fix(ltdz)!: adopt Huband formulation and canonical name

Keep LTDZ as a public, non-deprecated alias and document both naming conventions, the selected transcription, and the minimization transform.

BREAKING CHANGE: the canonical catalog key and problem name change from LTDZ to LTDZ1; LTDZ() remains available as an alias.

Author: Souza-DR

docs/make.jl

@@ -45,6 +45,7 @@ makedocs(
             "KW" => "problems/kw.md",
             "LE" => "problems/le.md",
             "Lov" => "problems/lov.md",
+            "LTDZ" => "problems/ltdz.md",
         ],
         "API Reference" => "api.md",
         "References" => "references.md",

docs/src/problems/index.md

@@ -53,3 +53,7 @@ when available, and registered analytical derivatives when implemented.
 - [Lovison (Lov)](@ref): six fixed-dimension examples from Alberto Lovison
   [Lovison2011](@cite), including a smooth regularization of ZDT3
   [ZDT2000](@cite), with documented minimization conventions.
+- [Laumanns–Thiele–Deb–Zitzler (LTDZ)](@ref): one fixed-dimension,
+  three-objective problem from Laumanns, Thiele, Deb, and Zitzler
+  [Laumanns2002](@cite), using the formulation and `LTDZ1` name given in
+  Table XVI of Huband et al. [Huband2006](@cite).

docs/src/problems/ltdz.md

@@ -0,0 +1,75 @@
+# Laumanns–Thiele–Deb–Zitzler (LTDZ)
+
+This family is represented by the canonical `LTDZ1` constructor. The test
+problem originates in Equation (8) of “Combining Convergence and Diversity in
+Evolutionary Multiobjective Optimization” by Laumanns, Thiele, Deb, and
+Zitzler [Laumanns2002](@cite).
+
+The public `LTDZ()` constructor is an alias for `LTDZ1()`. Fliege, Drummond,
+and Svaiter refer to the benchmark as `LTDZ` [FDS2009](@cite), whereas Huband
+et al. assign it the catalog name `LTDZ1` [Huband2006](@cite). MOProblems.jl
+uses `LTDZ1` as the canonical catalog identity while supporting both
+constructor names.
+
+!!! note "Source transcription and optimization convention"
+    Equation (8) of Laumanns et al. is formulated for maximization and prints
+    ``f_3`` with ``\cos(\pi x_1/2)\sin(\pi x_1/2)``. Huband et al. classify
+    `LTDZ1` as apparently containing a typographical error and list ``f_3``
+    with only ``\sin(\pi x_1/2)`` in Table XVI. `LTDZ1` adopts the latter
+    expression and negates the objectives for minimization.
+
+## Overview
+
+`LTDZ1` has `nvar = 3` and `nobj = 3`. The alias `LTDZ()` constructs the same
+canonical problem and therefore also reports `prob.name == "LTDZ1"`.
+Its componentwise bounds are shown below.
+
+| Problem | `nvar` | `nobj` | Lower bound | Upper bound |
+|:---|---:|---:|---:|---:|
+| `LTDZ1` | 3 | 3 | 0.0 | 1.0 |
+
+An analytical Jacobian is registered. **Hessians are not registered**. The
+catalog metadata classifies all three objectives as not strictly convex
+(`:not_strictly_convex`).
+
+## Mathematical formulation
+
+The formulas below describe the minimization objectives implemented by both
+constructors. Let ``F:\mathbb{R}^3\to\mathbb{R}^3`` be defined by
+``F(x)=(f_1(x),f_2(x),f_3(x))``, where
+``x=(x_1,x_2,x_3)\in[0,1]^3``. The objectives are
+
+```math
+\begin{aligned}
+f_1(x) &=
+-3+(1+x_3)\cos\left(\frac{\pi x_1}{2}\right)
+             \cos\left(\frac{\pi x_2}{2}\right),\\
+f_2(x) &=
+-3+(1+x_3)\cos\left(\frac{\pi x_1}{2}\right)
+             \sin\left(\frac{\pi x_2}{2}\right),\\
+f_3(x) &=
+-3+(1+x_3)\sin\left(\frac{\pi x_1}{2}\right).
+\end{aligned}
+```
+
+## Usage
+
+```julia
+using MOProblems
+
+prob = LTDZ1()
+x = [0.5, 0.5, 0.0]
+
+values = eval_f(prob, x)
+huband_maximization_values = -values
+J = eval_jacobian(prob, x)
+
+same_prob = LTDZ()
+```
+
+## Constructor reference
+
+```@docs
+MOProblems.LTDZ1
+MOProblems.LTDZ
+```

docs/src/refs.bib

@@ -186,6 +186,20 @@ @article{KW2005
   url = {https://doi.org/10.1007/s00158-004-0465-1}
 }
 
+@article{Laumanns2002,
+  author = {Laumanns, Marco and Thiele, Lothar and Deb, Kalyanmoy and Zitzler, Eckart},
+  title = {Combining Convergence and Diversity in Evolutionary Multiobjective Optimization},
+  journal = {Evolutionary Computation},
+  volume = {10},
+  number = {3},
+  pages = {263--282},
+  year = {2002},
+  month = {09},
+  issn = {1063-6560},
+  doi = {10.1162/106365602760234108},
+  url = {https://doi.org/10.1162/106365602760234108}
+}
+
 @inproceedings{LE1997,
   author = {Lis, J. and Eiben, A. E.},
   booktitle = {Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97)},

src/MOProblems.jl

@@ -55,7 +55,7 @@ export JOS1, JOS4, KW2
 export QV1
 export SD
 export SLCDT1, SLCDT2
-export LE1, Lov1, Lov2, Lov3, Lov4, Lov5, Lov6, LTDZ
+export LE1, Lov1, Lov2, Lov3, Lov4, Lov5, Lov6, LTDZ, LTDZ1
 export MGH9, MGH16, MGH26, MGH33
 export MHHM1, MHHM2
 export MLF1, MLF2

src/Meta/LTDZ.jl

@@ -0,0 +1,7 @@
+LTDZ1_meta = ProblemMeta(
+    dimension = FixedDimension(3, 3),
+    name = "LTDZ1",
+    has_bounds = true,
+    has_jacobian = true,
+    strict_convexity = [:not_strictly_convex, :not_strictly_convex, :not_strictly_convex],
+)

src/Meta/LTDZ1.jl

@@ -1,23 +1,19 @@
 """
-    LTDZ()
+    LTDZ1()
 
-Problem characteristics summary:
-- 3 variables
-- 3 objectives
-- Objectives:
-    f₁(x) = -3 + (1 + x₃)cos(πx₁/2)cos(πx₂/2)
-    f₂(x) = -3 + (1 + x₃)cos(πx₁/2)sin(πx₂/2)
-    f₃(x) = -3 + (1 + x₃)cos(πx₁/2)sin(πx₁/2)
-- Bounds: [0, 1] for all variables
+Construct the fixed-dimension `LTDZ1` benchmark with three variables and three
+objectives. Each variable is bounded by `[0, 1]`. An analytical Jacobian is
+registered; objective Hessians are not registered.
 
-Referência:
-M. Laumanns, L. Thiele, K. Deb, E. Zitzler, Combining Convergence and Diversity in Evolutionary
-Multiobjective Optimization, Evolutionary Computation, 10(3):263–282, 2002. DOI: 10.1162/106365602760234108
+The constructor uses the third objective given for `LTDZ1` in Table XVI of
+Huband et al. (2006), rather than a literal transcription of Equation (8) in
+Laumanns et al. (2002). It negates all three maximization objectives to follow
+the package's minimization convention.
 """
-function LTDZ()
-    meta = META["LTDZ"]
-    n = default_nvar(meta)  # 3
-    m = default_nobj(meta)  # 3
+function LTDZ1()
+    meta = META["LTDZ1"]
+    n = default_nvar(meta)
+    m = default_nobj(meta)
 
     f1 = function (x::AbstractVector{T}) where {T <: AbstractFloat}
         halfpi = T(π) / T(2)
@@ -36,7 +32,7 @@ function LTDZ()
     f3 = function (x::AbstractVector{T}) where {T <: AbstractFloat}
         halfpi = T(π) / T(2)
         a = x[1] * halfpi
-        return T(-3) + (one(T) + x[3]) * cos(a) * sin(a)
+        return T(-3) + (one(T) + x[3]) * sin(a)
     end
 
     df1_dx = function (g::AbstractVector{T}, x::AbstractVector{T}) where {T <: AbstractFloat}
@@ -45,7 +41,7 @@ function LTDZ()
         b = x[2] * halfpi
         g[1] = -halfpi * (one(T) + x[3]) * sin(a) * cos(b)
         g[2] = -halfpi * (one(T) + x[3]) * cos(a) * sin(b)
-        g[3] =  cos(a) * cos(b)
+        g[3] = cos(a) * cos(b)
         return g
     end
 
@@ -54,18 +50,17 @@ function LTDZ()
         a = x[1] * halfpi
         b = x[2] * halfpi
         g[1] = -halfpi * (one(T) + x[3]) * sin(a) * sin(b)
-        g[2] =  halfpi * (one(T) + x[3]) * cos(a) * cos(b)
-        g[3] =  cos(a) * sin(b)
+        g[2] = halfpi * (one(T) + x[3]) * cos(a) * cos(b)
+        g[3] = cos(a) * sin(b)
         return g
     end
 
     df3_dx = function (g::AbstractVector{T}, x::AbstractVector{T}) where {T <: AbstractFloat}
         halfpi = T(π) / T(2)
         a = x[1] * halfpi
-        cosa = cos(a); sina = sin(a)
-        g[1] = halfpi * (one(T) + x[3]) * (cosa * cosa - sina * sina)
+        g[1] = halfpi * (one(T) + x[3]) * cos(a)
         g[2] = zero(T)
-        g[3] =  cosa * sina
+        g[3] = sin(a)
         return g
     end
 
@@ -77,4 +72,12 @@ function LTDZ()
         bounds = (zeros(n), ones(n)),
         jacobian = (df1_dx, df2_dx, df3_dx),
     )
-end
+end
+
+"""
+    LTDZ()
+
+Alias for `LTDZ1()`. Fliege, Drummond, and Svaiter (2009) use the name `LTDZ`
+for this benchmark, while Huband et al. (2006) catalog it as `LTDZ1`.
+"""
+LTDZ() = LTDZ1()

src/problems/ltdz2002.jl

@@ -4,9 +4,10 @@ using MOProblems
 @testset "Catalog Listings" begin
     names = MOProblems.get_problem_names()
     # Presença de alguns problemas conhecidos
-    for expected in ("AP1", "DTLZ1", "MOP2", "ZDT1", "ZDT6")
+    for expected in ("AP1", "DTLZ1", "LTDZ1", "MOP2", "ZDT1", "ZDT6")
         @test expected in names
     end
+    @test "LTDZ" ∉ names
 
     meta = MOProblems.META["ZDT1"]
     @test meta isa MOProblems.ProblemMeta

test/catalog/listings.jl

@@ -138,3 +138,21 @@ end
     @test_throws ErrorException eval_constraint_jacobian(unconstrained, xu)
     @test_throws ErrorException eval_constraint_hessian(unconstrained, xu)
 end
+
+@testset "LTDZ naming and corrected formulation" begin
+    canonical = LTDZ1()
+    alias = LTDZ()
+
+    @test canonical.name == "LTDZ1"
+    @test alias.name == canonical.name
+    @test eval_f(alias, [0.25, 0.5, 0.75]) ≈ eval_f(canonical, [0.25, 0.5, 0.75])
+
+    # Huband et al.'s corrected third objective omits the extra cosine factor
+    # printed in Equation (8) of Laumanns et al.
+    @test eval_f(canonical, [1.0, 0.0, 0.0]) ≈ [-3.0, -3.0, -2.0]
+    @test eval_jacobian(canonical, [0.0, 0.0, 0.0]) ≈ [
+        0.0 0.0 1.0
+        0.0 π / 2 0.0
+        π / 2 0.0 0.0
+    ]
+end