Continuous Benchmark Functions - Self-Adaptive Heuristics for Evolutionary Computation - page 144

where

y 1 = x 2 + x 3 +41 . 6
c 1 =0 . 024 x 4 − 4 . 62

.
c 16 =1 . 104

(A.37)

− 0 . 72 y 15

c 17 = y 9 + x 5

with bounds 704 . 4148

≤ x 1 ≤

906 . 3855, 68 . 6

≤ x 2 ≤

288 . 88, 0

≤ x 3 ≤

134 . 75,

84 . 1988, best known solution x ∗ ≈
(705 . 174 , 68 . 599 , 102 . 899 , 282 . 324 , 37 . 584) T where f ( x ∗ )= − 1 . 90515525853479,
constraints and conditions can be found in [83].

≤ x 4 ≤

287 . 0966 and 25

≤ x 5 ≤

193

g24

Minimize

f ( x )= − x 1 − x 2 (A.38)

constraints

g 1 ( x )= − 2 x 1 +8 x 1 − 8 x 1 + x 2 − 2 ≤ 0

(A.39)

4 x 1 +32 x 1 − 88 x 1 +96 x 1 + x 2 −

g 2 ( x )= − 36 ≤ 0

4, optimum x ∗ =(2 . 329520197 , 3 . 178493074) T with 0 ≤ x 1 ≤ 3and0 ≤ x 2 ≤

with f ( x ∗ )= 5 . 508013271, feasible starting point x (0) =(0 , 0) T

− with

f ( x (0) )=0 . 0.

Properties of the g Problems

Table A.1 summarizes the properties of the g-problems as described in [83].

Table A.1. Properties of the g problems. N is the number of objective variables,
| F | / | S | is the estimated ratio between the feasible search space F and whole search
space S . LI is the number of linear inequality constraints, NI the number of nonlinear
inequality constraints, LE is the number of linear equality constraints, NE is the number
of nonlinear equality constraints, and active is the number of active constraints.

problem N type of function | F | / | S | (%)LINILENEactive

g01 13 quadratic 0.0111 9 0 0 0 6

g02 20 nonlinear 99.9971 0 2 0 0 1

g04 5 quadratic 52.1230 0 6 0 0 2

g06 2 cubic 0.0066 0 2 0 0 2

g07 10 quadratic 0.0003 3 5 0 0 6

g08 2 nonlinear 0.8560 0 2 0 0 0

g09 7 polynomial 0.5121 0 4 0 0 2

g11 2 quadratic 0.0000 0 0 0 1 1

g12 3 quadratic 4.7713 0 1 0 0 0

g16 5 nonlinear 0.0204 4 34 0 0 4

g24 2 linear 79.6556 0 2 0 0 2