Information Technology Reference
In-Depth Information
c. Maintaining infeasible solutions: A few researchers have proposed maintaining a
proportion of infeasible solutions in the population during the course of evolution.
For single-objective optimization, Coello Coello [4] proposed splitting the population
into various subpopulations, each of which uses either the objective or one of the
constraints as the fitness function to increase the diversity. Mezura and Coello [5]
introduced an archive of infeasible solutions in which the “best” infeasible solution
determined by its objective function value is allowed to be copied into the next gener-
ation. Cai and Wang [6] suggested a modification of Mezura and Coello [5] approach
by using a non-dominated ranking for all the solutions. To focus the search on
constraint boundaries with an aim of achieving good quality feasible as well as mar-
ginally infeasible solutions, Infeasibility Driven Evolutionary Algorithm (IDEA) was
proposed in [7]. IDEA uses a constraint violation measure which firstly ranked the
solutions according to each constraint violation, then the sum value of the relative
ranking number is defined as a extensional objective function to evolve;thus deliver-
ing good quality feasible solutions as well as marginally infeasible solutions for trade-
off considerations. This method adds an objective function, also increase the objective
space search difficulty.
d. Hybrid methods: A dynamic hybrid framework is proposed by Wang and Cai
[15] [16]. The proposed framework consists two major component: global search
model and local search model. The search engine used differential evolution [17] ,
and the selection mechanism of individuals is carried out under pareto-domination
concept. This framework has the advantage of implementing global and local search
dynamically based on the feasibility proprotion in the current population.
In this paper, Infeasibility driven and constrained-domination principles are em-
bedded into MOEA/D. This constraint handling approach intrinsically treats
constraint violation and aggregation function values separately and keeps a balance
between exploration and exploitation in the evolution process, wherein a number of
infeasible solutions are merged with feasible solutions to evolve and update offspring.
Experimental results on several benchmark problems show that the approach per-
forms more effectively and efficiently than the other methods for constrained multi-
objective optimization in comparison. The performance of the algorithm is also illu-
strated using a real-world constraint optimization problem i.e. the two-stage planetary
gear transmission system optimization [8] [12].
The remainder of the paper is organized as follows. The details of the proposed al-
gorithm are presented in Section 2 while the experimental results and performance of
the algorithm are presented in Section 3. Our proposed MOEA/D_CDP_ID is applied
to the two-stage planetary gear transmission system optimization in Section 4. Finally,
the paper concludes with some final remarks.
2
The Proposed Approach
The proposed approach extends the ability of MOEA/D [1] [17] to deal with
constrained multiobjective optimization problems. Infeasibility driven [7] and con-
strained-domination principle [3] are embedded to MOEA/D. The details of the
proposed schemes are discussed below:
Search WWH ::
Custom Search