From 79a297b11f24d287f987b280f5b8e335bb388ae6 Mon Sep 17 00:00:00 2001
From: Paras Puneet Singh <136245940+ParasPuneetSingh@users.noreply.github.com>
Date: Fri, 20 Sep 2024 21:52:51 +0530
Subject: [PATCH] Update evolutionary.md

MOO docs update.
---
 .../src/optimization_packages/evolutionary.md | 20 +++++++++++++++++++
 1 file changed, 20 insertions(+)

diff --git a/docs/src/optimization_packages/evolutionary.md b/docs/src/optimization_packages/evolutionary.md
index 9fa582c74..9ed2a2645 100644
--- a/docs/src/optimization_packages/evolutionary.md
+++ b/docs/src/optimization_packages/evolutionary.md
@@ -41,3 +41,23 @@ f = OptimizationFunction(rosenbrock)
 prob = Optimization.OptimizationProblem(f, x0, p, lb = [-1.0, -1.0], ub = [1.0, 1.0])
 sol = solve(prob, Evolutionary.CMAES(μ = 40, λ = 100))
 ```
+
+## Multi-objective optimization
+The Rosenbrock and Ackley functions can be optimized using the `Evolutionary.NSGA2()` as follows:
+
+```@example MOO-Evolutionary
+using Optimization, OptimizationEvolutionary
+function func(x, p=nothing)::Vector{Float64}
+  f1 = (1.0 - x[1])^2 + 100.0 * (x[2] - x[1]^2)^2  # Rosenbrock function
+  f2 = -20.0 * exp(-0.2 * sqrt(0.5 * (x[1]^2 + x[2]^2))) - exp(0.5 * (cos(2π * x[1]) + cos(2π * x[2]))) + exp(1) + 20.0  # Ackley function
+  return [f1, f2]
+end
+initial_guess = [1.0, 1.0]
+function gradient_multi_objective(x, p=nothing)
+    ForwardDiff.jacobian(func, x)
+end
+obj_func = MultiObjectiveOptimizationFunction(func, jac=gradient_multi_objective)
+algorithm = OptimizationEvolutionary.NSGA2()
+problem = OptimizationProblem(obj_func, initial_guess)
+result = solve(problem, algorithm)
+```