Ikeda–Kita–Kobayashi (IKK)

This family is represented by the IKK1 constructor. The problem is drawn from “Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal?” [13].

Overview

IKK1 has nvar = 2 and nobj = 3. Its componentwise bounds are shown below.

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

Let $F:\mathbb{R}^2 \to \mathbb{R}^3$ be defined by $F(x)=(f_1(x),f_2(x),f_3(x))$, where $x=(x_1,x_2) \in \mathbb{R}^2$. The objectives are

\[\begin{aligned} f_1(x) &= x_1^2,\\ f_2(x) &= (x_1-20)^2,\\ f_3(x) &= x_2^2. \end{aligned}\]

Usage

julia> using MOProblems

julia> using Random

julia> prob = IKK1();

julia> lower, upper = recommended_bounds(prob);

julia> rng = MersenneTwister(1234);

julia> α = rand(rng, prob.nvar);

julia> x = lower .+ α .* (upper .- lower);

julia> values = eval_f(prob, x);

julia> J = eval_jacobian(prob, x);

julia> (length(values), size(J))
(3, (3, 2))

Constructor reference

IKK1()