这是一个我认为可以满足您所有问题的示例模型。
一旦您将第二个索引设置为板块P = {1, 2, 3}
在本例中,对于 3 个板,那么我们需要对决策变量进行双重索引来表示材料的分配m
到盘子p
。在此示例中,有 4 种材料、3 个板。
这里可能存在许多其他约束变化,但我添加的约束回答了您关于聚合电导率的问题。请注意,我还添加了一个约束,以确保为每个板分配 1 个且仅 1 个材料。根据模型中的其他约束,您可能/可能不需要这个,但它是防止虚假答案的良好保险。这也是使用函数 - 规则组合的“for every”约束样式的示例pyomo
.
结果...铝和奶酪三明治...:)
# material selection model
import pyomo.environ as pyo
# data
materials = ['steel', 'alum', 'carbon', 'cheese']
density = { 'steel' : 1.2,
'alum' : 0.8,
'carbon': 1.8,
'cheese': 0.7}
conductivity = {'steel' : 40.8,
'alum' : 30.1,
'carbon': 42.4,
'cheese': 15.3}
price = { 'steel' : 2.3,
'alum' : 3.5,
'carbon': 5.8,
'cheese': 6.0}
# t area
plate_dims = { 1: (10, 150),
2: (12.5, 200),
3: (8, 125)}
mdl = pyo.ConcreteModel('material selector')
# SETS (used to index the decision variable and the parameters)
mdl.M = pyo.Set(initialize=materials)
mdl.P = pyo.Set(initialize=plate_dims.keys())
# VARIABLES
mdl.x = pyo.Var(mdl.M, mdl.P, domain=pyo.Binary) # select material M for plate P
# PARAMETERS
mdl.density = pyo.Param(mdl.M, initialize=density)
mdl.conductivity = pyo.Param(mdl.M, initialize=conductivity)
mdl.price = pyo.Param(mdl.M, initialize=price)
mdl.p_thickness = pyo.Param(mdl.P, initialize= {k:v[0] for k,v in plate_dims.items()})
mdl.p_area = pyo.Param(mdl.P, initialize= {k:v[1] for k,v in plate_dims.items()})
# OBJ (minimize total density)
mdl.obj = pyo.Objective(expr=sum(mdl.x[m, p] * mdl.p_thickness[p]
* mdl.p_area[p] * mdl.density[m]
for m in mdl.M for p in mdl.P))
# CONSTRAINTS
# minimum conductivity
mdl.c1 = pyo.Constraint(expr=sum(mdl.x[m, p] * mdl.conductivity[m]/mdl.p_thickness[p]
for m in mdl.M for p in mdl.P) >= 5.0)
# must populate all plates with 1 material
def c2(model, plate):
return sum(mdl.x[m, plate] for m in mdl.M) == 1
mdl.c2 = pyo.Constraint(mdl.P, rule=c2)
# solve it
solver = pyo.SolverFactory('glpk')
result = solver.solve(mdl)
mdl.display()
Yields:
Model material selector
Variables:
x : Size=12, Index=x_index
Key : Lower : Value : Upper : Fixed : Stale : Domain
('alum', 1) : 0 : 0.0 : 1 : False : False : Binary
('alum', 2) : 0 : 0.0 : 1 : False : False : Binary
('alum', 3) : 0 : 1.0 : 1 : False : False : Binary
('carbon', 1) : 0 : 0.0 : 1 : False : False : Binary
('carbon', 2) : 0 : 0.0 : 1 : False : False : Binary
('carbon', 3) : 0 : 0.0 : 1 : False : False : Binary
('cheese', 1) : 0 : 1.0 : 1 : False : False : Binary
('cheese', 2) : 0 : 1.0 : 1 : False : False : Binary
('cheese', 3) : 0 : 0.0 : 1 : False : False : Binary
('steel', 1) : 0 : 0.0 : 1 : False : False : Binary
('steel', 2) : 0 : 0.0 : 1 : False : False : Binary
('steel', 3) : 0 : 0.0 : 1 : False : False : Binary
Objectives:
obj : Size=1, Index=None, Active=True
Key : Active : Value
None : True : 3600.0
Constraints:
c1 : Size=1
Key : Lower : Body : Upper
None : 5.0 : 6.516500000000001 : None
c2 : Size=3
Key : Lower : Body : Upper
1 : 1.0 : 1.0 : 1.0
2 : 1.0 : 1.0 : 1.0
3 : 1.0 : 1.0 : 1.0