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Benders reformulation #823

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Apr 19, 2023
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Benders reformulation #823

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72 changes: 6 additions & 66 deletions src/decomposition.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -291,26 +291,15 @@ function create_side_vars_constrs!(
::Env,
::Annotations
)
for (_, spform) in get_benders_sep_sps(masterform.parent_formulation)
nu_var = collect(values(filter(
v -> getduty(v.first) == BendSpSlackSecondStageCostVar,
getvars(spform)
)))[1]

name = "η[$(split(getname(spform, nu_var), "[")[end])"
nu_id = VarId(
getid(nu_var);
duty = MasterBendSecondStageCostVar,
assigned_form_uid = getuid(masterform)
)
for (spid, spform) in get_benders_sep_sps(masterform.parent_formulation)
name = "η[$(spid)]"
setvar!(
masterform, name, MasterBendSecondStageCostVar;
cost = 1.0,
lb = getperenlb(spform, nu_var),
ub = getperenub(spform, nu_var),
lb = -Inf,
ub = Inf,
kind = Continuous,
is_explicit = true,
id = nu_id
is_explicit = true
)
end
return
Expand All @@ -327,7 +316,7 @@ function instantiate_orig_vars!(
if haskey(annotations.vars_per_ann, sp_ann)
vars = annotations.vars_per_ann[sp_ann]
for (_, var) in vars
clonevar!(origform, spform, spform, var, BendSpSepVar, cost = 0.0)
clonevar!(origform, spform, spform, var, BendSpSepVar, cost = getperencost(origform, var))
end
end
return
Expand Down Expand Up @@ -416,55 +405,6 @@ function create_side_vars_constrs!(
end
end
end

sp_has_second_stage_cost = false
global_costprofit_ub = 0.0
global_costprofit_lb = 0.0
for (varid, _) in getvars(spform)
getduty(varid) == BendSpSepVar || continue
orig_var = getvar(origform, varid)
cost = getperencost(origform, orig_var)
if cost > 0
global_costprofit_ub += cost * getcurub(origform, orig_var)
global_costprofit_lb += cost * getcurlb(origform, orig_var)
elseif cost < 0
global_costprofit_ub += cost * getcurlb(origform, orig_var)
global_costprofit_lb += cost * getcurub(origform, orig_var)
end
end

if global_costprofit_ub > 0 || global_costprofit_lb < 0
sp_has_second_stage_cost = true
end

if sp_has_second_stage_cost
sp_id = getuid(spform)
# Cost constraint
nu_pos = setvar!(
spform, "ν⁺[$sp_id]", BendSpSlackSecondStageCostVar;
cost = getobjsense(spform) == MinSense ? 1.0 : -1.0,
lb = global_costprofit_lb,
ub = global_costprofit_ub,
kind = Continuous,
is_explicit = true
)
setcurlb!(spform, nu_pos, 0.0)
setcurub!(spform, nu_pos, Inf)

cost = setconstr!(
spform, "cost[$sp_id]", BendSpSecondStageCostConstr;
rhs = 0.0,
kind = Essential,
sense = getobjsense(spform) == MinSense ? Greater : Less,
is_explicit = true
)
spcoef[getid(cost), getid(nu_pos)] = 1.0

for (varid, _) in getvars(spform)
getduty(varid) == BendSpSepVar || continue
spcoef[getid(cost), varid] = - getperencost(origform, varid)
end
end
return
end

Expand Down
181 changes: 181 additions & 0 deletions test/unit/MathProg/benders_decomposition.jl
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Original file line number Diff line number Diff line change
@@ -0,0 +1,181 @@
function benders_decomposition()
"""
original
min
x1 + 4x2 + 2y1 + 3y2
s.t.
x1 + x2 >= 0
- x1 + 3x2 - y1 + 2y2 >= 2
x1 + 3x2 + y1 + y2 >= 3
y1 + y2 >= 0

continuous
original
y1, y2

integer
original
x1, x2

bounds
x1 >= 0
x2 >= 0
y1 >= 0
y2 >= 0
"""

env = Coluna.Env{Coluna.MathProg.VarId}(Coluna.Params())

origform = Coluna.MathProg.create_formulation!(
env, Coluna.MathProg.Original()
)

# Variables
vars = Dict{String, Coluna.MathProg.VarId}()
variables_infos = [
("x1", 1.0, Coluna.MathProg.Integ),
("x2", 4.0, Coluna.MathProg.Integ),
("y1", 2.0, Coluna.MathProg.Continuous),
("y2", 3.0, Coluna.MathProg.Continuous)
]
for (name, cost, kind) in variables_infos
vars[name] = Coluna.MathProg.getid(Coluna.MathProg.setvar!(
origform, name, Coluna.MathProg.OriginalVar; cost = cost, lb = 0.0, kind = kind
))
end

# Constraints
constrs = Dict{String, Coluna.MathProg.ConstrId}()
constraints_infos = [
("c1", 2.0, Coluna.MathProg.Greater, Dict(vars["x1"] => -1.0, vars["x2"] => 4.0, vars["y1"] => 2.0, vars["y2"] => 3.0)),
("c2", 3.0, Coluna.MathProg.Greater, Dict(vars["x1"] => 1.0, vars["x2"] => 3.0, vars["y1"] => 1.0, vars["y2"] => 1.0)),
("c3", 0.0, Coluna.MathProg.Greater, Dict(vars["x1"] => 1.0, vars["x2"] => 1.0)),
("c4", 0.0, Coluna.MathProg.Greater, Dict(vars["y1"] => 1.0, vars["y2"] => 1.0))
]
for (name, rhs, sense, members) in constraints_infos
constrs[name] = Coluna.MathProg.getid(Coluna.MathProg.setconstr!(
origform, name, Coluna.MathProg.OriginalConstr; rhs = rhs, sense = sense, members = members
))
end

# Decomposition tree
m = JuMP.Model()
BlockDecomposition.@axis(axis, [1])
tree = BlockDecomposition.Tree(m, BlockDecomposition.Benders, axis)
mast_ann = tree.root.master
sp_ann = BlockDecomposition.Annotation(tree, BlockDecomposition.BendersSepSp, BlockDecomposition.Benders, [])
BlockDecomposition.create_leaf!(BlockDecomposition.getroot(tree), axis[1], sp_ann)


# Benders annotations
ann = Coluna.Annotations()
ann.tree = tree
Coluna.store!(ann, mast_ann, Coluna.MathProg.getvar(origform, vars["x1"]))
Coluna.store!(ann, mast_ann, Coluna.MathProg.getvar(origform, vars["x2"]))
Coluna.store!(ann, sp_ann, Coluna.MathProg.getvar(origform, vars["y1"]))
Coluna.store!(ann, sp_ann, Coluna.MathProg.getvar(origform, vars["y2"]))
Coluna.store!(ann, sp_ann, Coluna.MathProg.getconstr(origform, constrs["c1"]))
Coluna.store!(ann, sp_ann, Coluna.MathProg.getconstr(origform, constrs["c2"]))
Coluna.store!(ann, mast_ann, Coluna.MathProg.getconstr(origform, constrs["c3"]))
Coluna.store!(ann, sp_ann, Coluna.MathProg.getconstr(origform, constrs["c4"]))

problem = Coluna.MathProg.Problem(env)
Coluna.MathProg.set_original_formulation!(problem, origform)

Coluna.reformulate!(problem, ann, env)
reform = Coluna.MathProg.get_reformulation(problem)

# Test first stage variables & constraints
# Coluna.MathProg.MinSense + 1.0 x1 + 4.0 x2 + 1.0 η[5]
# c3 : + 1.0 x1 + 1.0 x2 >= 0.0 (MasterPureConstrConstraintu3 | true)
# 0.0 <= x1 <= Inf (Continuous | MasterPureVar | true)
# 0.0 <= x2 <= Inf (Continuous | MasterPureVar | true)
# 0.0 <= η[5] <= Inf (Continuous | MasterBendSecondStageCostVar | true)

master = Coluna.MathProg.getmaster(reform)
fs_vars = Dict(getname(master, varid) => var for (varid, var) in Coluna.MathProg.getvars(master))
fs_constrs = Dict(getname(master, constrid) => constr for (constrid, constr) in Coluna.MathProg.getconstrs(master))

@test length(fs_vars) == 3

@test Coluna.MathProg.getduty(Coluna.MathProg.getid(fs_vars["x1"])) <= Coluna.MathProg.MasterPureVar
@test Coluna.MathProg.getduty(Coluna.MathProg.getid(fs_vars["x2"])) <= Coluna.MathProg.MasterPureVar
@test Coluna.MathProg.getduty(Coluna.MathProg.getid(fs_vars["η[5]"])) <= Coluna.MathProg.MasterBendSecondStageCostVar

@test Coluna.MathProg.getcurlb(master, fs_vars["x1"]) == 0.0
@test Coluna.MathProg.getcurlb(master, fs_vars["x2"]) == 0.0
@test Coluna.MathProg.getcurlb(master, fs_vars["η[5]"]) == -Inf

@test Coluna.MathProg.getcurub(master, fs_vars["x1"]) == Inf
@test Coluna.MathProg.getcurub(master, fs_vars["x2"]) == Inf
@test Coluna.MathProg.getcurub(master, fs_vars["η[5]"]) == Inf

@test Coluna.MathProg.getcurcost(master, fs_vars["x1"]) == 1.0
@test Coluna.MathProg.getcurcost(master, fs_vars["x2"]) == 4.0
@test Coluna.MathProg.getcurcost(master, fs_vars["η[5]"]) == 1.0

@test length(fs_constrs) == 1

@test Coluna.MathProg.getduty(Coluna.MathProg.getid(fs_constrs["c3"])) <= Coluna.MathProg.MasterPureConstr

@test Coluna.MathProg.getcurrhs(master, fs_constrs["c3"]) == 0.0

# Test second stage variables & Constraints
# Coluna.MathProg.MinSense + 2.0 y1 + 3.0 y2 + 1.0 μ⁺[x1] + 1.0 μ⁻[x1] + 4.0 μ⁺[x2] + 4.0 μ⁻[x2]
# c1 : - 1.0 μ⁺[x1] + 4.0 μ⁺[x2] + 2.0 y1 + 3.0 y2 - 4.0 μ⁻[x2] + 1.0 μ⁻[x1] >= 2.0 (BendSpTechnologicalConstrConstraintu1 | true)
# c2 : + 1.0 μ⁺[x1] + 3.0 μ⁺[x2] + 1.0 y1 + 1.0 y2 - 3.0 μ⁻[x2] - 1.0 μ⁻[x1] >= 3.0 (BendSpTechnologicalConstrConstraintu2 | true)
# c4 : + 1.0 y1 + 1.0 y2 >= 0.0 (BendSpPureConstrConstraintu4 | true)
# 0.0 <= y1 <= Inf (Continuous | BendSpSepVar | true)
# 0.0 <= y2 <= Inf (Continuous | BendSpSepVar | true)
# 0.0 <= μ⁺[x1] <= Inf (Continuous | BendSpPosSlackFirstStageVar | true)
# 0.0 <= μ⁺[x2] <= Inf (Continuous | BendSpPosSlackFirstStageVar | true)
# 0.0 <= μ⁻[x1] <= Inf (Continuous | BendSpNegSlackFirstStageVar | true)
# 0.0 <= μ⁻[x2] <= Inf (Continuous | BendSpNegSlackFirstStageVar | true)

subprob = first(values(Coluna.MathProg.get_benders_sep_sps(reform)))
ss_vars = Dict(getname(subprob, varid) => var for (varid, var) in Coluna.MathProg.getvars(subprob))
ss_constrs = Dict(getname(subprob, constrid) => constr for (constrid, constr) in Coluna.MathProg.getconstrs(subprob))

@test length(ss_vars) == 6

@test Coluna.MathProg.getduty(Coluna.MathProg.getid(ss_vars["y1"])) <= Coluna.MathProg.BendSpSepVar
@test Coluna.MathProg.getduty(Coluna.MathProg.getid(ss_vars["y2"])) <= Coluna.MathProg.BendSpSepVar
@test Coluna.MathProg.getduty(Coluna.MathProg.getid(ss_vars["μ⁺[x1]"])) <= Coluna.MathProg.BendSpPosSlackFirstStageVar
@test Coluna.MathProg.getduty(Coluna.MathProg.getid(ss_vars["μ⁺[x2]"])) <= Coluna.MathProg.BendSpPosSlackFirstStageVar
@test Coluna.MathProg.getduty(Coluna.MathProg.getid(ss_vars["μ⁻[x1]"])) <= Coluna.MathProg.BendSpNegSlackFirstStageVar
@test Coluna.MathProg.getduty(Coluna.MathProg.getid(ss_vars["μ⁻[x2]"])) <= Coluna.MathProg.BendSpNegSlackFirstStageVar

@test Coluna.MathProg.getcurlb(subprob, ss_vars["y1"]) == 0.0
@test Coluna.MathProg.getcurlb(subprob, ss_vars["y2"]) == 0.0
@test Coluna.MathProg.getcurlb(subprob, ss_vars["μ⁺[x1]"]) == 0.0
@test Coluna.MathProg.getcurlb(subprob, ss_vars["μ⁺[x2]"]) == 0.0
@test Coluna.MathProg.getcurlb(subprob, ss_vars["μ⁻[x1]"]) == 0.0
@test Coluna.MathProg.getcurlb(subprob, ss_vars["μ⁻[x2]"]) == 0.0

@test Coluna.MathProg.getcurub(subprob, ss_vars["y1"]) == Inf
@test Coluna.MathProg.getcurub(subprob, ss_vars["y2"]) == Inf
@test Coluna.MathProg.getcurub(subprob, ss_vars["μ⁺[x1]"]) == Inf
@test Coluna.MathProg.getcurub(subprob, ss_vars["μ⁺[x2]"]) == Inf
@test Coluna.MathProg.getcurub(subprob, ss_vars["μ⁻[x1]"]) == Inf
@test Coluna.MathProg.getcurub(subprob, ss_vars["μ⁻[x2]"]) == Inf

@test Coluna.MathProg.getcurcost(subprob, ss_vars["y1"]) == 2.0
@test Coluna.MathProg.getcurcost(subprob, ss_vars["y2"]) == 3.0
@test Coluna.MathProg.getcurcost(subprob, ss_vars["μ⁺[x1]"]) == 1.0
@test Coluna.MathProg.getcurcost(subprob, ss_vars["μ⁺[x2]"]) == 4.0
@test Coluna.MathProg.getcurcost(subprob, ss_vars["μ⁻[x1]"]) == 1.0
@test Coluna.MathProg.getcurcost(subprob, ss_vars["μ⁻[x2]"]) == 4.0

@test Coluna.MathProg.getduty(Coluna.MathProg.getid(ss_constrs["c1"])) <= Coluna.MathProg.BendSpTechnologicalConstr
@test Coluna.MathProg.getduty(Coluna.MathProg.getid(ss_constrs["c2"])) <= Coluna.MathProg.BendSpTechnologicalConstr
@test Coluna.MathProg.getduty(Coluna.MathProg.getid(ss_constrs["c4"])) <= Coluna.MathProg.BendSpPureConstr

@test Coluna.MathProg.getcurrhs(subprob, ss_constrs["c1"]) == 2.0
@test Coluna.MathProg.getcurrhs(subprob, ss_constrs["c2"]) == 3.0
@test Coluna.MathProg.getcurrhs(subprob, ss_constrs["c4"]) == 0.0

@test length(ss_constrs) == 3
return
end
register!(unit_tests, "benders_decomposition", benders_decomposition)