Table 1 Multi-objective optimization test problems. We tested the JuPOETs implementation on three two-dimensional test problems, with one-, two- and three-dimensional parameter vectors. Each problem had parameter bounds constraints, however, on the Binh and Korn function had additional non-linear problem constraints. For the Fonesca and Fleming problem, N = 3

Schaffer function

1

O ₁(x)=x ²

−10≤x≤10

O ₂(x)=(x−2)²

Binh and Korn function

2

O ₁(x,y)=4x ²+4y ²

0≤x≤5

g ₁(x,y)=(x−5)²+y ²≤25

O ₂(x,y)=(x−5)²+(y−5)²

0≤x≤3

g ₂(x,y)=(x−8)²+(y+3)²≤7.7

Fonseca and Fleming function

3

\(O_{1}(x_{i})= 1 - \text {exp} \left (- \sum \limits ^{N}_{i= 1} \left (x_{i} - \frac {1}{\sqrt {N}}\right)^{2} \right) \)

−4≤x _i ≤4

\(O_{2}(x_{i})= 1 - \text {exp} \left (- \sum \limits ^{N}_{i= 1} \left (x_{i} + \frac {1}{\sqrt {N}}\right)^{2} \right) \)