choco 求解器中的资源分配

Question

我正在使用choco 来解决虚拟机分配问题，这就是我想要做的：

假设我们有 3 个阵列用于物理机属性（PMcpu、PMram、PMbw）和 3 个阵列用于我们的虚拟机（VMcpu、VMram、VMbw）。现在我们定义一个具有这些维度的矩阵：PM*VM，以便 choco 设置值（0 或 1 表示特定 VM 是否分配给 PM）。根据常识，我们知道 PM 资源应该大于或等于所有分配的 VM 资源的总量，因此我们将分配矩阵中的每个元素与相应的资源相乘，例如假设：

PMcpu = {8000, 7000, 3000};
PMram = {7000, 4000, 5000};
PMbw = {2000, 500, 7000};
VMcpu = {2000, 3000, 1000};
VMram = {1000, 2000, 3000};
VMbw = {100, 2000, 500};

分配矩阵：

0 1 0
1 0 0
0 0 1

行代表 PM，列代表 VM，所以在这里：

VM2 -> PM1
VM1 -> PM2
VM3 -> PM3

所以我写了这段代码：

    Model model = new Model("Resource Allocation Problem");
    int[] VMcpu = new int[number_of_vms];
    int[] VMram = new int[number_of_vms];
    int[] VMbw = new int[number_of_vms];
    // some initialization here

    int[] PMcpu = new int[number_of_pms];
    int[] PMram = new int[number_of_pms];
    int[] PMbw = new int[number_of_pms];
    // some initialization here

    IntVar[][] alloc_matrix = model.intVarMatrix("alloc_matrix", number_of_pms, number_of_vms, new int[] {0,1});

    // ensuring all columns have only one 1 in them
    ArrayList<IntVar> sum_of_col = new ArrayList<>();
    for(int j=0; j<number_of_vms; j++) {
        int count = 0;
        for(int i=0; i<number_of_pms; i++) {
            count += alloc_matrix[i][j].getValue();
        }
        IntVar tempInt = model.intVar(count);
        sum_of_col.add(tempInt);

    }
    for(int i=0; i<sum_of_col.size(); i++) {
        model.arithm(sum_of_col.get(i), "=", 1).post();

    }

    // ensuring that PMs can host that much VM (based on their resources)
    for (int i=0; i<number_of_pms; i++) {
        ArrayList<IntVar> pm_total_cpu = new ArrayList<>();
        ArrayList<IntVar> pm_total_ram = new ArrayList<>();
        ArrayList<IntVar> pm_total_bw = new ArrayList<>();
        for (int j=0; j<number_of_vms; j++) {
            IntVar temp_cpu = model.intVar(alloc_matrix[i][j].getValue() * VMcpu[j]);
            IntVar temp_ram = model.intVar(alloc_matrix[i][j].getValue() * VMram[j]);
            IntVar temp_bw = model.intVar(alloc_matrix[i][j].getValue() * VMbw[j]);
            pm_total_cpu.add(temp_cpu);
            pm_total_ram.add(temp_ram);
            pm_total_bw.add(temp_bw);
        }
        model.sum(ArrayUtils.toArray(pm_total_cpu), "<", PMcpu[i]).post();
        model.sum(ArrayUtils.toArray(pm_total_ram), "<", PMram[i]).post();
        model.sum(ArrayUtils.toArray(pm_total_bw), "<", PMbw[i]).post();
    }

    // getting the number of active PMs (those that have at least one 1 in their row)
    ArrayList<IntVar> pm_hostings = new ArrayList<>();
    for (int i=0; i<number_of_pms; i++) {
        ArrayList<IntVar> row = new ArrayList<>();
        for (int j=0; j<number_of_vms; j++) {
            IntVar temp_int_var = model.intVar(alloc_matrix[i][j].getValue());
            row.add(temp_int_var);
        }
        int has_one = 0;
        for(int iterator=0; iterator<row.size(); iterator++) {
            if (row.get(iterator).getValue() == 1) {
                has_one = 1;
                break;
            }
        }
        IntVar temp = model.intVar(has_one);
        pm_hostings.add(temp);
    }
    // sum will be the number of active PMs
    int sum = 0;
    for (int i=0; i<pm_hostings.size(); i++) {
        sum += pm_hostings.get(i).getValue();
    }

    // setting objective to minimize that number of active PMs
    IntVar answer = model.intVar(sum);
    model.setObjective(Model.MINIMIZE, answer);
    while(model.getSolver().solve()) {
        System.out.println("answer: " + answer.getValue());
        for(int i=0;i<sum_of_col.size();i++) {
            System.out.println("=== " + sum_of_col.get(i).getValue());
        }
        for(int i=0;i<number_of_pms;i++) {
            for(int j=0;j<number_of_vms;j++) {
                System.out.print(alloc_matrix[i][j].getValue() + " ");
            }
            System.out.println();
        }
    }

我试图通过检查矩阵的每一列来确保所有虚拟机都被分配到model.arithm(sum_of_col.get(i), "=", 1).post(); 行中。如果我评论约束和目标，矩阵将被随机分配，但是在应用约束时，choco 不会解决任何问题（没有输出，因为while(model.getSolver().solve() 永远不会为真，所以 choco 似乎没有解决它）。我不知道我在哪里做错了。任何帮助表示赞赏:)

提前致谢

编辑：我意识到问题是 choco 只在第一次检查这些约束，所以当一切都为 0 时它会检查它，这就是它不会继续的原因，但是在 solve() 循环中添加约束后我仍然得到同样的结果，也许我应该以 choco 理解它们的另一种方式应用这些约束，我现在真的很沮丧:(

Answer 1

我的问题是对 CSP 问题解决的基本理解，基本上所有变量一开始都是未知的，但是当 choco 求解器尝试解决问题时，它们将由值设置。所以不可能检索值并设置这样的约束（即使在while(solve()){} 中也不行。基本上我们应该在 choco 解决它之前对那些未知变量应用整个约束。所以我改变了整个模型并得到了 choco 的帮助开发人员（查看他们的 gitter 聊天以获取帮助）。所以在下面你会看到代码的样子：

    Model model = new Model("Resource Allocation Problem");
    // here we are using number_of_sth+1 because we need to use a scalar function of choco
    // that will calculate sum(arr[i] * arr2[i]) and we need to specify the lack of PM
    // assignment by the 0 in them so that we can add a constraint later to prevent such
    // a happening (not assigning a VM to a PM)

    int[] VMcpu = new int[number_of_vms+1];
    int[] VMram = new int[number_of_vms+1];
    VMcpu[0] = 0;
    VMram[0] = 0;
    for (int i=1; i<number_of_vms+1; i++) {
        VMcpu[i] = vms.get(i-1).get_cpu();
        VMram[i] = vms.get(i-1).get_ram();
    }
    System.out.println();

    int[] PMcpu = new int[number_of_pms+1];
    int[] PMram = new int[number_of_pms+1];
    PMcpu[0] = 0;
    PMram[0] = 0;
    for (int i=1; i<number_of_pms+1; i++) {
        PMcpu[i] = pms.get(i-1).get_cpu();
        PMram[i] = pms.get(i-1).get_ram();
    }

    IntVar[] VMS = model.intVarArray("VMS", number_of_vms, 0, number_of_pms);

    // capacity constraints
    BoolVar[][] VMi_hosted_by_PMj = model.boolVarMatrix(number_of_pms+1, number_of_vms+1);

    for (int i=0; i<number_of_vms; i++) {
        model.arithm(VMS[i], "!=", 0).post();
    }

    for (int pm_i=1; pm_i<number_of_pms+1; pm_i++) {
        for (int vm_i=1; vm_i<number_of_vms+1; vm_i++) {
            // below is the functionality for 2 lines below
            // reifyXeqC(X, C, A) => (X == C) ? A=1 : A=0;
            model.reifyXeqC(VMS[vm_i-1], pm_i, VMi_hosted_by_PMj[pm_i][vm_i]);
        }
    }

    // here is the constraint to make sure the total VMs assigned to a PM
    // demand less that the PM's resources
    for (int i=1; i<number_of_pms+1; i++) {
        model.scalar(VMi_hosted_by_PMj[i], VMcpu, "<=", PMcpu[i]).post();
        model.scalar(VMi_hosted_by_PMj[i], VMram, "<=", PMram[i]).post();
    }

    // a constraint to have a number of PMs
    IntVar no_of_PM = model.intVar("#PM", 0, number_of_pms+1);

    // here we link the no_of_PM to the count of unique values in VMS (basically we
    // get a number of used PMs)
    model.nValues(VMS, no_of_PM).post();

    model.setObjective(false, no_of_PM); //false => model.MINIMIZE

    // here we define the array that will hold the final allocation vector (basically
    // we get a copy of VMS' values so that we have it later)
    int[] vm_alloc = new int[number_of_vms];
    int no_of_allocated_pms = number_of_pms;

    while(model.getSolver().solve()) {
        for (int i = 0; i < number_of_vms; i++) {
            vm_alloc[i] = VMS[i].getValue();
        }

        System.out.println("Number of used PMs: " + (no_of_PM.getValue()));
        no_of_allocated_pms = no_of_PM.getValue();

    }