ICSI 2011: International conference on swarm intelligence id-1 Cergy, France, June 14-15, 2011 Hybrid PSO-tabu search for solving non-linear con- strained problem Abdelghani Bekrar 1 , Sondes Chaabane 1 , Damien Trentesaux 1 , Augusto Bornschlegell 2 , Julien Pellé 2 , Souad Harmand 2 1 Université de Valenciennes, TEMPO/PSI Le Mont Houy, 59313, Valenciennes cedex 9, France abdelghani.bekrar@univ-valenciennes.fr, sondes.chaabane@univ-valenciennes.fr, Damien.Trentesaux@univ- valenciennes.fr 2 Université de Valenciennes, TEMPO/DF2T Le Mont Houy, 59313, Valenciennes cedex 9, France augusto.s.b@gmail.com, jpelle@univ-valenciennes.fr, Souad.Harmand@univ-valenciennes.fr Abstract In this paper we present a new method to solve a constrained non-linear problem. The method is based on hybridizing the Particle Swarm Optimization and tabu-search meta-heuristics (PSO- TS). Tow tabu-lists are used within the PSO algorithm: the first one aims to diversify the best solu- tions obtained by particles when the second bans temporarily solutions non-respecting the con- straints. The obtained meta-heuristic is validated on real thermal problem called T-junction prob- lem. It consists on optimizing the thermal management of the system and minimizing its over heat- ing by improving its design and the flow distribution. Our results are compared with Genetic algo- rithm. Key words Constrained non-linear problem, Particle Swarm Optimization (PSO), Tabu-search (TS), hybrid method, flow and heat transfer optimization. 1 Introduction Non-linear optimization problems are defined by non-linearity constraints and/or non-linearity objec- tive. These problems are considered in several domains: chemical engineering, energy, environment, biotechnology, thermal process… Different techniques and methods are employed to model and solve these problems. A literature survey shows that the most used techniques are: Evolutionary algorithms [1, 2], the mathematic programming algorithm [6] and other known optimization techniques. Leyffer and Maha- jan (2010) present a survey of non-linearly constrained software and methods. Two methods classes are presented: Local method and Globalization strategy [15]. Some of those approaches as Genetic algorithm need a lot of initial parameters and effort in implementations. In the thermal engineering field, many complex optimization problems are studied. More recently, non-linear optimization problems are studied using a non-traditional optimization technique. Patel and Rao [17, 18] recommended the use of the PSO. Theses study cases show that PSO is simple in con- cept, few in parameters and easy for implementation and give a good performance compared to tradi- tional techniques like genetic algorithm [17, 18]. The PSO method is applied to a large wide of optimization problems and gave generally best solu- tions. However, as mentioned by many authors its main inconvenience is the difficulty to diversify the population (see [8, 24]). To deal with this problem, researchers proposed to hybridize the PSO with other meta-heuristics.