Automatica, Vol.27, No. 4. pp. 691-697, 1991 Printedin Great Britain. 0005-1098/91 $3.00 + 0.00 PergamonPressplc t~) 1991InternationalFederation of Automatic Control Brief Paper Large Scale Systems with Multiple Objectives: An Interactive Negotiation Procedure* FERNANDO ANTONIO GOMIDE,t JOS]~ ROBERTO CARDARELLI~ and KYOSTI TARVAINEN§ Key Words--Large scale systems; multiobjective optimization; interactive methods; power management; electric power systems. Abslraet--An interactive negotiation procedure for large scale systems with multiple objectives is proposed. It is assumed that there are multiple decision-makers, who have their own multiple objectives and who are dependent on each other via common resources or physical connections. The negotiation procedure includes two repeated main steps: the decision-makers' independent multicriteria optimization of their subsystems, and a convenient step for tradeoff between the decision makers. Assumptions guaranteeing the convergence of the negotiation scheme are established; among these one assumption, concerning independence of subsystems, is essential. The negotiation procedure is applied in the operation planning of two coupled hydroelectrical power systems of the southeast region of Brazil, and simulation results are included to show its usefulness in solving real world problems. The same operation planning problem is also solved by the SEMOPS method. A comparison is made from the viewpoint of methodology, practice and computational effort. The results obtained from the comparisons show that the proposed scheme is very effective in solving complex, multiobjective problems. Finally, conclusions and further work are addressed. 1. Introduction REAL WORLDproblems, in greater number, are complex and difficult to model and to solve. Most of the time the classical, single objective optimization theory is not enough to present more realistic solutions. The problems can involve more than one decision-maker, who needs to agree with one preferred solution. In addition, usually we have a multiplicity of solutions that arise due to the several objective functions inserted in the model to search the best compromise solution. Considering that the reality does not have an ordinary and well known behaviour, new theories, methods and tools have been developed to aid in looking for better solutions. An example is the multiobjective optimization theory (Chankong and Haimes, 1983) which enables an analyst to take into * Received 6 January 1990; revised 1 September 1990; received in final form 31 December 1990. The original version of this paper was presented at the llth IFAC World Congress on Automatic Control at the Service of Mankind which was held in Tallinn, Estonia, USSR during August, 1990. The published proceedings of this IFAC Meeting may be ordered from: Pergamon Press plc, Headington Hill Hall, Oxford OX3 0BW, U.K. This paper was recommended for publication in revised form by Associate Editor Y. Haimes under the direction of Editor A. P. Sage. t Unicamp/FEE/DCA, Caixa Postal 6101, 13.081 Cam- pinas SP, Brazil. Author to whom all correspondence should be addressed. ~:Villares Indtistrias de Base S.A., Av. do Estado, 01516 S~o Paulo SP, Brazil. § Helsinki University of Technology, Otakaari 1, 02150 Espoo, Finland. 691 consideration more than one objective, including the relationships among them (tradeoffs). Decision-making theory (Keeney and Raiffa, 1976), with a group utility function that possibly leads the decision-maker to use criteria explicitly from the model, and the decomposition theory (Tarvainen, 1980; Gomide, 1982) which helps an analyst to transform complex problems into a set of simpler problems with special characteristics are further examples of these developments intended to help analysts and decision-makers to search for the best compromise or preferred solution in complex, large scale systems. This paper proposes an interactive negotiation procedure--INP for large scale systems with multiple objectives as a method to obtain preferred solutions for a class of problems characterized by systems that have common resources or physical interconnections. It is based on the exchange of (tradeoff) information between an analyst and the decision-makers aiming at a best compromise solution for a problem. The INP assumes that there is a natural or induced decomposition structure in the problem, where a set of coupled (through resources) subproblems are selected. Thus, problems involving multiple decision-makers who have their own multiple objectives, and that depend on each other via common resources, and where it is possible to decompose the overall problem into a set of subproblems, are members of the class of problems addressed by the negotiation procedure proposed. The subproblems can be treated as a set of independent subproblems if one essential assumption is satisfied. This assumption guarantees the autonomy of the decision-makers, when the coupling resources are fixed. It is assumed that the decision-makers are not interested in each others preference structure per se, that is, when the couplings are fixed, the decision-makers are free to tradeoff their respective objectives in their subproblems. The INP proposed in this paper is based on tradeoff information, and there are no display difficulties. The decision-makers have information on their interdependence in the form of tradeoffs. Many others methods have been developed within the framework of multiobjective decision-making problems (Chankong et al., 1985). Regarding the class of interactive methods, Zionts and Wallenius (1976, 1980) have proposed a procedure based on the tradeoff concept and a surrogate problem. Their method is similar to the weighting method, with a basic difference in the type of information exchanged between the decision- maker and the analyst to achieve a compromise solution. The formulation assumes linear constraint set, linear or convex objective functions, and linearly additive or concave surrogate function. Another well known method is the Interactive Surrogate Worth Tradeoff procedure (Haimes and Chankong, 1983). Here, a sequence of single objective optimization problems are solved, each parameterized by the direction of the decision-maker's preferences as expressed by the tradeoffs.