Added multi-objective support, modifed relevant doc strings and added an instructional subsection to the objective document.

Author: Skye Vidler

docs/src/guide/objective.md

@@ -14,6 +14,7 @@ One key idea is that the objective must evaluate to a finite expression which me
 it must only explicitly contain finite variables and point variables. Infinite 
 expressions must be summarized by a measure (e.g., taking the expectation of a random variable).
 
+
 ## [Basic Usage](@id obj_basic)
 Principally, the objective function is specified via 
 [`@objective`](https://jump.dev/JuMP.jl/v1/api/JuMP/#JuMP.@objective) 
@@ -139,3 +140,17 @@ more efficient at parsing expressions.
     [`@objective`](https://jump.dev/JuMP.jl/v1/api/JuMP/#JuMP.@objective) 
     since it is more stable and efficient than the `set_objective_[aspect]` 
     methods due to its enhanced methodology for parsing expressions.
+
+### Multi-Objective Problems
+`InfiniteOpt` also supports multi-objective problems by supplying the model with a vector of scalar values.
+Instead of a `JuMP.AbstractJuMPScalar`, these become `AbstractVector` within the model.
+
+These models are defined the same way as scalar, single-objective models with `@objective`, with some slight differences in definition. Looking at the aforementioned example and modifying it a bit, it becomes:
+
+```jldoctest obj_multi
+julia> @objective(model, Max, [0.5x[1], 0.5x[2]])
+ 0.5 x[1]
+ 0.5 x[2]
+```
+If a scalarization method of solving the model is the goal, the individual `@expression` scalars within the vector can be compiled into a single objective. The weight- or priority- of these expressions can be changed by multiplying each component in the vector by fractions, with the sum of the fractions being 1.
+In hierarchical model solving, the order of the scalars determines the priority of the model.

src/TranscriptionOpt/transcribe.jl

@@ -565,6 +565,15 @@ function transcription_expression(
     return zero(JuMP.AffExpr) + num
 end
 
+# Vectors
+function transcription_expression(
+    func::AbstractVector,
+    backend::TranscriptionBackend,
+    support::Vector{Float64}
+    )
+    return map(f -> transcription_expression(f, backend, support), func)
+end
+
 ################################################################################
 #                         MEASURE TRANSCRIPTION METHODS
 ################################################################################
@@ -750,7 +759,7 @@ end
 function _process_constraint(
     backend::TranscriptionBackend, 
     constr::JuMP.VectorConstraint, 
-    func::Vector{<:JuMP.AbstractJuMPScalar}, 
+    func::AbstractVector,
     set::MOI.AbstractVectorSet, 
     raw_supp::Vector{Float64}, 
     name::String

src/datatypes.jl

@@ -1398,7 +1398,7 @@ mutable struct InfiniteModel <: JuMP.AbstractModel
 
     # Objective Data
     objective_sense::MOI.OptimizationSense
-    objective_function::JuMP.AbstractJuMPScalar
+    objective_function::Union{JuMP.AbstractJuMPScalar, AbstractVector{<:JuMP.AbstractJuMPScalar}}
     objective_has_measures::Bool
 
     # Operator Registration

src/objective.jl

@@ -18,18 +18,24 @@ function JuMP.objective_sense(model::InfiniteModel)::MOI.OptimizationSense
 end
 
 """
-    JuMP.objective_function(model::InfiniteModel)::JuMP.AbstractJuMPScalar
+    JuMP.objective_function(model::InfiniteModel)::Union{JuMP.AbstractJuMPScalar, AbstractVector}
 
 Extend `JuMP.objective_function` to return the objective of infinite model 
-`model`.
+`model`. Supports scalar values or vectors of scalar values.
 
 **Example**
 ```julia-repl
-julia> objective_function(model)
-1
+julia> objective_function(scalar_model)
+2 x + 1
+
+```julia-repl
+julia> objective_function(multiobjective_model)
+2 x + 1
+5 y - 1
+
 ```
 """
-function JuMP.objective_function(model::InfiniteModel)::JuMP.AbstractJuMPScalar
+function JuMP.objective_function(model::InfiniteModel)::Union{JuMP.AbstractJuMPScalar, AbstractVector}
     return model.objective_function
 end
 
@@ -74,23 +80,30 @@ end
 ################################################################################
 """
     JuMP.set_objective_function(model::InfiniteModel,
-                                func::JuMP.AbstractJuMPScalar)::Nothing
+                                func::Union{JuMP.AbstractJuMPScalar, AbstractVector})::Nothing
 
 Extend `JuMP.set_objective_function` to set the objective expression of
 infinite model `model`. Errors if `func` contains infinite variables and/or
-parameters. Also errors if `func` contains invalid variables.
+parameters. Also errors if `func` contains invalid variables. 
+Supports scalar values or vectors of scalar values.
 
 **Example**
 ```julia-repl
 julia> set_objective_function(model, 2x + 1)
 
 julia> objective_function(model)
 2 x + 1
+
+julia> set_objective_function(model, [2x + 1, 5y - 1)
+
+julia> objective_function(model)
+2 x + 1
+5 y - 1
 ```
 """
 function JuMP.set_objective_function(
     model::InfiniteModel,
-    func::JuMP.AbstractJuMPScalar
+    func::Union{JuMP.AbstractJuMPScalar, AbstractVector}
     )::Nothing
     # gather the unique list of variable references for testing and mapping
     new_vrefs = all_expression_variables(func)
@@ -172,24 +185,30 @@ end
 
 """
     JuMP.set_objective(model::InfiniteModel, sense::MOI.OptimizationSense,
-                       func::Union{JuMP.AbstractJuMPScalar, Real})::Nothing
+                       func::Union{JuMP.AbstractJuMPScalar, AbstractVector, Real})::Nothing
 
 Extend `JuMP.set_objective` to set the objective of infinite model
 `model`. Errors if `func` contains infinite variables and/or parameters, or if
-it does not belong to the model.
+it does not belong to the model. Supports scalar values or vectors of scalar values.
 
 **Example**
 ```julia-repl
 julia> set_objective(model, MOI.MIN_SENSE, 2x + 1)
 
 julia> objective_function(model)
 2 x + 1
+
+julia> set_objective(model, MOI.MIN_SENSE, [2x + 1, 5y - 1])
+
+julia> objective_function(model)
+2 x + 1
+5 y - 1
 ```
 """
 function JuMP.set_objective(
     model::InfiniteModel, 
     sense::MOI.OptimizationSense,
-    func::Union{JuMP.AbstractJuMPScalar, Real}
+    func::Union{JuMP.AbstractJuMPScalar, AbstractVector, Real}
     )::Nothing
     JuMP.set_objective_sense(model, sense)
     JuMP.set_objective_function(model, func)