CPLEX 约束

Question

我需要优化具有最高总体影响的投资选择。 限制是总投资可以最大为 8.0 另一个限制是每个类别只能评估两次

我面临的问题是最大投资的约束不起作用。我也找不到如何实现类别约束。也欢迎提供相关表格的链接。

我的代码附在下面

非常感谢

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int NumberofProjects = 12;
range Project = 1..NumberofProjects; // 12 different projects

//Declaration of Parameters
float Impact[Project] = [0.1, 0.03, 0.07, 0.13, 0.01, 0.04, 0.07, 0.08, 0.15, 0.12, 0.02, 0.04]; // Impact to maximize 
float Investment[Project] = [2.0, 1.6, 2.5, 12.0, 10.3, 0.6, 1.2, 1.9, 4.0, 5.0, 0.2, 0.5]; // costs --> can be max 8.0 
string Category[Project] = [1,1,1,1,1,2,2,2,3,3,3,3] 
float Budget = 8.0;
// Declaration of Parameters 

//Expression of Decision 
dexpr float Reduction = sum(p in Project) Impact[p];

//Objective Function
maximize Reduction;

//Constraints
constraint ctCapResources[Project];
subject to {
forall (p in Project)
    ctCapResources[p]: sum(p in Project)
        Investment[p] <= Budget;
}

Answer 1

@alexfleischer - 非常感谢亚历克斯。非常感激。我有一个后续问题。 我已经包含了两种制造方法（即内部和外部）的索引，并想添加以下限制： • 最多可以在内部完成以下三个项目之一：项目 1、项目 4、项目 5。 此外，我注意到，虽然实现了最佳结果（最高影响），但它没有考虑成本（有两个答案产生相同的影响但成本不同），而我想将其作为次要（不太重要）目标（应该CPLEX 12.9 可以吗？）

int NumberofProduction = 2;
range Production = 1..NumberofProduction; // Internal vs External production

int NumberofProjects = 12;
range Project = 1..NumberofProjects; // 12 different projects

//Declaration of Parameters
float Impact[Project] = [0.1, 0.03, 0.07, 0.13, 0.01, 0.04, 0.07, 0.08, 0.15, 0.12, 0.02, 0.04]; // Impact to maximize 
//float Investment[Project] = [2.3, 1.7, 2.9, 2.3, 0.4, 0.7, 1.4, 2.2, 4.5, 5.5, 0.3, 0.6]; // costs --> can be max 8.0 
// float Setupcosts[Project] = [0.3, 0.1, 0.4, 0.3, 0.1, 0.1, 0.2, 0.3, 0.5, 0.5, 0.1, 0.1];
// float ExInvestment[Project] = [2.5, 1.7, 2.0, 2.5, 0.4, 0.7, 1.8, 2.2, 4.5, 1.0, 0.4, 0.5];
float InExInvestment[Production][Project] = [[2.3, 1.7, 2.9, 2.3, 0.4, 0.7, 1.4, 2.2, 4.5, 5.5, 0.3, 0.6],[2.5, 1.7, 2.0, 2.5, 0.4, 0.7, 1.8, 2.2, 4.5, 1.0, 0.4, 0.5]];
int Category[Project] = [1,1,1,1,1,2,2,2,3,3,3,3];
float Budget = 8.0;

// decision variable
dvar boolean invest[Production][Project];

//Expression of Decision 
dexpr float Reduction = sum(q in Production, p in Project) Impact[p]*invest[q][p];
// dexpr float Costs = sum(q in Production, p in Project) -1*InExInvestment[q][p]; // Second decision to mimimize costs if two options for Reduction with same outcome
//Constraints
constraint ctCapResources[Project];
constraint ctProject[Project];


//Objective Function
maximize Reduction;


subject to {

 //  each Category can only be assessed twice
 forall (p in Project)
        ctProject[p]: sum(q in Production)invest[q][p] <=1;
 
 forall(c in 1..3) sum(p in Project:Category[p]==c, q in Production) invest[q][p]<=2;
 
 forall (p in Project)
    ctCapResources[p]: sum(q in Production, p in Project)
        InExInvestment[q][p]*invest[q][p] <= Budget;
}

Answer 2

主要问题是您忘记添加决策变量。

int NumberofProjects = 12;
range Project = 1..NumberofProjects; // 12 different projects

//Declaration of Parameters
float Impact[Project] = [0.1, 0.03, 0.07, 0.13, 0.01, 0.04, 0.07, 0.08, 0.15, 0.12, 0.02, 0.04]; // Impact to maximize 
float Investment[Project] = [2.0, 1.6, 2.5, 12.0, 10.3, 0.6, 1.2, 1.9, 4.0, 5.0, 0.2, 0.5]; // costs --> can be max 8.0 
int Category[Project] = [1,1,1,1,1,2,2,2,3,3,3,3];
float Budget = 8.0;
// Declaration of Parameters 

// decision variable
dvar boolean invest[Project];

//Expression of Decision 
dexpr float Reduction = sum(p in Project) Impact[p]*invest[p];

//Objective Function
maximize Reduction;

//Constraints
constraint ctCapResources[Project];
subject to {
forall (p in Project)
    ctCapResources[p]: sum(p in Project)
        Investment[p]*invest[p] <= Budget;
        
 //  each Category can only be assessed twice
 
 forall(c in 1..3) sum(p in Project:Category[p]==c) invest[p]<=2;
}

效果会更好

对于你的第二个问题，你可以改变

maximize Reduction;

进入

maximize staticLex(Reduction,-Cost);