Biogeography-Based Optimization

Biogeography is the study of the geographical distribution 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 biogeography 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 optimization algorithms. We also demonstrate BBO on a real-world sensor selection problem for aircraft engine health estimation.

[1]  A. Wallace.  The geographical distribution of animals , 1876 .

[2]  V. Ball,et al.  The Geographical Distribution of Animals , 1868, The American Naturalist.

[3]  N. Pierce.  Origin of Species , 1914, Nature.

[4]  R. Macarthur,et al.  The Theory of Island Biogeography , 1969 .

[5]  B. Noble.  Applied Linear Algebra , 1969 .

[6]  T. Wesche,et al.  Modified Habitat Suitability Index Model for Brown Trout in Southeastern Wyoming , 1987 .

[7]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[8]  P. Holgate,et al.  Matrix Population Models. , 1990 .

[9]  C. Chen,et al.  Principles and Techniques in Combinatorics , 1992 .

[10]  Heinz Mühlenbein,et al.  Predictive Models for the Breeder Genetic Algorithm I. Continuous Parameter Optimization , 1993, Evolutionary Computation.

[11]  A. Hastings,et al.  Persistence of Transients in Spatially Structured Ecological Models , 1994, Science.

[12]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[13]  David B. Fogel,et al.  Evolutionary algorithms in theory and practice , 1997, Complex.

[14]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms in Engineering Applications , 1997, Springer Berlin Heidelberg.

[15]  Rainer Storn,et al.  Differential Evolution-A simple evolution strategy for fast optimization , 1997 .

[16]  Peter J. Fleming,et al.  The Stud GA: A Mini Revolution? , 1998, PPSN.

[17]  Rainer Storn,et al.  System design by constraint adaptation and differential evolution , 1999, IEEE Trans. Evol. Comput..

[18]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

[19]  Ian C. Parmee,et al.  Evolutionary and adaptive computing in engineering design , 2001 .

[20]  Hans-Georg Beyer,et al.  The Theory of Evolution Strategies , 2001, Natural Computing Series.

[21]  Phillip D. Stroud,et al.  Kalman-extended genetic algorithm for search in nonstationary environments with noisy fitness evaluations , 2001, IEEE Trans. Evol. Comput..

[22]  Thomas Stützle,et al.  Guest editorial: special section on ant colony optimization , 2002, IEEE Trans. Evol. Comput..

[23]  Y. Ho,et al.  Simple Explanation of the No-Free-Lunch Theorem and Its Implications , 2002 .

[24]  Russell C. Eberhart,et al.  Guest Editorial Special Issue on Particle Swarm Optimization , 2004, IEEE Trans. Evol. Comput..

[25]  Marco Dorigo.  Ant colony optimization , 2004, Scholarpedia.

[26]  Godfrey C. Onwubolu,et al.  New optimization techniques in engineering , 2004, Studies in Fuzziness and Soft Computing.

[27]  Carlos A. Coello Coello,et al.  A simple multimembered evolution strategy to solve constrained optimization problems , 2005, IEEE Transactions on Evolutionary Computation.

[28]  D. Simon,et al.  On optimization of sensor selection for aircraft gas turbine engines , 2005, 18th International Conference on Systems Engineering (ICSEng'05).

[29]  Christian Blum,et al.  Ant colony optimization: Introduction and recent trends , 2005 .

[30]  Edmund K. Burke,et al.  The Speciating Island Model: An alternative parallel evolutionary algorithm , 2006, J. Parallel Distributed Comput..

[31]  M. Clerc,et al.  Particle Swarm Optimization , 2006 .

[32]  D. S. Bernstein,et al.  Optimization R Us [from the Editor] , 2006 .

[33]  Dennis S. Bernstein,et al.  Quiet, please? [from the Editor] , 2006 .

[34]  Dan Simon,et al.  Kalman Filter Constraint Switching for Turbofan Engine Health Estimation , 2006, Eur. J. Control.

[35]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[36]  Yong Wang,et al.  A Multiobjective Optimization-Based Evolutionary Algorithm for Constrained Optimization , 2006, IEEE Transactions on Evolutionary Computation.

[37]  Jiatao Song,et al.  A Genetic Algorithm with Age and Sexual Features , 2006, ICIC.

[38]  S. Schreiber,et al.  On dispersal and population growth for multistate matrix models , 2006 .

[39]  Mauro Birattari,et al.  Swarm Intelligence , 2012, Lecture Notes in Computer Science.

[40]  Manuel López-Ibáñez,et al.  Ant colony optimization , 2010, GECCO '10.