Extended Nondominated Sorting Genetic
Algorithm (ENSGA-II)
for Multi-Objective Optimization
Problem in Interval Environment
Asoke Kumar Bhunia, Amiya Biswas and Ali Akbar Shaikh
1 Introduction
In the existing literature of optimization, most of the works have been reported for
optimization of single objective. However, in real-world design or decision-making
problems, it is often required to simultaneously optimize more than one objective
functions which are conflicting in nature. The goal of these problems is to maximize
or minimize several conflicting objectives simultaneously. These types of problems
are known as multi-objective optimization problems. In this subarea, most of the
works have been done in crisp environment. However, in reality, due to uncertainty
or ambiguity, the parameters of the problems are not always precise and should
be considered as imprecise. To represent the impreciseness of a parameter, several
approaches like stochastic, fuzzy, fuzzy stochastic and interval approaches have been
reported in the existing literature. Among these approaches, interval approach is
more significant. Due to this representation, either all the objectives or some of the
objectives would be interval valued.
Thus, the general form of multi-objective optimization problem with interval
objectives can be written as
Minimize { A
1
(x ), A
2
(x ),..., A
k
(x )}
A. K. Bhunia (B ) · A. A. Shaikh
Department of Mathematics, The University of Burdwan, Burdwan 713104, West Bengal, India
e-mail: akbhunia@math.buruniv.ac.in
A. A. Shaikh
e-mail: aliashaikh@math.buruniv.ac.in
A. Biswas
Department of Mathematics, A. B. N. Seal College, Cooch Behar 736101, India
e-mail: amiya2al@gmail.com
© Springer Nature Singapore Pte Ltd. 2018
J. K. Mandal et al. (eds.), Multi-Objective Optimization,
https://doi.org/10.1007/978-981-13-1471-1_10
215