Computers & Operations Research 29 (2002) 1537}1558 Hierarchical generation of Pareto optimal solutions in large-scale multiobjective systems R. Caballero*,T.Go H mez, M. Luque, F. Miguel, F. Ruiz Department of Applied Economics (Mathematics), University of Ma & laga, Campus El Ejido s/n, 29071-Ma & laga, Spain Received 1 March 2000; received in revised form 1 December 2000 Abstract Inthispaper,theproblemofthedeterminationofParetooptimalsolutionsforcertainlarge-scalesystems with multiple con#icting objectives is considered. As a consequence, a two-level hierarchical method is proposed,wheretheglobalproblemisdecomposedintosmallermultiobjectiveproblems(lowerlevel)which are coordinated by an upper level that has to take into account the relative importance assigned to each subsystem. The scheme that has been developed is an iterative one, so that a continuous information exchange is carried out between both levels in order to obtain e$cient solutions for the initial global problem. The practical implementation of the developed scheme allows us to prove its e$ciency in terms of processing time. Scope and Purpose Many are the problems that can arise when attempting to modelize and solve real problems using mathematicaltechniques.Amongthem,twoquestionsmustbepointedout.First,decisionsareusuallytaken accordingtoseveralcriteriawhichareincon#ictamongthem,ratherthanastheresultoftheoptimizationof asingleobjective.ThisfacthasbeenfacedbytheMultipleCriteriaDecisionAnalysisinitsmanyaspects(see, for example, Ignizio, Goal Programming and Extensions, Lexington Books, Massachusets, 1976 or Steuer, Multiple Criteria Optimization: Theory, Computation and Application, Wiley, New York, 1986 for an overview of the problems and techniques). Second, real problems are usually very large and complex, in the sense that many variables and constraints are involved, and complex relations hold among them. In particular, many companies have a hierarchical structure with di!erent decision levels. Such models have been studied in the literature (see Singh, Titli, Systems: Decomposition, Optimization and Control, Per- gamon Press, New York, 1978). This paper follows the line of others like Haimes et al. (Hierarchical- Multiobjective Analysis of Large-Scale Systems, Hemisphere, New York, 1990), where both aspects are combined.Namely,analgorithmisdesignedtogeneratenon-dominatedsolutionsforahierarchicalmultiple objective model.  2002 Elsevier Science Ltd. All rights reserved. * Corresponding author. Tel.: #34-5-2131168; fax: #34-5-2132061. E-mail address: r } caballero@uma.es (R. Caballero). 0305-0548/02/$-see front matter  2002 Elsevier Science Ltd. All rights reserved. PII:S0305-0548(01)00045-4