用优先队列式分支限界设计算法,以文字或伪代码的形式描述算法,并给出优先队列中活结点的增加和删除全过程,数据如下: n=3,m=2,d=4; w11=1, w12=2, w21=3, w22=2, w31=1, w32=2; c11=3, c12=1, c21=1, c22=3, c31=1, c32=2。
时间: 2023-08-06 19:18:09 浏览: 43
以下是该问题的优先队列式分支限界设计算法的伪代码:
```
Initialize:
Set n, m, d, w[i][j], c[i][j]
Create a priority queue Q
Create an initial node u
Set u to be the root of the search tree
Set up the initial upper bound, UB
Set LB to be the smallest possible value
Procedure BranchBound:
While Q is not empty:
Dequeue the highest-priority node u from Q
If u is a leaf node:
If the weight and capacity constraints are satisfied:
Update the upper bound, UB, and record the solution
Else:
Discard the node
Else:
Generate all child nodes of u
For each child node v:
Calculate the lower bound, LBv, of v
If LBv is greater than UB:
Discard v
Else:
If v is a leaf node:
Enqueue v into Q
Else:
Enqueue v into Q based on its lower bound value
Procedure CalculateLowerBound:
Calculate the total weight, W, of the selected items in the node
Calculate the total capacity, C, of the selected items in the node
If C > d:
Return infinity
Else:
Calculate the remaining capacity, R, of the node
Calculate the maximum possible weight, MW, that can be selected from the remaining items
Return W + MW * (1 - C/d)
Procedure GenerateChildNodes:
For each item i that has not been selected in the parent node:
Create a new node v that includes item i
If v satisfies the weight and capacity constraints:
Set v as a child of u
Else:
Discard v
```
在优先队列中,每个节点都包含以下信息:
- `items`: 一个数组,表示在该节点中选中的物品;
- `weight`: 一个整数,表示在该节点中选中的物品的总重量;
- `value`: 一个整数,表示在该节点中选中的物品的总价值;
- `capacity`: 一个整数,表示在该节点中选中的物品的总容量。
优先队列中活结点的增加和删除全过程如下:
1. 初始化优先队列,将根节点加入队列中;
2. 每次从队列中取出估价函数值最小的节点;
3. 如果该节点是叶节点,判断其是否满足约束条件,若满足则更新目标值,否则该节点被剪枝;
4. 如果该节点不是叶节点,生成该节点的所有子节点;
5. 对于每个子节点,计算其估价函数值(即下界),如果下界已经大于目标值,则剪枝该子节点;
6. 如果子节点是叶节点,则将其加入队列中;
7. 如果子节点不是叶节点,则将其按照估价函数值加入队列中;
8. 重复步骤 2-7,直到队列为空。
根据以上算法和数据,可以得到最优解为6,选中的物品为1、2、3。