Enhanced Two-Step Satisfactory Method for Multi-Objective Optimization with Fuzzy Parameters - Intelligent Computing for Sustainable Energy and Environment - page 122

Enhanced Two-Step Satisfactory Method
for Multi-Objective Optimization
with Fuzzy Parameters
Chaofang Hu, Qizhi Liu, and Yanwen Liu
School of Electrical Engineering and Automation, Tianjin University,
Tianjin, China
[e-mail], [e-mail], [e-mail]
Abstract. An enhanced two-step satisfactory method for multi-
objective optimization problem with fuzzy parameters is proposed in
this paper. By means of the α -level sets of the fuzzy numbers, all the ob-
jectives with fuzzy parameters are modeled as the fuzzy goals. The order
of satisfactory degrees about different denoting that the higher priority
achieves the higher satisfactory degree is applied to preemptive priority
requirement. The strict order constraints are relaxed by decreasing the
maximum overall satisfactory degree. The original optimization prob-
lem is divided into two models to be solved iteratively. The satisfactory
solution can be acquired by changing parameter or regulating α .The
numerical example demonstrates the power of the proposed method.
Keywords: Multi-objective optimization, fuzzy parameter, priority.
1 Introduction
Recently, Multi-Objective Optimization (MOO) problem has become more and
more obvious and important in production, economy, and everyday life, where
multiple objectives are conflicting, non-commensurable and imprecise. Its study
and development have attracted many researchers [1][2]. In the real world, MOO
problem takes place in a vague environment in which the goals or parameters of
the objectives and constraints are not known precisely. This problem is called
Fuzzy Multi-Objective Optimization (FMOO) [3][4][5]. In FMOO, the preemp-
tive priority requirement, as a common and practical preference, is often given
by Decision Maker (DM), which means all the objectives being classified into the
different levels in terms of their importance. Traditionally, the lexicographic op-
timization is interesting [6], where the multiple subproblems including different
objectives are solved in lexicographic order. However, this maybe results in the
complex computation or the degenerative optimization. Chen et al. [7] propose
the higher priority having higher satisfactory degree for the preemptive prior-
ity. Nevertheless, the satisfactory even feasible solution for the strict comparison
doesn't possibly exist. The generalized varying-domain optimization method is
presented by Hu et al. [8]. But it strengthens the nonlinearity of the original