本次澳洲代写主要为数学统计相关

MAST 90014针对工业CA第3部分的优化,2021

问题1
1考虑一下Land和Doig在其开创性论文中使用的以下问题:
最高77.9×1 + 76.8×2 + 89.6×3 + 97.1y1 + 31.3y2(1)
2 s.t.
10.9×1 + 3.6×2-40.8×3 + 43.9y1 + 7.1y2 + y3 = 82.3(2)
−86.8×1 + 32.7×2 + 24.3×3 + 13.8y1 − 12.6y2 + y4 = 77.3(3)
60.9×1 + 68.9×2 + 69.0×3-56.9y1 + 22.5y2 = 86.5(4)

x,x,x∈Z(5)
— 1 2 3 +
y,y,y,y∈R(6)
1 2 3 4 +

(7)
(a)使用以下规则获得完整的分支定界树。对于每个节点,
指示其编号(按浏览顺序)。同时指出分支约束
和修剪叶节点的原因。

变量选择:始终分支到索引最小的分数变量。

f•节点选择:深度优先(始终使用分支≤的子对象进行探索
约束。

(b)使用以下规则获得完整的分支定界树。 对于每个节点,
指示其编号(按浏览顺序)。 同时指出修剪的原因
叶节点。
•变量选择:始终分支到具有最大索引的分数变量。
•节点选择:节点选择:最佳绑定(始终以最佳方式探索孩子
有前途的界限)

MAST 90014 Optimisation for Industry CA Part 3, 2021
Question 1
Consider the following problem, used by Land and Doig in their seminal paper:
max 77.9×1 + 76.8×2 + 89.6×3 + 97.1y1 + 31.3y2 (1)
s.t.
10.9×1 + 3.6×2 − 40.8×3 + 43.9y1 + 7.1y2 + y3 = 82.3 (2)
−86.8×1 + 32.7×2 + 24.3×3 + 13.8y1 − 12.6y2 + y4 = 77.3 (3)
60.9×1 + 68.9×2 + 69.0×3 − 56.9y1 + 22.5y2 = 86.5 (4)
x1, x2, x3 ∈ Z+ (5)
y1, y2, y3, y4 ∈ R+ (6)
(7)
(a) obtain the complete branch-and-bound tree using the following rules. For each node,
indicate its number (in order of exploration). Also indicate the branching constraints
and the reason for pruning leaf nodes.
• variable selection: always branch on the fractional variable with smallest index.
• node selection: depth-first (always explore first the child with the ≤ branching
constraint.

(b) obtain the complete branch-and-bound tree using the following rules. For each node,
indicate its number (in order of exploration). Also indicate the reason for pruning in
leaf nodes.
• variable selection: always branch on the fractional variable with largest index
• node selection: node selection: best-bound (always explore the child with the best
promising bound)


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