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)