Maximal: Comparison of Optimization Modeling Software for Python - Oct 2012
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The document compares several Python-based optimization modeling software tools: MPLPY, PULP-OR, PYOMO, CPLEX API for Python, and GUROBI API for Python. It provides examples of how to define indexes, data, variables, objectives, and constraints for a sample cutstock optimization model using each tool.
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![Indexing
MPL:
cutNames # [w1, w2, ... w8]
patternNames # [p1, p2, ..., p29]
priceSheet # 28
sheetsAvail # 2000
sutDemand # [500, 400, 300, 450, 350, 200, 800, 200]
cutsInPattern # [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],.. ,
0, 0, 0, 0, 0, 0, 0, 0, 0]
Model model = mpl.Models.Add(CutStock")
mod.IndexSets.AddNameSet("cuts", cutNames)
mod.IndexSets.AddNameSet("patterns", patternNames)
Copyright 息 2012 Maximal Software, Inc. All rights reserved](https://image.slidesharecdn.com/informsphoenixoct2012pythonmod-121204035934-phpapp02/85/Maximal-Comparison-of-Optimization-Modeling-Software-for-Python-Oct-2012-3-320.jpg)
![Data
MPL:
model.DataConstants.Add("PriceSheet", priceSheet)
model.DataConstants.Add("SheetsAvail", sheetsAvail)
model.DataVectors.AddDense("CutDemand[cuts]", cutDemand)
model.DataVectors.Add("CutsInPattern[patterns, cuts]",
cutsInPattern)
PULP-OR:
CutsInPattern = makeDict([Cuts,Patterns],CutsInPattern)
CutDemand = makeDict([Cuts],CutDemand)
PYOMO:
tmp = {}
for i in range(len(Cuts)):
tmp[Cuts[i]] = CutDemand[i]
CutDemand = tmp
Copyright 息 2012 Maximal Software, Inc. All rights reserved](https://image.slidesharecdn.com/informsphoenixoct2012pythonmod-121204035934-phpapp02/85/Maximal-Comparison-of-Optimization-Modeling-Software-for-Python-Oct-2012-4-320.jpg)
![Variables
MPL:
model.PlainVariables.Add("SheetsCut", "-> T1")
model.PlainVariables.Add("TotalCost", "-> TC")
model.VariableVectors.Add("PatternCount[patterns]", "-> """)
model.VariableVectors.Add("ExcessCuts[cuts]", "-> X")
PULP-OR:
SheetsCut = LpVariable("SheetsCut",0)
TotalCost = LpVariable("TotalCost",0)
PatternCount = LpVariable.dicts("PatternCount",Patterns, lowBound
= 0)
ExcessCuts = LpVariable.dicts("ExcessCuts",Cuts, lowBound = 0)
PYOMO:
model.SheetsCut = Var()
model.TotalCost = Var()
model.PatternCount = Var(Patterns, bounds=(0,None))
model.ExcessCuts = Var(Cuts, bounds=(0,None))
Copyright 息 2012 Maximal Software, Inc. All rights reserved](https://image.slidesharecdn.com/informsphoenixoct2012pythonmod-121204035934-phpapp02/85/Maximal-Comparison-of-Optimization-Modeling-Software-for-Python-Oct-2012-5-320.jpg)
![Variables
CPLEX:
cpx = cplex.Cplex()
cpx.variables.add(names = ["SheetsCut"], lb = [0], ub =
[cplex.infinity])
cpx.variables.add(names = ["TotalCost"], lb = [0], ub =
[cplex.infinity], obj = [1])
cpx.variables.add(names = Patterns)
cpx.variables.add(names = Cuts)
GUROBI:
SheetsCut = m.addVar(0, GRB.INFINITY, 0,
GRB.CONTINUOUS,"SheetsCut")
TotalCost = m.addVar(0, GRB.INFINITY, 1, GRB.CONTINUOUS,"TotCost")
PatternCount = []
for i in range(patcount):
newvar = m.addVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS,
Patterns[i])
PatternCount += [newvar]
Copyright 息 2012 Maximal Software, Inc. All rights reserved](https://image.slidesharecdn.com/informsphoenixoct2012pythonmod-121204035934-phpapp02/85/Maximal-Comparison-of-Optimization-Modeling-Software-for-Python-Oct-2012-6-320.jpg)
![Constraints
MPL:
model.PlainConstraints.Add("TotCost",
"TotalCost = PriceSheet*SheetsCut")
model.PlainConstraints.Add("RawAvail", "SheetsCut < SheetsAvail")
model.PlainConstraints.Add("Sheets",
"SheetsCut = SUM(patterns: PatternCount[patterns])")
model.ConstraintVectors.Add("CutReq[cuts]",
"SUM(patterns: CutsInPattern[patterns, cuts] *
PatternCount[patterns])=
CutDemand[cuts] + ExcessCuts[cuts]")
Copyright 息 2012 Maximal Software, Inc. All rights reserved](https://image.slidesharecdn.com/informsphoenixoct2012pythonmod-121204035934-phpapp02/85/Maximal-Comparison-of-Optimization-Modeling-Software-for-Python-Oct-2012-8-320.jpg)
![Constraints
PULP-OR:
prob += TotalCost == PriceSheet*SheetsCut,"TotCost
prob += SheetsCut <= SheetsAvail,"RawAvail
for c in Cuts:
prob += lpSum([CutsInPattern[c][p]*PatternCount[p] for p in
Patterns]) == CutDemand[c] + ExcessCuts[c],"CutReq" + str(c)
PYOMO:
model.TotCost = Constraint(expr = model.TotalCost
== PriceSheet* model.SheetsCut)
model.RawAvail = Constraint(expr = model.SheetsCut <= SheetsAvail)
model.CutReq = Constraint(Cuts)
for c in Cuts:
model.CutReq.add(c,expr=
sum(CutsInPattern[c][p]*model.PatternCount[p] for p in Patterns)
== CutDemand[c] + model.ExcessCuts[c])
Copyright 息 2012 Maximal Software, Inc. All rights reserved](https://image.slidesharecdn.com/informsphoenixoct2012pythonmod-121204035934-phpapp02/85/Maximal-Comparison-of-Optimization-Modeling-Software-for-Python-Oct-2012-9-320.jpg)
![Constraints
CPLEX:
cpx.linear_constraints.add(lin_expr =
[cplex.SparsePair(ind = ["SheetsCut", "TotalCost"],
val = [-PriceSheet, 1.0])], senses = ["E"], rhs = [0])
cpx.linear_constraints.add(lin_expr =
[cplex.SparsePair(ind = indA,val = valA)], senses = ["E"], rhs =
[0])
for c in range(cutcount):
cpx.linear_constraints.add(lin_expr = [cplex.SparsePair(ind =
indP[c],val = valP[c])], senses = ["E"], rhs = [CutDemand[c]])
Copyright 息 2012 Maximal Software, Inc. All rights reserved](https://image.slidesharecdn.com/informsphoenixoct2012pythonmod-121204035934-phpapp02/85/Maximal-Comparison-of-Optimization-Modeling-Software-for-Python-Oct-2012-10-320.jpg)
![Constraints
GUROBI:
m.addConstr(LinExpr(PriceSheet, SheetsCut), GRB.EQUAL,
TotalCost,"TotCostCalc")
m.addConstr(LinExpr(1, SheetsCut), GRB.LESS_EQUAL, SheetsAvail,"RawAvail")
sheetsB = LinExpr()
for i in range(patcount):
sheetsB.addTerms(1, PatternCount[i])m.addConstr(sheetsB, GRB.EQUAL,
sheetsCut,"Sheets")
for c in range(cutcount):
cutReqB = LinExpr()
cutReqB.addTerms(-1,ExcessCuts[c])
for p in range(patcount):
cutReqB.addTerms(CutsInPattern[c][p],PatternCount[p])
m.addConstr(cutReqB, GRB.EQUAL, CutDemand[c],"CutReq_")
Copyright 息 2012 Maximal Software, Inc. All rights reserved](https://image.slidesharecdn.com/informsphoenixoct2012pythonmod-121204035934-phpapp02/85/Maximal-Comparison-of-Optimization-Modeling-Software-for-Python-Oct-2012-11-320.jpg)
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- 1. INFORMS Phoenix October 2012 Comparison of Optimization Modeling Software for Python Presented by Bjarni Kristjansson Maximal Software, Inc. Copyright 息 2012 Maximal Software, Inc. All rights reserved 1
- 2. Optimization Modeling Tools for Python MPLPY MPL Optimax PULP-OR PYOMO CPLEX API for Python GUROBI API for Python GAMS API for Python Copyright 息 2012 Maximal Software, Inc. All rights reserved 2
- 3. Indexing MPL: cutNames # [w1, w2, ... w8] patternNames # [p1, p2, ..., p29] priceSheet # 28 sheetsAvail # 2000 sutDemand # [500, 400, 300, 450, 350, 200, 800, 200] cutsInPattern # [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],.. , 0, 0, 0, 0, 0, 0, 0, 0, 0] Model model = mpl.Models.Add(CutStock") mod.IndexSets.AddNameSet("cuts", cutNames) mod.IndexSets.AddNameSet("patterns", patternNames) Copyright 息 2012 Maximal Software, Inc. All rights reserved
- 4. Data MPL: model.DataConstants.Add("PriceSheet", priceSheet) model.DataConstants.Add("SheetsAvail", sheetsAvail) model.DataVectors.AddDense("CutDemand[cuts]", cutDemand) model.DataVectors.Add("CutsInPattern[patterns, cuts]", cutsInPattern) PULP-OR: CutsInPattern = makeDict([Cuts,Patterns],CutsInPattern) CutDemand = makeDict([Cuts],CutDemand) PYOMO: tmp = {} for i in range(len(Cuts)): tmp[Cuts[i]] = CutDemand[i] CutDemand = tmp Copyright 息 2012 Maximal Software, Inc. All rights reserved
- 5. Variables MPL: model.PlainVariables.Add("SheetsCut", "-> T1") model.PlainVariables.Add("TotalCost", "-> TC") model.VariableVectors.Add("PatternCount[patterns]", "-> """) model.VariableVectors.Add("ExcessCuts[cuts]", "-> X") PULP-OR: SheetsCut = LpVariable("SheetsCut",0) TotalCost = LpVariable("TotalCost",0) PatternCount = LpVariable.dicts("PatternCount",Patterns, lowBound = 0) ExcessCuts = LpVariable.dicts("ExcessCuts",Cuts, lowBound = 0) PYOMO: model.SheetsCut = Var() model.TotalCost = Var() model.PatternCount = Var(Patterns, bounds=(0,None)) model.ExcessCuts = Var(Cuts, bounds=(0,None)) Copyright 息 2012 Maximal Software, Inc. All rights reserved
- 6. Variables CPLEX: cpx = cplex.Cplex() cpx.variables.add(names = ["SheetsCut"], lb = [0], ub = [cplex.infinity]) cpx.variables.add(names = ["TotalCost"], lb = [0], ub = [cplex.infinity], obj = [1]) cpx.variables.add(names = Patterns) cpx.variables.add(names = Cuts) GUROBI: SheetsCut = m.addVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS,"SheetsCut") TotalCost = m.addVar(0, GRB.INFINITY, 1, GRB.CONTINUOUS,"TotCost") PatternCount = [] for i in range(patcount): newvar = m.addVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, Patterns[i]) PatternCount += [newvar] Copyright 息 2012 Maximal Software, Inc. All rights reserved
- 7. Objective MPL: model.Objectives.Add("TotalCost", ObjectSense.Minimize) PULP-OR: prob += TotalCost," PYOMO: model.objective = Objective(expr=1.0*model.TotalCost) CPLEX: cpx.objective.set_sense(cpx.objective.sense.minimize) GUROBI: m.ModelSense = 1 m.update() Copyright 息 2012 Maximal Software, Inc. All rights reserved
- 8. Constraints MPL: model.PlainConstraints.Add("TotCost", "TotalCost = PriceSheet*SheetsCut") model.PlainConstraints.Add("RawAvail", "SheetsCut < SheetsAvail") model.PlainConstraints.Add("Sheets", "SheetsCut = SUM(patterns: PatternCount[patterns])") model.ConstraintVectors.Add("CutReq[cuts]", "SUM(patterns: CutsInPattern[patterns, cuts] * PatternCount[patterns])= CutDemand[cuts] + ExcessCuts[cuts]") Copyright 息 2012 Maximal Software, Inc. All rights reserved
- 9. Constraints PULP-OR: prob += TotalCost == PriceSheet*SheetsCut,"TotCost prob += SheetsCut <= SheetsAvail,"RawAvail for c in Cuts: prob += lpSum([CutsInPattern[c][p]*PatternCount[p] for p in Patterns]) == CutDemand[c] + ExcessCuts[c],"CutReq" + str(c) PYOMO: model.TotCost = Constraint(expr = model.TotalCost == PriceSheet* model.SheetsCut) model.RawAvail = Constraint(expr = model.SheetsCut <= SheetsAvail) model.CutReq = Constraint(Cuts) for c in Cuts: model.CutReq.add(c,expr= sum(CutsInPattern[c][p]*model.PatternCount[p] for p in Patterns) == CutDemand[c] + model.ExcessCuts[c]) Copyright 息 2012 Maximal Software, Inc. All rights reserved
- 10. Constraints CPLEX: cpx.linear_constraints.add(lin_expr = [cplex.SparsePair(ind = ["SheetsCut", "TotalCost"], val = [-PriceSheet, 1.0])], senses = ["E"], rhs = [0]) cpx.linear_constraints.add(lin_expr = [cplex.SparsePair(ind = indA,val = valA)], senses = ["E"], rhs = [0]) for c in range(cutcount): cpx.linear_constraints.add(lin_expr = [cplex.SparsePair(ind = indP[c],val = valP[c])], senses = ["E"], rhs = [CutDemand[c]]) Copyright 息 2012 Maximal Software, Inc. All rights reserved
- 11. Constraints GUROBI: m.addConstr(LinExpr(PriceSheet, SheetsCut), GRB.EQUAL, TotalCost,"TotCostCalc") m.addConstr(LinExpr(1, SheetsCut), GRB.LESS_EQUAL, SheetsAvail,"RawAvail") sheetsB = LinExpr() for i in range(patcount): sheetsB.addTerms(1, PatternCount[i])m.addConstr(sheetsB, GRB.EQUAL, sheetsCut,"Sheets") for c in range(cutcount): cutReqB = LinExpr() cutReqB.addTerms(-1,ExcessCuts[c]) for p in range(patcount): cutReqB.addTerms(CutsInPattern[c][p],PatternCount[p]) m.addConstr(cutReqB, GRB.EQUAL, CutDemand[c],"CutReq_") Copyright 息 2012 Maximal Software, Inc. All rights reserved