y")
val or = OrFunction(listOf(x, y), "or")
val solver = ScipLinearSolver()

val model1 = LinearMetaModel()
model1.add(x)
model1.add(y)
model1.add(or)
model1.minimize(or)
val result1 = runBlocking { solver(model1) }
assert(result1.value!!.obj eq Flt64.zero)
assert(result1.value!!.solution[0] eq Flt64.zero)
assert(result1.value!!.solution[1] eq Flt64.zero)

val model2 = LinearMetaModel()
model2.add(x)
model2.add(y)
model2.add(or)
model2.addConstraint(or eq Flt64.one)
model2.minimize(x + y)
val result2 = runBlocking { solver(model2) }
assert(result2.value!!.obj eq Flt64.one)
assert((result2.value!!.solution[0] eq Flt64.one) xor (result2.value!!.solution[1] eq Flt64.one))

完整实现请参考：

• Kotlin

完整样例请参考：

• Kotlin