Center-Based Initialization for Large-Scale Black-Box Problems Shahryar Rahnamayan University of Ontario Institute of Technology (UOIT) Faculty of Engineering and Applied Science 2000 Simcoe Street North Oshawa, ON, L1H 7K4, Canada Shahryar.Rahnamayan@uoit.ca G. Gary Wang Simon Fraser University (SFU) Mechatronic Systems Engineering 250-13450 102 Avenue Surrey, BC, V3T 0A3, Canada Gary Wang@sfu.ca Abstract: Nowadays, optimization problems with a few thousands of variables become more common. Population- based algorithms, such as Differential Evolution (DE), Particle Swarm Optimization (PSO), Genetic Algorithms (GAs), and Evolutionary Strategies (ES) are commonly used approaches to solve complex large-scale problems from science and engineering. These approaches all work with a population of candidate solutions. On the other hand, for high-dimensional problems, no matter what is the individuals’ distribution, the population is highly sparse. Therefore, intelligent employment of individual candidates can play a crucial role to find optimal solu- tion(s) faster. The most majority of population-based algorithms utilize pseudo-random population initialization when there is no a priori knowledge about the solution. In this paper, a center-based population initialization is proposed and investigated on seven benchmark functions. The obtained results are compared with the results of Normal, Pseudo Random, and Latin Hypercube population initialization schemes. Furthermore, the advantages of the proposed center-based sampling method are investigated by a mathematical proof and also Monte Carlo (simulation) method. The detailed experimental verifications are provided for problems with 50, 500, and 1000 dimensions. Key–Words: Population Initialization, Center-Based Sampling, Evolutionary Algorithms, High-Dimensional Search Spaces, Large-Scale Problems. 1 Introduction Population-based algorithms are utilized to solve real-world complex problems. These algorithms start with a randomly generated candidate solutions when there is no a priori knowledge about the loca- tion of the global optima. We call this process popu- lation initialization. There are various sampling methods (such as Nor- mal, Halton, Sobol, and Faure). Applying these methods to initialize the population can affect the best found objective function value. Effects of pop- ulation initialization are noticeable when we solve real-life problems (mostly expensive optimizations) and when the algorithm has been stopped prema- turely because of a long computation time [1]. It means the best found objective function value is dif- ferent just in early generations. Generally, the ef- fects of population initialization diminish when the dimensionality of the search space increases and the population becomes highly sparse [1]. In the current paper, to address this shortcoming, a new sampling approach, called Center-Based Sampling, for high- dimensional search spaces is proposed. Center-based sampling tries to generate candidate solutions which have a higher chance to be closer to an unknown solution. Given mathematical proofs and reported simulation results in this paper support the proposed sampling method. Furthermore, this method has been utilized to initialize the population for seven benchmark functions (with dimensions of 50, 500, and 1000), then its results have been compared with the results of three other initialization methods. The obtained results for the proposed method are promis- ing. Sometimes the sampling methods are used not only in the initialization stage, but also during the search, learning, and optimization processes. To mention some examples, Random Search (RS) and Mode-Pursing Sampling (MPS) methods [6, 7] use Proceedings of the 8th WSEAS Int. Conf. on ARTIFICIAL INTELLIGENCE, KNOWLEDGE ENGINEERING & DATA BASES (AIKED '09) ISSN: 1790-5109 531 ISBN: 978-960-474-051-2