WIP: begin support for vector-valued objectives

To be read in conjunction with jump-dev/MathOptInterface.jl#2070

A proof-of-concept solver and JuMP examples are available at jump-dev/MultiObjectiveAlgorithms.jl#2

The issue #2099 discussed two approaches
for implementing MO in JuMP.

 1. Treat multicriteria as a vector of scalar objectives and a vector of
    scalar senses. This would let someone write [Min, Max], [f(x), g(x)].
    The main reason for this approach is that it matches what users want
    to do.
 2. Treat multicriteria as an optimization problem with a vector-valued
    objective function. Users could write only Min, f(x) where f(x) is a
    vector. The main reason for this approach is that it matches what
    MathOptInterface wants.

This PR implements option 2. The strongest reason in support of option 2
is that it requires very little code to implement, suggesting that it is
a natural extension of MOI.

The biggest downside is that it doesn't overcome the Min-Max issue; but
I think we can work around this with user-facing cosmetic tooling in JuMP;
solvers would be forced to accept a single sense.

Author: odow

src/objective.jl

@@ -26,7 +26,7 @@ end
 Return the best known bound on the optimal objective value after a call to
 `optimize!(model)`.
 """
-function objective_bound(model::Model)::Float64
+function objective_bound(model::Model)
     return MOI.get(model, MOI.ObjectiveBound())
 end
 
@@ -38,7 +38,7 @@ most-recent solution returned by the solver.
 
 See also: [`result_count`](@ref).
 """
-function objective_value(model::Model; result::Int = 1)::Float64
+function objective_value(model::Model; result::Int = 1)
     return MOI.get(model, MOI.ObjectiveValue(result))
 end
 
@@ -90,7 +90,7 @@ functions; the recommended way to set the objective is with the
 """
 function set_objective_function end
 
-function set_objective_function(model::Model, func::MOI.AbstractScalarFunction)
+function set_objective_function(model::Model, func::MOI.AbstractFunction)
     attr = MOI.ObjectiveFunction{typeof(func)}()
     if !MOI.supports(backend(model), attr)
         error(
@@ -123,6 +123,16 @@ function set_objective_function(model::Model, func::Real)
     )
 end
 
+function set_objective_function(
+    model::Model,
+    func::AbstractVector{<:AbstractJuMPScalar},
+)
+    for f in func
+        check_belongs_to_model(f, model)
+    end
+    return set_objective_function(model, moi_function(func))
+end
+
 function set_objective_function(model::AbstractModel, func)
     return error("The objective function `$(func)` is not supported by JuMP.")
 end

src/solution_summary.jl

@@ -16,8 +16,8 @@ struct _SolutionSummary
     has_values::Bool
     has_duals::Bool
     # Candidate solution
-    objective_value::Union{Missing,Float64}
-    objective_bound::Union{Missing,Float64}
+    objective_value::Union{Missing,Float64,Vector{Float64}}
+    objective_bound::Union{Missing,Float64,Vector{Float64}}
     relative_gap::Union{Missing,Float64}
     dual_objective_value::Union{Missing,Float64}
     primal_solution::Union{Missing,Dict{String,Float64}}
@@ -216,3 +216,9 @@ function _print_if_not_missing(io, header, value::Real)
     println(io, header, Printf.@sprintf("%.5e", value))
     return
 end
+
+function _print_if_not_missing(io, header, value::Vector{<:Real})
+    array = join([Printf.@sprintf("%.5e", v) for v in value], ",")
+    println(io, header, "[", array, "]")
+    return
+end