Add tree-decomposition-based partitioning.

Project.toml

@@ -5,6 +5,7 @@ authors = ["Jordan Jalving <jhjalving@gmail.com>"]
 repo = "https://github.com/plasmo-dev/Plasmo.jl.git"
 
 [deps]
+CliqueTrees = "60701a23-6482-424a-84db-faee86b9b1f8"
 DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 DistributedArrays = "aaf54ef3-cdf8-58ed-94cc-d582ad619b94"
@@ -21,6 +22,7 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 
 [compat]
+CliqueTrees = "1"
 DataStructures = "0.18, 0.19"
 DistributedArrays = "0.6"
 GraphOptInterface = "0.1"

src/Plasmo.jl

@@ -79,6 +79,10 @@ export OptiGraph,
     n_subpartitions,
     all_subpartitions,
 
+    # clique tree
+
+    apply_clique_tree!,
+
     # aggregate
 
     aggregate,
@@ -173,6 +177,8 @@ include("graph_functions/topology.jl")
 
 include("graph_functions/partition.jl")
 
+include("graph_functions/cliquetree.jl")
+
 include("utils.jl")
 
 include("distributed/local_conversions.jl")

src/graph_functions/cliquetree.jl

@@ -0,0 +1,208 @@
+import CliqueTrees:
+    BipartiteGraph,
+    cliquetree,
+    cliquetree!,
+    linegraph,
+    neighbors,
+    parentindex,
+    residual,
+    reverse,
+    rootindex,
+    separator
+
+using JuMP: GenericAffExpr, add_to_expression!
+
+function get_edge_to_node(graph::OptiGraph)
+    nodes = all_nodes(graph)
+    edges = all_edges(graph)
+    node_to_idx = Dict(node => i for (i, node) in enumerate(nodes))
+
+    I = Int[]
+    J = Int[]
+
+    for (e, edge) in enumerate(edges)
+        for node in all_nodes(edge)
+            push!(I, node_to_idx[node])
+            push!(J, e)
+        end
+    end
+
+    matrix = sparse(I, J, ones(Int, length(I)), length(nodes), length(edges))
+    return BipartiteGraph(matrix)
+end
+
+function opti_clique_tree(graph::OptiGraph; kw...)
+    nodes = all_nodes(graph)
+    edges = all_edges(graph)
+
+    # Construct hypergraph
+    edge_to_node = get_edge_to_node(graph)
+    node_to_edge = reverse(edge_to_node)
+
+    # Find integral nodes
+    int_nodes = [
+        i for i in eachindex(nodes)
+        if any(v -> JuMP.is_binary(v) || JuMP.is_integer(v), JuMP.all_variables(nodes[i]))
+    ]
+
+    # Construct line graph, forcing integer nodes to form a clique
+    node_to_node = sparse(linegraph(node_to_edge, edge_to_node))
+    node_to_node[int_nodes, int_nodes] .= 1
+
+    # Construct clique tree
+    perm, tree = cliquetree(node_to_node; kw...)
+
+    # Pivot clique tree, moving integer nodes to root
+    if !isempty(int_nodes)
+        invp = invperm(perm)
+        permute!(perm, cliquetree!(tree, invp[int_nodes]))
+    end
+
+    # Assign each edge to its highest containing bag
+    edge_to_bag = zeros(Int, length(edges))
+
+    for j in eachindex(tree)
+        for v in residual(tree, j)
+            for e in neighbors(node_to_edge, perm[v])
+                if edge_to_bag[e] == 0
+                    edge_to_bag[e] = j
+                end
+            end
+        end
+    end
+
+    return perm, tree, edge_to_bag
+end
+
+function apply_clique_tree!(
+    graph::OptiGraph,
+    perm::AbstractVector{<:Integer},
+    tree,
+    edge_to_bag::AbstractVector{<:Integer}
+)
+    optinodes = all_nodes(graph)[perm]
+    optiedges = all_edges(graph)
+
+    empty!(graph.optinodes)
+    empty!(graph.optiedges)
+
+    V = NodeVariableRef
+    bag_to_var_map = [Dict{V, V}() for _ in eachindex(tree)]
+    bag_to_graph = Vector{OptiGraph}(undef, length(tree))
+
+    # For each bag in the clique tree, construct a
+    # subgraph on the residual
+    for j in eachindex(tree)
+        subgraph = bag_to_graph[j] = OptiGraph()
+
+        for v in residual(tree, j)
+            add_node!(subgraph, optinodes[v])
+        end
+
+        set_to_node_objectives(subgraph)
+        add_subgraph!(graph, subgraph)
+    end
+
+    # Link each bag with its parent using equality constraints
+    for j in reverse(eachindex(tree))
+        for v in residual(tree, j)
+            node = optinodes[v]
+
+            for var in JuMP.all_variables(node)
+                bag_to_var_map[j][var] = var
+            end
+        end
+
+        k = parentindex(tree, j)
+
+        if !isnothing(k)
+            @optinode(bag_to_graph[j], _sep_copy_node)
+
+            for v in separator(tree, j)
+                node = optinodes[v]
+
+                for orig_var in JuMP.all_variables(node)
+                    copy_var = @variable(bag_to_graph[j][:_sep_copy_node])
+                    bag_to_var_map[j][orig_var] = copy_var
+                    @linkconstraint(graph, copy_var == bag_to_var_map[k][orig_var])
+                end
+            end
+        end
+    end
+
+    # Add internal constraints to each bag
+    for (e, j) in enumerate(edge_to_bag)
+        for con in JuMP.all_constraints(optiedges[e])
+            con_obj = JuMP.constraint_object(con)
+            _add_substituted_constraint!(con_obj, bag_to_graph[j], bag_to_var_map[j])
+        end
+    end
+
+    root = rootindex(tree)
+    return bag_to_graph[root]
+end
+
+"""
+    apply_clique_tree!(graph::OptiGraph; kw...)
+
+Transform an opti-graph into a tree of subgraphs.
+"""
+function apply_clique_tree!(graph::OptiGraph; kw...)
+    perm, tree, edge_to_bag = opti_clique_tree(graph; kw...)
+    return apply_clique_tree!(graph, perm, tree, edge_to_bag)
+end
+
+function _add_substituted_constraint!(
+    con_obj::JuMP.ScalarConstraint{GenericAffExpr{Float64, V}, S},
+    subgraph::OptiGraph,
+    var_map::Dict{V, V}
+) where {V <: JuMP.AbstractVariableRef, S}
+    new_expr = GenericAffExpr{Float64, V}()
+
+    first_node = nothing
+    is_link = false
+
+    for (var, coef) in con_obj.func.terms
+        sub_var = var_map[var]
+        add_to_expression!(new_expr, coef, sub_var)
+        node = JuMP.owner_model(sub_var)
+
+        if isnothing(first_node)
+            first_node = node
+        elseif node != first_node
+            is_link = true
+        end
+    end
+
+    new_expr.constant = con_obj.func.constant
+
+    if is_link
+        _add_link_constraint!(subgraph, new_expr, con_obj.set)
+    else
+        _add_node_constraint!(first_node, new_expr, con_obj.set)
+    end
+end
+
+function _add_node_constraint!(node::OptiNode, expr::GenericAffExpr, set::MOI.LessThan)
+    @constraint(node, expr <= set.upper)
+end
+
+function _add_node_constraint!(node::OptiNode, expr::GenericAffExpr, set::MOI.GreaterThan)
+    @constraint(node, expr >= set.lower)
+end
+
+function _add_node_constraint!(node::OptiNode, expr::GenericAffExpr, set::MOI.EqualTo)
+    @constraint(node, expr == set.value)
+end
+
+function _add_link_constraint!(sg::OptiGraph, expr::GenericAffExpr, set::MOI.LessThan)
+    @linkconstraint(sg, expr <= set.upper)
+end
+
+function _add_link_constraint!(sg::OptiGraph, expr::GenericAffExpr, set::MOI.GreaterThan)
+    @linkconstraint(sg, expr >= set.lower)
+end
+
+function _add_link_constraint!(sg::OptiGraph, expr::GenericAffExpr, set::MOI.EqualTo)
+    @linkconstraint(sg, expr == set.value)
+end