error raised when a JuMP variable with two indexes is used with GLPK and MOA

[xgandibleux]

The following error is raised on the following line (see code 3 and code 4 below), but no for codes 1 and 2 (who use the same definition of the expression):

julia> @objective(model, Max, [objective1, objective2])
ERROR: The solver does not support an objective function of type MathOptInterface.VectorAffineFunction{Float64}.       

This happens with a variable JuMP with two indexes and MOA+GLPK.
The problem does not appear with HiGHS, or without solver.

My configuration:
julia v"1.10.5"
JuMP v1.23.6
MultiObjectiveAlgorithms v1.3.5
GLPK v1.2.1
HiGHS v1.13.0

Codes:

using JuMP
using GLPK
import MultiObjectiveAlgorithms as MOA
       
m=2; n=3
p1 = rand(1:10,m,n)
p2 = rand(1:10,m,n)
w  = rand(1:10,m,n)
b  = Vector{Int64}(undef,m)
for i=1:m
    b[i] = floor(Int64,sum(w[i,:])/2.0) 
end

# CODE 1 (single objective GAP with objective1): no problem
model = Model(GLPK.Optimizer)
@variable(model, x[1:m, 1:n], Bin)
@expression(model, objective1, sum(p1[i,j]*x[i,j] for i in 1:m, j in 1:n) )
@expression(model, objective2, sum(p2[i,j]*x[i,j] for i in 1:m, j in 1:n) )
@objective(model, Max, objective1)
@constraint(model, [i=1:m], sum(w[i,j]*x[i,j] for j = 1:n) <= b[i])
@constraint(model, [j=1:n], sum(x[i,j] for i = 1:m) == 1)
optimize!(model)

# CODE 2 (single objective GAP with objective2): no problem
model = Model(GLPK.Optimizer)
@variable(model, x[1:m, 1:n], Bin)
@expression(model, objective1, sum(p1[i,j]*x[i,j] for i in 1:m, j in 1:n) )
@expression(model, objective2, sum(p2[i,j]*x[i,j] for i in 1:m, j in 1:n) )
@objective(model, Max, objective2)
@constraint(model, [i=1:m], sum(w[i,j]*x[i,j] for j = 1:n) <= b[i])
@constraint(model, [j=1:n], sum(x[i,j] for i = 1:m) == 1)
optimize!(model)

# CODE 3 (bi-objective GAP with [objective1,objective2] ): error raised
model = Model(GLPK.Optimizer)
@variable(model, x[1:m, 1:n], Bin)
@expression(model, objective1, sum(p1[i,j]*x[i,j] for i in 1:m, j in 1:n) )
@expression(model, objective2, sum(p2[i,j]*x[i,j] for i in 1:m, j in 1:n) )
@objective(model, Max, [objective1, objective2])
@constraint(model, [i=1:m], sum(w[i,j]*x[i,j] for j = 1:n) <= b[i])
@constraint(model, [j=1:n], sum(x[i,j] for i = 1:m) == 1)

# CODE 4: error raised 
model = Model(GLPK.Optimizer)
@variable(model, x[1:2, 1:2], Bin)
@expression(model, objective1, x[1,1]+x[1,2] )
@expression(model, objective2, x[2,1]+x[2,2] )
@objective(model, Max, [objective1, objective2])

[odow]

You're not using MOA as the solver. Instead of

model = Model(GLPK.Optimizer)

You need:

model = Model(() -> MOA.Optimizer(GLPK.Optimizer))

[odow]

For example:

julia> using JuMP

julia> import HiGHS

julia> import MultiObjectiveAlgorithms as MOA

julia> begin
           m, n = 2, 3
           p1 = rand(1:10, m, n)
           p2 = rand(1:10, m, n)
           w  = rand(1:10, m, n)
           b  = [floor(Int, sum(w[i,:]) / 2) for i in 1:m]
           model = Model(() -> MOA.Optimizer(HiGHS.Optimizer))
           set_silent(model)
           set_attribute(model, MOA.Algorithm(), MOA.EpsilonConstraint())
           @variable(model, x[1:m, 1:n], Bin)
           @expression(model, objective1, sum(p1[i,j]*x[i,j] for i in 1:m, j in 1:n) )
           @expression(model, objective2, sum(p2[i,j]*x[i,j] for i in 1:m, j in 1:n) )
           @objective(model, Max, [objective1, objective2])
           @constraint(model, [i=1:m], sum(w[i,j]*x[i,j] for j = 1:n) <= b[i])
           @constraint(model, [j=1:n], sum(x[i,j] for i = 1:m) == 1)
           optimize!(model)
           solution_summary(model)
       end
* Solver : MOA[algorithm=MultiObjectiveAlgorithms.EpsilonConstraint, optimizer=HiGHS]

* Status
  Result count       : 2
  Termination status : OPTIMAL
  Message from the solver:
  "Solve complete. Found 2 solution(s)"

* Candidate solution (result #1)
  Primal status      : FEASIBLE_POINT
  Dual status        : NO_SOLUTION
  Objective value    : [2.00000e+01,1.40000e+01]
  Objective bound    : [2.50000e+01,1.40000e+01]

* Work counters
  Solve time (sec)   : 5.47600e-03

Closing this issue because it is not a bug in MOA.