261
An Interactive Procedure for Multiobjective
Optimization Using Nash
Bargaining Principle
V. VENUGOPAL and T.T. NARENDRAN
Indian Institute of Technology, Madras-600 036, India
This paper outlines an interactive procedure for finding a
'satisfactory' solution to the multiobjective optimization prob-
lems using Nash Bargaining Principle. The concept of 'mea-
sure of conflict' has been introduced to elicit tradeoffs between
the objectives. The suggested procedure has been implemented
on a personal computer and its performance has been com-
pared with the GDF procedure reported in the literature.
Keywords: Multiobjective optimization, Decision making, Nash
principle, Decision support.
T.T. Narendran took his PhD in In-
dustrial Engineering from the Indian
Institute of Technology, Madras, In-
dia in 1984. His professional experi-
ence includes teaching and research at
I.I.T., Madras in the fields of Oper-
ations Research, Operations Manage-
ment and Computer Simulation. His
current areas of interest include Group
Technology, Flexible Manufacturing
Systems, Scheduling, Multiobjective
Decision Making and Discrete Event
Simulation.
V. Venugopal took his M.S. in In-
dustrial Management from the Indian
Institute of Technology, Madras, In-
dia in 1987. He is currently a Research
Scholar at I.I.T., Madras. He was a
senior Software Engineer at INFO-
SYS CONSULTANTS Private Ltd.
Areas of interest include Multi-objec-
tive Decision Making, Decision Sup-
port Systems, and Flexible Manufac-
turing Systems.
North-Holland
Decision Support Systems 6 (1990) 261-268
1. Introduction
1.1. Introduction
Multiobjective optimization problems are gen-
erally complex and do not admit 'optimal' solu-
tions easily. A 'satisfactory' solution, in general, is
all that can be found. There may be a number of
acceptable solutions for such problems; yet con-
trol over the selection of a 'satisfactory' solution
requires the active participation of the decision
maker. In view of this requirement, there is an
increasing acceptance of interactive procedures,
where the decison maker is actively involved in
reaching a satisfactory solution.
Amongst the many interactive procedures that
have been developed, the GDF procedure [3] was
a pioneering effort. It finds the solution using a
series of linear approximations coupled with inter-
action with the decision maker to elicit local
tradeoffs. Subsequently a number of procedures
emerged, all of them using the idea of interaction
with the decision maker(s). The GDF procedure
has served as a benchmark for all subsequent
interactive methods that have been developed for
MODM problems. Most methods have been com-
pared with the GDF procedure for evaluation of
their relative performance. We now briefly report
other interactive methods that have been devel-
oped, to solve MODM problems.
Zionts and Wallenius [15] procedure consists of
generating a series of extreme points by minimiz-
ing the weighted sum of objective functions.
Sadagopan and Ravindran [11] developed an ex-
tended procedure to solve the non-linear case,
using the Generalized Reduced Gradient al-
gorithm. Marcotte and Soland [8] and Karwan,
Zionts and Villarreal [6] proposed interactive pro-
cedures for situations involving integer decision
variables as well. Zeleny [14] proposed an interac-
tive procedure using the independent concept of
the 'displaced ideal'. In this paper, we present an
0167-9236/90/$3.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)