702 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 12, NO. 6, DECEMBER 2008 Biogeography-Based Optimization Dan Simon, Senior Member, IEEE Abstract—Biogeography is the study of the geographical dis- tribution of biological organisms. Mathematical equations that govern the distribution of organisms were first discovered and developed during the 1960s. The mindset of the engineer is that we can learn from nature. This motivates the application of bio- geography to optimization problems. Just as the mathematics of biological genetics inspired the development of genetic algorithms (GAs), and the mathematics of biological neurons inspired the development of artificial neural networks, this paper considers the mathematics of biogeography as the basis for the development of a new field: biogeography-based optimization (BBO). We discuss natural biogeography and its mathematics, and then discuss how it can be used to solve optimization problems. We see that BBO has features in common with other biology-based optimization methods, such as GAs and particle swarm optimization (PSO). This makes BBO applicable to many of the same types of problems that GAs and PSO are used for, namely, high-dimension problems with multiple local optima. However, BBO also has some features that are unique among biology-based optimization methods. We demonstrate the performance of BBO on a set of 14 standard benchmarks and compare it with seven other biology-based opti- mization algorithms. We also demonstrate BBO on a real-world sensor selection problem for aircraft engine health estimation. Index Terms—Biogeography, evolutionary algorithms, Kalman filter, optimization, sensor selection. LIST OF ACRONYMS ACO Ant colony optimization. BBO Biogeography-based optimization. CPU Central processing unit. DARE Discrete algebraic Riccati equation. DE Differential evolution. ES Evolutionary strategy. GA Genetic algorithm. HSI Habitat suitability index. MAPSS Modular aero propulsion system simulation. PBIL Probability-based incremental learning. PSO Particle swarm optimization. SGA Stud genetic algorithm. SIV Suitability index variable. SVD Singular value decomposition. Manuscript received March 28, 2007; revised September 14, 2007. First pub- lished March 18, 2008; current version published December 2, 2008. The author is with the Department of Electrical Engineering, Cleveland State University, Cleveland, OH 44115 USA (e-mail: d.j.simon@csuohio.edu). Digital Object Identifier 10.1109/TEVC.2008.919004 I. INTRODUCTION T HE SCIENCE OF biogeography can be traced to the work of nineteenth century naturalists such as Alfred Wallace [1] and Charles Darwin [2]. Until the 1960s, bio- geography was mainly descriptive and historical. In the early 1960s, Robert MacArthur and Edward Wilson began working together on mathematical models of biogeography, their work culminating with the classic 1967 publication The Theory of Island Biogeography [3]. Their interest was primarily focused on the distribution of species among neighboring islands. They were interested in mathematical models for the extinction and migration of species. Since MacArthur and Wilson’s work, biogeography has become a major area of research [4]. A recent search of Biological Abstracts (a biology research index) reveals that 25,452 papers were written in the year 2005 that were related to the subject of biogeography. However, a search of INSPEC, an engineering research index, reveals that no biogeography papers have ever been written. In view of this, part of the motivation of this paper is to merge the burgeoning field of biogeography with engineering in order to see how the two disciplines can be of mutual benefit. The application of biogeography to engineering is similar to what has occurred in the past few decades with genetic algorithms (GAs), neural networks, fuzzy logic, particle swarm optimization (PSO), and other areas of computer intelligence. Mathematical models of biogeography describe how species migrate from one island to another, how new species arise, and how species become extinct. The term “island” here is used de- scriptively rather than literally. That is, an island is any habitat that is geographically isolated from other habitats. We there- fore use the more generic term “habitat” in this paper (rather than “island”) [4]. Geographical areas that are well suited as residences for biological species are said to have a high habitat suitability index (HSI) [5]. Features that correlate with HSI in- clude such factors as rainfall, diversity of vegetation, diversity of topographic features, land area, and temperature. The vari- ables that characterize habitability are called suitability index variables (SIVs). SIVs can be considered the independent vari- ables of the habitat, and HSI can be considered the dependent variable. Habitats with a high HSI tend to have a large number of species, while those with a low HSI have a small number of species. Habitats with a high HSI have many species that em- igrate to nearby habitats, simply by virtue of the large number of species that they host. Habitats with a high HSI have a low species immigration rate because they are already nearly satu- rated with species. Therefore, high HSI habitats are more static in their species distribution than low HSI habitats. By the same token, high HSI habitats have a high emigration rate; the large number of species on high HSI islands have many opportunities 1089-778X/$25.00 © 2008 IEEE Authorized licensed use limited to: IEEE Xplore. Downloaded on December 4, 2008 at 21:09 from IEEE Xplore. Restrictions apply.