Need a working example to use Gurobi for multi objective

Specific Domains Optimization (Mathematical)
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Hi Everyone, can some one provide working example for Gurobi Multi objective.

Thanks in advance

2

Something like this? Of course the solver is not Gurobi in the docs but JuMP makes it easy to switch

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3

To use multi-objective, see:

You almost certainly want to use MultiObjectiveAlgorithms.jl [docs] instead of Gurobi directly.

See these tutorials:

To use Gurobi directly, just pass a vector of objectives to @objective, but note that it returns only a single solution, not the Pareto frontier:

julia> using JuMP, Gurobi

julia> model = Model(Gurobi.Optimizer)
Set parameter LicenseID to value 890341
A JuMP Model
├ solver: Gurobi
├ objective_sense: FEASIBILITY_SENSE
├ num_variables: 0
├ num_constraints: 0
└ Names registered in the model: none

julia> @variable(model, 0 <= x[1:2] <= 1)
2-element Vector{VariableRef}:
 x[1]
 x[2]

julia> @constraint(model, sum(x) == 1)
x[1] + x[2] = 1

julia> @objective(model, Max, [x[1], 2.0 * x[2] + 1.0])
2-element Vector{AffExpr}:
 x[1]
 2 x[2] + 1

julia> optimize!(model)
Gurobi Optimizer version 12.0.0 build v12.0.0rc1 (mac64[x86] - Darwin 24.1.0 24B83)

CPU model: Intel(R) Core(TM) i5-8259U CPU @ 2.30GHz
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 1 rows, 2 columns and 2 nonzeros
Model fingerprint: 0x99aa5868
Variable types: 2 continuous, 0 integer (0 binary)
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 2e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+00, 1e+00]

---------------------------------------------------------------------------
Multi-objectives: starting optimization with 2 objectives (1 combined)...
---------------------------------------------------------------------------
---------------------------------------------------------------------------

Multi-objectives: optimize objective 1 (weighted) ...
---------------------------------------------------------------------------

Optimize a model with 1 rows, 2 columns and 2 nonzeros
Model fingerprint: 0xf6d0909a
Coefficient statistics:
  Matrix range     [1e+00, 1e+00]
  Objective range  [1e+00, 2e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+00, 1e+00]
Presolve removed 1 rows and 2 columns
Presolve time: 0.00s
Presolve: All rows and columns removed
Iteration    Objective       Primal Inf.    Dual Inf.      Time
       0    3.0000000e+00   0.000000e+00   0.000000e+00      0s

Solved in 0 iterations and 0.00 seconds (0.00 work units)
Optimal objective  3.000000000e+00

---------------------------------------------------------------------------
Multi-objectives: solved in 0.00 seconds (0.00 work units), solution count 1


User-callback calls 43, time in user-callback 0.00 sec

julia> @assert is_solved_and_feasible(model)

julia> objective_value.(model)
2-element Vector{Float64}:
 0.0
 3.0

julia> solution_summary(model)
* Solver : Gurobi

* Status
  Result count       : 1
  Termination status : OPTIMAL
  Message from the solver:
  "Model was solved to optimality (subject to tolerances), and an optimal solution is available."

* Candidate solution (result #1)
  Primal status      : FEASIBLE_POINT
  Dual status        : NO_SOLUTION
  Objective value    : [0.00000e+00,3.00000e+00]

* Work counters
  Solve time (sec)   : 8.91924e-04
  Simplex iterations : 0
  Barrier iterations : 0
  Node count         : 0
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