Shim–Suh–Furukawa–Yagawa–Yoshimura (SSFYY)

This family is represented by the SSFYY2 constructor. It implements Test problem 2, Equation (24), from “Pareto‐based continuous evolutionary algorithms for multiobjective optimization” [32]. The package currently provides no constructors for the paper's other test problems.

Overview

SSFYY2 has fixed dimensions and is unconstrained.

The source says that the variable is initialized in $[-100,100]$ for its numerical experiment; it does not state this interval as a feasibility constraint. Accordingly, SSFYY2 does not register variable bounds. The same interval is recommended when reproducing the source's initialization setup.

An analytical Jacobian is registered. Hessians are not registered. The catalog metadata classifies $f_1$ as not strictly convex (:not_strictly_convex) and $f_2$ as strictly convex (:strictly_convex).

Mathematical formulation

Let $F:\mathbb{R}\to\mathbb{R}^2$ be defined by $F(x)=(f_1(x),f_2(x))$, where $x=(x_1)$. The constructor implements

\[\begin{aligned} f_1(x) &= 10+x_1^2-10\cos\left(\frac{\pi x_1}{2}\right),\\ f_2(x) &= (x_1-4)^2. \end{aligned}\]

Usage

julia> using MOProblems

julia> using Random

julia> prob = SSFYY2();

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))
(2, (2, 1))

Constructor reference

SSFYY2()