Abstract— This paper presents a variant of diversity guided Particle Swarm Optimization (PSO) algorithm named QIPSO for solving global optimization problems. In QIPSO the conventional framework of PSO is modified by including a crossover operator to maintain the level of diversity in the swarm population. Numerical results show that the induction of a crossover operator not only discourages premature convergence to the local optima but also explores promising regions of the search space effectively. Empirical results show the superior performance of QIPSO with conventional PSO and ARPSO. Efficiency of QIPSO is further validated by applying it to a set of five real life problems (RLPs) with constraints. Penalty method is used for dealing with constraints. Once again the simulation results show the compatibility of QIPSO for solving real life problems. Index Terms— Particle Swarm Optimization, Crossover operator, Quadratic Interpolation, Real life problems. I. INTRODUCTION Population based search algorithms like Genetic Algorithms (GA), Evolutionary Programming (EP), Differential Evolution (DE), Particle Swarm Optimization (PSO) etc. are perhaps some of the most popular stochastic techniques for solving continuous global optimization problems. These techniques have shown their efficiency for solving complex test as well as real life problems. Of the above mentioned algorithms other than PSO all other algorithms are inspired by the phenomenon of Darwin’s concept of ‘survival of the fittest’. Classical PSO on the other hand follows the policy of cooperation and social behavior displayed by various species like ants, birds, fish etc. Nevertheless all the above mentioned algorithms share some common features as pointed out by Angeline [1]: ｾ All are population based search techniques. ｾ None of the above mentioned algorithms require the auxiliary knowledge (like continuity, differentiability etc.) of the problem. ｾ In all the algorithms solutions belonging to the same population interact with each other during the search process. ｾ The quality of the solutions are improved using techniques inspired from real world phenomenon like human Manuscript received June 19, 2008. Millie Pant is with the Department of Paper Technology, Indian Institute of Technology Roorkee, (Saharanpur Campus), Saharanpur – 247001, India. (e-mail: millifpt@iitr.ernet.in ). Radha Thangaraj is with the Department of Paper Technology, Indian Institute of Technology Roorkee, (Saharanpur Campus), Saharanpur – 247001, India. (e-mail: t.radha@ieee.org ). V.P.Singh is with the Department of Paper Technology, Indian Institute of Technology Roorkee, (Saharanpur Campus), Saharanpur – 247001, India. (e-mail: singhfpt@iitr.ernet.in ). genetics in case of EA and cooperative behavior in case of PSO. It is worth mentioning that although these algorithms have been successful in solving a wide variety of problems, their performance is criticized one certain aspects. For example the problem of the loss of diversity after subsequent iterations which lead to premature convergence leading to suboptimal solution [2]. Loss of diversity becomes more prominent for multimodal functions having several optima or noisy functions where the optimum keeps shifting from one position to other. Loss of diversity generally takes place when the balance between the two antagonists processes exploration (searching of the search space) and exploitation (convergence towards the optimum) is disturbed. In case of evolutionary algorithms the population diversity is generally lost during the process of evolution (crossover and mutation), whereas in case of PSO the diversity loss is generally attributed to the fast information flow between the swarm particles. Thus in absence of a good diversity enhancing mechanism the optimization algorithms are unable to explore the search space effectively. One of the simplest methods to overcome the problem of diversity loss is to capitalize the strengths of EA and PSO together in an algorithm. A variety of methods combining the aspects of EA and PSO are available in literature. For detailed study, the reader is suggested [3] - [5], etc. Out of the EA operators, mutation is the most widely used EA tool applied in PSO [6] - [9] etc. However very few examples of selection and crossover operator are available in literature. Keeping this in mind we proposed a variant of diversity guided PSO called QIPSO which make use of crossover operator to maintain the diversity of the population [10]. In [10], we defined a new nonlinear quadratic crossover operator which makes use of three members of the swarm to produce a new member. This operator is activated when the diversity of the swarm becomes less than a certain threshold (say d low ) and stops when the required diversity (say d high ) is achieved. We checked the QIPSO algorithm with thirteen test suit of benchmark problems (unconstrained), the experimental results shown that the new algorithm gave better results. Motivated by the preliminary good results shown by QIPSO and to further validate its efficiency, we used it to solve real life engineering design problems with constraints associated with them. Penalty function approach is used to deal with constraints. The structure of the paper is as follows: in section II, we briefly explain the BPSO and ARPSO (another diversity guided PSO [11]), in section III; we describe the QIPSO algorithm and its performance on thirteen standard benchmark problems taken from literature. Section IV deals with the performance of QIPSO algorithm for constrained optimization problems. Finally the paper concludes with section V. Particle Swarm Optimization with Crossover Operator and its Engineering Applications Millie Pant, Member, IAENG, Radha Thangaraj, Member, IAENG, and V. P. Singh IAENG International Journal of Computer Science, 36:2, IJCS_36_2_02 ______________________________________________________________________________________ (Advance online publication: 22 May 2009)