Hybridizing Infeasibility Driven and Constrained- Domination Principle with MOEA/D for Constrained Multiobjective Evolutionary Optimization - Technologies and Applications of Artificial Intelligence - page 255

Table 2. Summary of Test Problem

problem obj/D Search Range Constraints

Ineq. Eq.

CONSTR 2/2 [0.1,1],[0,5] 2 0

[-20,20] D

SRN 2/2 2 0

[0,10],[0,10],[1,5]
[0,6],[1,5],[0,10]

OSY 2/6 6 0

Table 3. Mean and standard deviation of hypervolume metric values obtained by four
Algorithm for benchmark problems

Instance
Hypervolume
(Runs=30)

CONSTR
( ref [1,10] )

SRN
( ref [300,150] )

OSY
( ref [0,200] )

mean std mean std mean std

MOEA/D-CDP-ID 3.95e-1 1.07e+5 1.15e+5

1.054e+1 6.66e+5 1.58e+5

MOEA/D-CDP 1.049e+1 5.49e-3 3.48e+5 3.01e+4 7.42e+4 2.21e+4

NSGAII-CDP-ID 1.050e+1 5.34e-3 9.00e+5 9.46e+4 1.35e+5 6.29e+4

NSGAII-CDP 1.051e+1 2.881e-3 6.98e+5 7.09e+4 7.82e+4 7.42e+3

4 Engineering Optimization Problem

4.1 Two-Stage Planetary Gear Transmission System Optimization Problems

The design problem of two-stage planetary gear transmission system is a ten-variable
and bi-objective constrained multiobjective optimization problem [8] [12]. The goal
of the design is to minimize volume and the maximize efficiency of the two-stage
planetary gear transmission system.

Fig. 3. Two-stage planetary gear transmission system