Research Article Hybridization of Adaptive Differential Evolution with an Expensive Local Search Method Rashida Adeeb Khanum, 1 Muhammad Asif Jan, 2 Nasser Mansoor Tairan, 3 and Wali Khan Mashwani 2 1 Department of Mathematics, Jinnah College for Women, University of Peshawar, Khyber Pakhtunkhwa 25000, Pakistan 2 Department of Mathematics, Kohat University of Science & Technology (KUST), Kohat, Khyber Pakhtunkhwa 26000, Pakistan 3 College of Computer Science, King Khalid University, Abha 61321, Saudi Arabia Correspondence should be addressed to Muhammad Asif Jan; majan.math@gmail.com Received 27 December 2015; Revised 9 June 2016; Accepted 14 June 2016 Academic Editor: Manlio Gaudioso Copyright © 2016 Rashida Adeeb Khanum et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Diferential evolution (DE) is an efective and efcient heuristic for global optimization problems. However, it faces difculty in exploiting the local region around the approximate solution. To handle this issue, local search (LS) techniques could be hybridized with DE to improve its local search capability. In this work, we hybridize an updated version of DE, adaptive diferential evolution with optional external archive (JADE) with an expensive LS method, Broydon-Fletcher-Goldfarb-Shano (BFGS) for solving continuous unconstrained global optimization problems. Te new hybrid algorithm is denoted by DEELS. To validate the performance of DEELS, we carried out extensive experiments on well known test problems suits, CEC2005 and CEC2010. Te experimental results, in terms of function error values, success rate, and some other statistics, are compared with some of the state- of-the-art algorithms, self-adaptive control parameters in diferential evolution (jDE), sequential DE enhanced by neighborhood search for large-scale global optimization (SDENS), and diferential ant-stigmergy algorithm (DASA). Tese comparisons reveal that DEELS outperforms jDE and SDENS except DASA on the majority of test instances. 1. Introduction Optimization is concerned with fnding best solution for an objective function. In general, an unconstrained optimization problem can be stated as follows: Find global optimum x ∗ of an objective function (x), where x = ( 1 , 2 ,...,  )∈  and  is the dimension of the problem. Evolutionary algorithms (EAs) are inspired from Dar- winian theory of evolution [1]. Tey are very efcient for fnding global optimum of many real world problems, includ- ing problems from mathematics, engineering, economics, business, and medicines. EA family consists of a variety of stochastic algorithms, like Genetic Algorithms (GAs) [2], Particle Swarm Optimization (PSO) [3, 4], Evolutionary Strategies (ES) [5], and diferential evolution algorithm (DE) [6, 7]. Among EAs, DE is the most recent algorithm and is efcient in solving many optimization problems. DE has many advantages. For example, it is simple to understand and implement, has a few control parameters, and is robust [8]. Tere is no doubt that DE is a remarkable optimizer for many optimization problems. But it has few limitations, like stagna- tion, premature convergence, and loss of population diversity [9, 10]. Being a global optimizer, DE sufers from searching the neighborhood of the approximate solution to the given problem. Tis makes room for hybridizing DE with other techniques to improve its poor exploitation (exploring the neighborhood of the approximate solutions). On the other hand, the role of LS methods is to stabilize the search especially in the environs of a local optimum. Tus, they can be combined with global search algorithms to enhance their local searching. Te main aim of this paper is to experiment with and validate the performance of our newly proposed hybrid algo- rithm, DEELS, which combines JADE [11, 12] and BFGS [13]. As a result, we want to see whether this hybridization will Hindawi Publishing Corporation Journal of Optimization Volume 2016, Article ID 3260940, 14 pages http://dx.doi.org/10.1155/2016/3260940