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‎extend/backup/VRP&MST/data.md‎

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| | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P |
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|----|----|----|------|--------|------|-------|--------|----|-----|------|------|------|--------|------|---------|------|
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| A | | 4 | | 3.5 | | 6.2 | 3.5 | 6 | | | | | | | | |
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| B | | | 3.7 | | 4.5 | | | | 3 | | | | | | | |
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| C | | | | 3.4 | | | | | | 5.9 | | | | | | |
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| D | | | | | | | | | | | | | | | | |
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| E | | | | | | 3.3 | | | | | | | | | | |
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| F | | | | | | | | | | | 7.2 | 3 | | | | |
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| G | | | | | | | | | | | 7 | | 7.3 | | | |
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| H | | | | | | | | | | | | | 8.8 | | 5.8 | 3.4 |
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| I | | | | | | | | | | | | 11 | | | | |
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| J | | | | | | | | | | | | | | | 4.5 | |
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| K | | | | | | | | | | | | 7.5 | 3.1 | | | |
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| L | | | | | | | | | | | | | | | | |
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| M | | | | | | | | | | | | | | 4.3 | | |
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| N | | | | | | | | | | | | | | | | 8.4 |
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| O | | | | | | | | | | | | | | | | 6.9 |
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| P | | | | | | | | | | | | | | | | |
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‎extend/backup/VRP&MST/demo1.py‎

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import gurobipy
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model = gurobipy.Model("model")
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xs : gurobipy.tupledict = model.addVars(3, 4, lb=1, ub=5)
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cs = model.addConstrs((xs.sum(i, "*") == 1 for i in range(3)))
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model.setObjective()
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model.update()
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model.write('test.lp')

‎extend/backup/VRP&MST/demo2.py‎

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"""
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max: x + y + 2z
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s.t. x + 2y + 3z <= 4
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x + y >= 1
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x, y, z ∈{0, 1}
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"""
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from gurobipy import *
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model = Model("model")
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x = model.addVar(lb=0, ub=1, vtype=GRB.BINARY, name='xaxis')
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y = model.addVar(lb=0, ub=1, vtype=GRB.BINARY, name='yaxis')
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z = model.addVar(lb=0, ub=1, vtype=GRB.BINARY, name='zaxis')
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objectFunc = model.setObjective(x + y + 2 * z, sense=GRB.MAXIMIZE)
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constraint1 = model.addConstr(x + 2 * y + 3 * z <= 4, name='constraint1')
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constraint2 = model.addConstr(x + y >= 1, name='constraint2')
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model.update()
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model.optimize()
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xvar : Var = model.getVarByName('xaxis')
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print(xvar.x)

‎extend/backup/VRP&MST/demo3.py‎

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from gurobipy import *
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dic = multidict({
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"k1" : [1, 2, 45],
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"k2" : [3, 65, 1]
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})
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print(dic)
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from pympler import asizeof
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class MyClass:
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def __init__(self, data):
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self.data : list = data
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obj = MyClass([1, 2, 3, 67, 1, 2, 3, 671, 1, 2, 3, 617, 1, 2, 3, 67, 1, 2, 3, 67, 1, 2, 11])
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print(asizeof.asizeof(obj.data))
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‎extend/backup/VRP&MST/demo4.py‎

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import gurobipy
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from gurobipy import GRB
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import numpy
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# https://zhuanlan.zhihu.com/p/651080846
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# 边的定义和距离矩阵的初始化
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edges = {
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(0, 1): 4, (0, 3): 3.5, (0, 5): 6.2, (0, 7): 3.5, (0, 8): 6,
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(1, 2): 3.7, (1, 4): 4.5, (1, 9): 3,
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(2, 3): 3.4, (2, 10): 5.9,
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(4, 5): 3.3,
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(5, 10): 7.2, (5, 11): 3,
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(6, 10): 7, (6, 12): 7.3,
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(7, 12): 8.8, (7, 14): 5.8, (7, 15): 3.4,
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(8, 11): 11,
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(9, 14): 4.5,
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(10, 12): 7.5, (10, 13): 3.1,
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(12, 13): 4.3,
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(13, 15): 8.4,
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(14, 15): 6.9
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}
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distances = numpy.full((16, 16), GRB.INFINITY)
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for k, v in edges.items():
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i, j = k
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distances[i][j] = v
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distances[j][i] = v
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numpy.fill_diagonal(distances, 0) # 自己到自己的距离为0
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# 问题参数：客户数量和车辆数
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n = 15 # 客户点数目
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m = 3 # 车辆数目
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# 创建优化模型
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model = gurobipy.Model("VRP")
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# 决策变量：X[k, i, j] 表示车辆k是否从i点行驶到j点
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X = model.addVars(m, 1 + n, 1 + n, vtype=GRB.BINARY, name='X')
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# 目标函数：最小化总行驶距离
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objFunc = gurobipy.quicksum(
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distances[i, j] * X[k, i, j]
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for k in range(m)
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for i in range(n + 1)
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for j in range(n + 1)
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)
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model.setObjective(objFunc, GRB.MINIMIZE)
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# 约束条件：每辆车从起点出发
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for k in range(m):
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model.addConstr(gurobipy.quicksum(X[k, 0, j] for j in range(1, n + 1)) == 1)
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# 约束条件：每辆车必须回到起点
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for k in range(m):
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model.addConstr(gurobipy.quicksum(X[k, j, 0] for j in range(1, n + 1)) == 1)
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# 流量平衡约束：每个客户点的进出流量必须相同
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for k in range(m):
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for j in range(1, n + 1):
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model.addConstr(
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gurobipy.quicksum(X[k, i, j] for i in range(n + 1) if i != j) ==
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gurobipy.quicksum(X[k, j, i] for i in range(n + 1) if i != j),
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name=''
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)
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# 访问所有客户点的约束：每个客户点必须被访问一次
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for j in range(1, n + 1):
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model.addConstr(
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gurobipy.quicksum(X[k, i, j] for k in range(m) for i in range(n + 1) if i != j) == 1
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)
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# 禁止不可达的路径
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for k in range(m):
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for i in range(n + 1):
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for j in range(n + 1):
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if distances[i, j] == GRB.INFINITY:
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model.addConstr(X[k, i, j] == 0)
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if i == j:
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model.addConstr(X[k, i, j] == 0)
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# https://zhuanlan.zhihu.com/p/159270139
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# 子回路消除约束：基于 MTZ
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U = model.addVars(m, 1 + n, lb=0, ub=n, vtype=GRB.INTEGER, name='U')
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# MTZ 约束：防止车辆走子回路
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for k in range(m):
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for i in range(1, n + 1):
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for j in range(1, n + 1):
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if i != j:
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model.addConstr(U[k, i] - U[k, j] + n * X[k, i, j] <= n - 1)
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# 起点顺序号为0
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for k in range(m):
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model.addConstr(U[k, 0] == 0)
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# 更新模型并求解
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model.update()
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model.optimize()
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# 检查是否找到最优解
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if model.status == GRB.OPTIMAL:
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print(f"最小总行驶距离: {model.objVal}")
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else:
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print(f"没有找到最优解，状态码: {model.status}")
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model.computeIIS()
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model.write("model.lp")

‎extend/backup/VRP&MST/demo5.py‎

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import gurobipy
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from gurobipy import GRB
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# 点数目
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n = 16
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# 点名字
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nodes = [chr(x) for x in range(n + 65)]
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# 距离邻接矩阵
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edges = [
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('A', 'B', 4), ('A', 'D', 3.5), ('A', 'F', 6.2), ('A', 'G', 3.5), ('A', 'H', 6),
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('B', 'C', 3.7), ('B', 'E', 4.5), ('B', 'I', 3),
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('C', 'D', 3.4), ('C', 'J', 5.9),
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('E', 'F', 3.3),
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('F', 'K', 7.2), ('F', 'L', 3),
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('G', 'K', 7), ('G', 'M', 7.3),
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('H', 'M', 8.8), ('H', 'O', 5.8), ('H', 'P', 3.4),
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('I', 'L', 11),
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('J', 'O', 4.5),
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('K', 'L', 7.5), ('K', 'M', 3.1),
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('M', 'N', 4.3),
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('N', 'P', 8.4),
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('O', 'P', 6.9)
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] # len == 25
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# 创建模型
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model = gurobipy.Model('mst')
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# 建立变量，X[i,j]表示边(i,j)是否被选中
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X = model.addVars(edges, vtype=GRB.BINARY, name="X")
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# 目标函数：最小化边的权重和
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model.setObjective(gurobipy.quicksum(X.select(i, j, '*')[0] * w for i, j, w in edges), GRB.MINIMIZE)
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# 添加约束：选择的边数等于节点数减一
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model.addConstr(gurobipy.quicksum(X.select(i, j, '*')[0] for i, j, w in edges) == n - 1, "edge_count")
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# 求解模型
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model.update()
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model.optimize()
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# 输出结果
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if model.status == GRB.OPTIMAL:
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print("最优解找到")
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ws = 0.0
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for i, j, w in edges:
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if X.select(i, j, '*')[0].X > 0.5:
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print(f"边 ({i}, {j}) 被选中，权重: {w}")
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ws += w
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print("总权重：%f" % ws)
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else:
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print("没有找到最优解")

‎extend/backup/VRP&MST/demo6.py‎

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import gurobipy
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from gurobipy import GRB
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import numpy
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from itertools import combinations
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# 边的定义和距离矩阵的初始化
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edges = {
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(0, 1): 4, (0, 3): 3.5, (0, 5): 6.2, (0, 7): 3.5, (0, 8): 6,
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(1, 2): 3.7, (1, 4): 4.5, (1, 9): 3,
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(2, 3): 3.4, (2, 10): 5.9,
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(4, 5): 3.3,
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(5, 10): 7.2, (5, 11): 3,
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(6, 10): 7, (6, 12): 7.3,
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(7, 12): 8.8, (7, 14): 5.8, (7, 15): 3.4,
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(8, 11): 11,
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(9, 14): 4.5,
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(10, 12): 7.5, (10, 13): 3.1,
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(12, 13): 4.3,
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(13, 15): 8.4,
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(14, 15): 6.9
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}
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distances = numpy.full((16, 16), GRB.INFINITY)
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for k, v in edges.items():
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i, j = k
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distances[i][j] = v
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distances[j][i] = v
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numpy.fill_diagonal(distances, 0) # 自己到自己的距离为0
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# 问题参数：客户数量和车辆数
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n = 15 # 客户点数目
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m = 3 # 车辆数目
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# 创建优化模型
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model = gurobipy.Model("VRP")
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# 决策变量：X[k, i, j] 表示车辆k是否从i点行驶到j点
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X = model.addVars(m, 1 + n, 1 + n, vtype=GRB.BINARY, name='X')
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# 目标函数：最小化总行驶距离
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objFunc = gurobipy.quicksum(
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distances[i, j] * X[k, i, j]
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for k in range(m)
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for i in range(n + 1)
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for j in range(n + 1)
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)
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model.setObjective(objFunc, GRB.MINIMIZE)
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# 约束条件：每辆车从起点出发
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for k in range(m):
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model.addConstr(gurobipy.quicksum(X[k, 0, j] for j in range(1, n + 1)) == 1)
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# 约束条件：每辆车必须回到起点
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for k in range(m):
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model.addConstr(gurobipy.quicksum(X[k, j, 0] for j in range(1, n + 1)) == 1)
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# 流量平衡约束：每个客户点的进出流量必须相同
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for k in range(m):
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for j in range(1, n + 1):
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model.addConstr(
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gurobipy.quicksum(X[k, i, j] for i in range(n + 1) if i != j) ==
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gurobipy.quicksum(X[k, j, i] for i in range(n + 1) if i != j)
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)
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# 访问所有客户点的约束：每个客户点必须被访问一次
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for j in range(1, n + 1):
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model.addConstr(
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gurobipy.quicksum(X[k, i, j] for k in range(m) for i in range(n + 1) if i != j) == 1
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)
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# 禁止不可达的路径
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for k in range(m):
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for i in range(n + 1):
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for j in range(n + 1):
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if distances[i, j] == GRB.INFINITY:
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model.addConstr(X[k, i, j] == 0)
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if i == j:
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model.addConstr(X[k, i, j] == 0)
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# DFJ子回路消除约束：对于每一个真子集S，确保边数不超过|S|-1
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for k in range(m):
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for S_size in range(2, n + 1): # 从大小2的子集开始
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for S in combinations(range(1, n + 1), S_size): # 获取顶点集合V的真子集S
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# 计算集合S中每一对节点i, j的连通边数
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model.addConstr(
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gurobipy.quicksum(X[k, i, j] for i in S for j in range(1, n + 1) if j not in S) +
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gurobipy.quicksum(X[k, j, i] for j in S for i in range(1, n + 1) if i not in S)
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<= S_size - 1
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)
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# 更新模型并求解
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model.update()
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model.optimize()
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# 检查是否找到最优解
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if model.status == GRB.OPTIMAL:
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print(f"最小总行驶距离: {model.objVal}")
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else:
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# print(f"没有找到最优解，状态码: {model.status}")
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model.computeIIS()
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model.write("model.lp")

‎extend/backup/VRP&MST/facilityPY.lp‎

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\ Model facility
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\ LP format - for model browsing. Use MPS format to capture full model detail.
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Minimize
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12000 open[0] + 15000 open[1] + 17000 open[2] + 13000 open[3]
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+ 16000 open[4] + 4000 trans[0,0] + 2000 trans[0,1] + 3000 trans[0,2]
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+ 2500 trans[0,3] + 4500 trans[0,4] + 2500 trans[1,0] + 2600 trans[1,1]
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+ 3400 trans[1,2] + 3000 trans[1,3] + 4000 trans[1,4] + 1200 trans[2,0]
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+ 1800 trans[2,1] + 2600 trans[2,2] + 4100 trans[2,3] + 3000 trans[2,4]
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+ 2200 trans[3,0] + 2600 trans[3,1] + 3100 trans[3,2] + 3700 trans[3,3]
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+ 3200 trans[3,4]
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Subject To
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Capacity[0]: - 20 open[0] + trans[0,0] + trans[1,0] + trans[2,0]
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+ trans[3,0] <= 0
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Capacity[1]: - 22 open[1] + trans[0,1] + trans[1,1] + trans[2,1]
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+ trans[3,1] <= 0
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Capacity[2]: - 17 open[2] + trans[0,2] + trans[1,2] + trans[2,2]
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+ trans[3,2] <= 0
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Capacity[3]: - 19 open[3] + trans[0,3] + trans[1,3] + trans[2,3]
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+ trans[3,3] <= 0
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Capacity[4]: - 18 open[4] + trans[0,4] + trans[1,4] + trans[2,4]
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+ trans[3,4] <= 0
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Demand[0]: trans[0,0] + trans[0,1] + trans[0,2] + trans[0,3] + trans[0,4]
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= 15
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Demand[1]: trans[1,0] + trans[1,1] + trans[1,2] + trans[1,3] + trans[1,4]
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= 18
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Demand[2]: trans[2,0] + trans[2,1] + trans[2,2] + trans[2,3] + trans[2,4]
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= 14
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Demand[3]: trans[3,0] + trans[3,1] + trans[3,2] + trans[3,3] + trans[3,4]
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= 20
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Bounds
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Binaries
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open[0] open[1] open[2] open[3] open[4]
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End

‎extend/backup/VRP&MST/gurobi-mst.png‎

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