diff --git a/src/MultiObjectiveAlgorithms.jl b/src/MultiObjectiveAlgorithms.jl
index 4447c85..b0d269e 100644
--- a/src/MultiObjectiveAlgorithms.jl
+++ b/src/MultiObjectiveAlgorithms.jl
@@ -579,6 +579,30 @@ function _compute_ideal_point(model::Optimizer, start_time)
     return
 end
 
+function optimize_multiobjective!(
+    algorithm::AbstractAlgorithm,
+    model::Optimizer,
+)
+    sense = MOI.get(model.inner, MOI.ObjectiveSense())
+    if sense == MOI.FEASIBILITY_SENSE
+        return MOI.INVALID_MODEL, nothing
+    elseif sense == MOI.MAX_SENSE
+        old_obj = copy(model.f)
+        neg_obj = MOI.Utilities.operate(-, Float64, model.f)
+        MOI.set(model, MOI.ObjectiveFunction{typeof(neg_obj)}(), neg_obj)
+        MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+        status, solutions = minimize_multiobjective!(algorithm, model)
+        MOI.set(model, MOI.ObjectiveFunction{typeof(old_obj)}(), old_obj)
+        MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
+        if solutions !== nothing
+            solutions = [SolutionPoint(s.x, -s.y) for s in solutions]
+        end
+        model.ideal_point *= -1
+        return status, solutions
+    end
+    return minimize_multiobjective!(algorithm, model)
+end
+
 function MOI.optimize!(model::Optimizer)
     start_time = time()
     empty!(model.solutions)
diff --git a/src/algorithms/Chalmet.jl b/src/algorithms/Chalmet.jl
index 4eb44a7..5439b90 100644
--- a/src/algorithms/Chalmet.jl
+++ b/src/algorithms/Chalmet.jl
@@ -40,24 +40,12 @@ function _solve_constrained_model(
     return status, SolutionPoint(X, Y)
 end
 
-function optimize_multiobjective!(algorithm::Chalmet, model::Optimizer)
+function minimize_multiobjective!(algorithm::Chalmet, model::Optimizer)
+    @assert MOI.get(model.inner, MOI.ObjectiveSense()) == MOI.MIN_SENSE
     start_time = time()
     if MOI.output_dimension(model.f) != 2
         error("Chalmet requires exactly two objectives")
     end
-    sense = MOI.get(model.inner, MOI.ObjectiveSense())
-    if sense == MOI.MAX_SENSE
-        old_obj, neg_obj = copy(model.f), -model.f
-        MOI.set(model, MOI.ObjectiveFunction{typeof(neg_obj)}(), neg_obj)
-        MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
-        status, solutions = optimize_multiobjective!(algorithm, model)
-        MOI.set(model, MOI.ObjectiveFunction{typeof(old_obj)}(), old_obj)
-        MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
-        if solutions !== nothing
-            solutions = [SolutionPoint(s.x, -s.y) for s in solutions]
-        end
-        return status, solutions
-    end
     solutions = SolutionPoint[]
     E = Tuple{Int,Int}[]
     Q = Tuple{Int,Int}[]
diff --git a/src/algorithms/DominguezRios.jl b/src/algorithms/DominguezRios.jl
index 8fe8984..b88f842 100644
--- a/src/algorithms/DominguezRios.jl
+++ b/src/algorithms/DominguezRios.jl
@@ -142,22 +142,9 @@ function _update!(
     return
 end
 
-function optimize_multiobjective!(algorithm::DominguezRios, model::Optimizer)
+function minimize_multiobjective!(algorithm::DominguezRios, model::Optimizer)
+    @assert MOI.get(model.inner, MOI.ObjectiveSense()) == MOI.MIN_SENSE
     start_time = time()
-    sense = MOI.get(model.inner, MOI.ObjectiveSense())
-    if sense == MOI.MAX_SENSE
-        old_obj, neg_obj = copy(model.f), -model.f
-        MOI.set(model, MOI.ObjectiveFunction{typeof(neg_obj)}(), neg_obj)
-        MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
-        status, solutions = optimize_multiobjective!(algorithm, model)
-        MOI.set(model, MOI.ObjectiveFunction{typeof(old_obj)}(), old_obj)
-        MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
-        if solutions !== nothing
-            solutions = [SolutionPoint(s.x, -s.y) for s in solutions]
-        end
-        model.ideal_point .*= -1
-        return status, solutions
-    end
     n = MOI.output_dimension(model.f)
     L = [_DominguezRiosBox[] for i in 1:n]
     scalars = MOI.Utilities.scalarize(model.f)
@@ -166,7 +153,7 @@ function optimize_multiobjective!(algorithm::DominguezRios, model::Optimizer)
     # Ideal and Nadir point estimation
     for (i, f_i) in enumerate(scalars)
         MOI.set(model.inner, MOI.ObjectiveFunction{typeof(f_i)}(), f_i)
-        MOI.set(model.inner, MOI.ObjectiveSense(), sense)
+        MOI.set(model.inner, MOI.ObjectiveSense(), MOI.MIN_SENSE)
         MOI.optimize!(model.inner)
         status = MOI.get(model.inner, MOI.TerminationStatus())
         if !_is_scalar_status_optimal(status)
@@ -175,18 +162,17 @@ function optimize_multiobjective!(algorithm::DominguezRios, model::Optimizer)
         _, Y = _compute_point(model, variables, f_i)
         yI[i] = Y
         model.ideal_point[i] = Y
-        rev_sense = sense == MOI.MIN_SENSE ? MOI.MAX_SENSE : MOI.MIN_SENSE
-        MOI.set(model.inner, MOI.ObjectiveSense(), rev_sense)
+        MOI.set(model.inner, MOI.ObjectiveSense(), MOI.MAX_SENSE)
         MOI.optimize!(model.inner)
         status = MOI.get(model.inner, MOI.TerminationStatus())
         if !_is_scalar_status_optimal(status)
-            _warn_on_nonfinite_anti_ideal(algorithm, sense, i)
+            _warn_on_nonfinite_anti_ideal(algorithm, MOI.MIN_SENSE, i)
             return status, nothing
         end
         _, Y = _compute_point(model, variables, f_i)
         yN[i] = Y + 1
     end
-    MOI.set(model.inner, MOI.ObjectiveSense(), sense)
+    MOI.set(model.inner, MOI.ObjectiveSense(), MOI.MIN_SENSE)
     ϵ = 1 / (2 * n * (maximum(yN - yI) - 1))
     # If ϵ is small, then the scalar objectives can contain terms that fall
     # below the tolerance level of the solver. To fix this, we rescale the
diff --git a/src/algorithms/EpsilonConstraint.jl b/src/algorithms/EpsilonConstraint.jl
index 58e7605..0f230f5 100644
--- a/src/algorithms/EpsilonConstraint.jl
+++ b/src/algorithms/EpsilonConstraint.jl
@@ -65,10 +65,11 @@ function MOI.get(alg::EpsilonConstraint, ::ObjectiveAbsoluteTolerance)
     return MOI.get(alg, EpsilonConstraintStep())
 end
 
-function optimize_multiobjective!(
+function minimize_multiobjective!(
     algorithm::EpsilonConstraint,
     model::Optimizer,
 )
+    @assert MOI.get(model.inner, MOI.ObjectiveSense()) == MOI.MIN_SENSE
     start_time = time()
     if MOI.output_dimension(model.f) != 2
         error("EpsilonConstraint requires exactly two objectives")
@@ -87,12 +88,7 @@ function optimize_multiobjective!(
     end
     a, b = solution_1[1].y[1], solution_2[1].y[1]
     left, right = min(a, b), max(a, b)
-    sense = MOI.get(model.inner, MOI.ObjectiveSense())
-    if sense == MOI.MIN_SENSE
-        model.ideal_point .= min.(solution_1[1].y, solution_2[1].y)
-    else
-        model.ideal_point .= max.(solution_1[1].y, solution_2[1].y)
-    end
+    model.ideal_point .= min.(solution_1[1].y, solution_2[1].y)
     # Compute the epsilon that we will be incrementing by each iteration
     ε = MOI.get(algorithm, EpsilonConstraintStep())
     n_points = MOI.get(algorithm, SolutionLimit())
@@ -104,16 +100,12 @@ function optimize_multiobjective!(
     MOI.set(model.inner, MOI.ObjectiveFunction{typeof(f2)}(), f2)
     # Add epsilon constraint
     variables = MOI.get(model.inner, MOI.ListOfVariableIndices())
-    SetType, bound = if sense == MOI.MIN_SENSE
-        MOI.LessThan{Float64}, right - ε
-    else
-        MOI.GreaterThan{Float64}, left + ε
-    end
+    bound = right - ε
     constant = MOI.constant(f1, Float64)
     ci = MOI.Utilities.normalize_and_add_constraint(
         model,
         f1,
-        SetType(bound);
+        MOI.LessThan{Float64}(bound);
         allow_modify_function = true,
     )
     bound -= constant
@@ -123,7 +115,7 @@ function optimize_multiobjective!(
             status = MOI.TIME_LIMIT
             break
         end
-        MOI.set(model, MOI.ConstraintSet(), ci, SetType(bound))
+        MOI.set(model, MOI.ConstraintSet(), ci, MOI.LessThan{Float64}(bound))
         MOI.optimize!(model.inner)
         if !_is_scalar_status_optimal(model)
             break
@@ -132,12 +124,8 @@ function optimize_multiobjective!(
         if isempty(solutions) || !(Y ≈ solutions[end].y)
             push!(solutions, SolutionPoint(X, Y))
         end
-        if sense == MOI.MIN_SENSE
-            bound = min(Y[1] - constant - ε, bound - ε)
-        else
-            bound = max(Y[1] - constant + ε, bound + ε)
-        end
+        bound = min(Y[1] - constant - ε, bound - ε)
     end
     MOI.delete(model, ci)
-    return status, filter_nondominated(sense, solutions)
+    return status, filter_nondominated(MOI.MIN_SENSE, solutions)
 end
diff --git a/src/algorithms/Hierarchical.jl b/src/algorithms/Hierarchical.jl
index cd0e882..f7783f1 100644
--- a/src/algorithms/Hierarchical.jl
+++ b/src/algorithms/Hierarchical.jl
@@ -85,7 +85,8 @@ function _sorted_priorities(priorities::Vector{Int})
     return [findall(isequal(u), priorities) for u in unique_priorities]
 end
 
-function optimize_multiobjective!(algorithm::Hierarchical, model::Optimizer)
+function minimize_multiobjective!(algorithm::Hierarchical, model::Optimizer)
+    @assert MOI.get(model.inner, MOI.ObjectiveSense()) == MOI.MIN_SENSE
     objectives = MOI.Utilities.eachscalar(model.f)
     N = length(objectives)
     variables = MOI.get(model.inner, MOI.ListOfVariableIndices())
@@ -109,14 +110,9 @@ function optimize_multiobjective!(algorithm::Hierarchical, model::Optimizer)
         end
         # Add tolerance constraints
         X, Y = _compute_point(model, variables, new_vector_f)
-        sense = MOI.get(model.inner, MOI.ObjectiveSense())
         for (i, fi) in enumerate(MOI.Utilities.eachscalar(new_vector_f))
             rtol = MOI.get(algorithm, ObjectiveRelativeTolerance(i))
-            set = if sense == MOI.MIN_SENSE
-                MOI.LessThan(Y[i] + rtol * abs(Y[i]))
-            else
-                MOI.GreaterThan(Y[i] - rtol * abs(Y[i]))
-            end
+            set = MOI.LessThan(Y[i] + rtol * abs(Y[i]))
             ci = MOI.Utilities.normalize_and_add_constraint(model, fi, set)
             push!(constraints, ci)
         end
diff --git a/src/algorithms/KirlikSayin.jl b/src/algorithms/KirlikSayin.jl
index 987b462..bcf7fe0 100644
--- a/src/algorithms/KirlikSayin.jl
+++ b/src/algorithms/KirlikSayin.jl
@@ -74,23 +74,9 @@ function _update_list(L::Vector{_Rectangle}, f::Vector{Float64})
     return L_new
 end
 
-function optimize_multiobjective!(algorithm::KirlikSayin, model::Optimizer)
+function minimize_multiobjective!(algorithm::KirlikSayin, model::Optimizer)
+    @assert MOI.get(model.inner, MOI.ObjectiveSense()) == MOI.MIN_SENSE
     start_time = time()
-    sense = MOI.get(model.inner, MOI.ObjectiveSense())
-    if sense == MOI.MAX_SENSE
-        old_obj, neg_obj = copy(model.f), -model.f
-        MOI.set(model, MOI.ObjectiveFunction{typeof(neg_obj)}(), neg_obj)
-        MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
-        status, solutions = optimize_multiobjective!(algorithm, model)
-        MOI.set(model, MOI.ObjectiveFunction{typeof(old_obj)}(), old_obj)
-        MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
-        if solutions !== nothing
-            solutions = [SolutionPoint(s.x, -s.y) for s in solutions]
-        end
-        model.ideal_point .*= -1
-        return status, solutions
-    end
-    @assert sense == MOI.MIN_SENSE
     solutions = SolutionPoint[]
     # Problem with p objectives.
     # Set k = 1, meaning the nondominated points will get projected
diff --git a/src/algorithms/TambyVanderpooten.jl b/src/algorithms/TambyVanderpooten.jl
index b4b0a96..83fa1f0 100644
--- a/src/algorithms/TambyVanderpooten.jl
+++ b/src/algorithms/TambyVanderpooten.jl
@@ -81,25 +81,12 @@ function _select_search_zone(
     return k_star, upper_bounds[j_star]
 end
 
-function optimize_multiobjective!(
+function minimize_multiobjective!(
     algorithm::TambyVanderpooten,
     model::Optimizer,
 )
+    @assert MOI.get(model.inner, MOI.ObjectiveSense()) == MOI.MIN_SENSE
     start_time = time()
-    sense = MOI.get(model.inner, MOI.ObjectiveSense())
-    if sense == MOI.MAX_SENSE
-        old_obj, neg_obj = copy(model.f), -model.f
-        MOI.set(model, MOI.ObjectiveFunction{typeof(neg_obj)}(), neg_obj)
-        MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
-        status, solutions = optimize_multiobjective!(algorithm, model)
-        MOI.set(model, MOI.ObjectiveFunction{typeof(old_obj)}(), old_obj)
-        MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
-        if solutions !== nothing
-            solutions = [SolutionPoint(s.x, -s.y) for s in solutions]
-        end
-        model.ideal_point .*= -1
-        return status, solutions
-    end
     warm_start_supported = false
     if MOI.supports(model, MOI.VariablePrimalStart(), MOI.VariableIndex)
         warm_start_supported = true
@@ -111,7 +98,7 @@ function optimize_multiobjective!(
     scalars = MOI.Utilities.scalarize(model.f)
     for (i, f_i) in enumerate(scalars)
         MOI.set(model.inner, MOI.ObjectiveFunction{typeof(f_i)}(), f_i)
-        MOI.set(model.inner, MOI.ObjectiveSense(), sense)
+        MOI.set(model.inner, MOI.ObjectiveSense(), MOI.MIN_SENSE)
         MOI.optimize!(model.inner)
         status = MOI.get(model.inner, MOI.TerminationStatus())
         if !_is_scalar_status_optimal(status)
@@ -124,7 +111,7 @@ function optimize_multiobjective!(
         MOI.optimize!(model.inner)
         status = MOI.get(model.inner, MOI.TerminationStatus())
         if !_is_scalar_status_optimal(status)
-            _warn_on_nonfinite_anti_ideal(algorithm, sense, i)
+            _warn_on_nonfinite_anti_ideal(algorithm, MOI.MIN_SENSE, i)
             return status, nothing
         end
         _, Y = _compute_point(model, variables, f_i)
diff --git a/test/algorithms/Chalmet.jl b/test/algorithms/Chalmet.jl
index 8ffefb7..6ddd404 100644
--- a/test/algorithms/Chalmet.jl
+++ b/test/algorithms/Chalmet.jl
@@ -165,6 +165,23 @@ function test_unbounded()
     return
 end
 
+function test_invalid_feasibility()
+    model = MOA.Optimizer(HiGHS.Optimizer)
+    MOI.set(model, MOA.Algorithm(), MOA.Chalmet())
+    MOI.set(model, MOI.Silent(), true)
+    x = MOI.add_variables(model, 2)
+    MOI.add_constraint.(model, x, MOI.GreaterThan(0.0))
+    MOI.add_constraint(model, 1.0 * x[1] + 1.0 * x[2], MOI.LessThan(-1.0))
+    MOI.set(model, MOI.ObjectiveSense(), MOI.FEASIBILITY_SENSE)
+    f = MOI.Utilities.operate(vcat, Float64, 1.0 .* x...)
+    MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
+    MOI.optimize!(model)
+    @test MOI.get(model, MOI.TerminationStatus()) == MOI.INVALID_MODEL
+    @test MOI.get(model, MOI.PrimalStatus()) == MOI.NO_SOLUTION
+    @test MOI.get(model, MOI.DualStatus()) == MOI.NO_SOLUTION
+    return
+end
+
 function test_infeasible()
     model = MOA.Optimizer(HiGHS.Optimizer)
     MOI.set(model, MOA.Algorithm(), MOA.Chalmet())
@@ -172,6 +189,7 @@ function test_infeasible()
     x = MOI.add_variables(model, 2)
     MOI.add_constraint.(model, x, MOI.GreaterThan(0.0))
     MOI.add_constraint(model, 1.0 * x[1] + 1.0 * x[2], MOI.LessThan(-1.0))
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
     f = MOI.Utilities.operate(vcat, Float64, 1.0 .* x...)
     MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
     MOI.optimize!(model)
diff --git a/test/algorithms/DominguezRios.jl b/test/algorithms/DominguezRios.jl
index fab67d1..8720bef 100644
--- a/test/algorithms/DominguezRios.jl
+++ b/test/algorithms/DominguezRios.jl
@@ -42,6 +42,7 @@ function test_infeasible()
     x = MOI.add_variables(model, 2)
     MOI.add_constraint.(model, x, MOI.GreaterThan(0.0))
     MOI.add_constraint(model, 1.0 * x[1] + 1.0 * x[2], MOI.LessThan(-1.0))
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
     f = MOI.Utilities.operate(vcat, Float64, 1.0 .* x...)
     MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
     MOI.optimize!(model)
diff --git a/test/algorithms/EpsilonConstraint.jl b/test/algorithms/EpsilonConstraint.jl
index d8f978e..0755659 100644
--- a/test/algorithms/EpsilonConstraint.jl
+++ b/test/algorithms/EpsilonConstraint.jl
@@ -245,6 +245,7 @@ function test_infeasible()
     x = MOI.add_variables(model, 2)
     MOI.add_constraint.(model, x, MOI.GreaterThan(0.0))
     MOI.add_constraint(model, 1.0 * x[1] + 1.0 * x[2], MOI.LessThan(-1.0))
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
     f = MOI.Utilities.operate(vcat, Float64, 1.0 .* x...)
     MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
     MOI.optimize!(model)
diff --git a/test/algorithms/Hierarchical.jl b/test/algorithms/Hierarchical.jl
index ab71063..ca7b59f 100644
--- a/test/algorithms/Hierarchical.jl
+++ b/test/algorithms/Hierarchical.jl
@@ -88,6 +88,7 @@ function test_infeasible()
     x = MOI.add_variables(model, 2)
     MOI.add_constraint.(model, x, MOI.GreaterThan(0.0))
     MOI.add_constraint(model, 1.0 * x[1] + 1.0 * x[2], MOI.LessThan(-1.0))
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
     f = MOI.Utilities.operate(vcat, Float64, 1.0 .* x...)
     MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
     MOI.optimize!(model)
diff --git a/test/algorithms/TambyVanderpooten.jl b/test/algorithms/TambyVanderpooten.jl
index 231fc4c..3226b7d 100644
--- a/test/algorithms/TambyVanderpooten.jl
+++ b/test/algorithms/TambyVanderpooten.jl
@@ -39,6 +39,7 @@ function test_infeasible()
     x = MOI.add_variables(model, 2)
     MOI.add_constraint.(model, x, MOI.GreaterThan(0.0))
     MOI.add_constraint(model, 1.0 * x[1] + 1.0 * x[2], MOI.LessThan(-1.0))
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
     f = MOI.Utilities.operate(vcat, Float64, 1.0 .* x...)
     MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
     MOI.optimize!(model)