Goal programming using multiple objective tabu search
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Goal programming using multiple objective tabu search A Baykasogˇlu* University of Gaziantep, Gaziantep, Turkey Goal programming (GP) is one of the most commonly used mathematical programming tools to model multiple objective optimisation (MOO) problems. There are numerous MOO problems of various complexity modelled using GP in the literature. One of the main difficulties in the GP is to solve their mathematical formulations optimally. Due to difficulties imposed by the classical solution techniques there is a trend in the literature to solve mathematical programming formulations including goal programmes, using the modern heuristics optimisation techniques, namely genetic algorithms (GA), tabu search (TS) and simulated annealing (SA). This paper uses the multiple objective tabu search (MOTS) algorithm, which was proposed previously by the author to solve GP models. In the proposed approach, GP models are first converted to their classical MOO equivalent by using some simple conversion procedures. Then the problem is solved using the MOTS algorithm. The results obtained from the computational experiment show that MOTS can be considered as a promising candidate tool for solving GP models. Keywords: goal programming; multiple objective tabu search; multi-objective optimisation
Introduction Charnes and Cooper1 proposed using GP to solve multi objective optimisation (MOO) problems. GP has been studied by many researchers2,3 and successfully applied4,5 to many problems. There are two basic types of GP. These are pre-emptive goal programming and weighted goal programming. Pre-emptive goal programming is a special case of GP, in which the more important (upper level) goals are optimised before lower level goals are considered. In non-pre-emptive models, the goals are assigned weights and considered simultaneously. There are several classical techniques for solving GP models. Some of these are: simplex based approaches (separable programming, approximation programming, etc3), modified pattern search,6 interactive approach,7 and gradient-based approach.3 Unfortunately, classical techniques impose several limitations on solving mathematical programming models including the GP ones.8 The problem is mainly related to inherent solution mechanisms of these techniques. Their solution strategies are generally dependent on the type of objective and constraint functions (linear, non-linear, etc) and the type of variables used in the problem modelling (integer, real, etc).9 Their efficiency is also dependent on the size of the solution space, number of variables and constraints used in the problem modelling, and the structure of the solution space (convex, non-convex, etc).10 They also do not offer a general solution strategy that can be applied to problem formulations where different type of variables, objective and *Correspondence: A Baykasogˇlu, Department of Industrial Engineering, University of Gaziantep, 27310 Gaziant
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