Memetic-Based Biogeography Optimization Model for the Optimal Design of Mechanical Systems

Arcílio Carlos Ferreira Peixoto and Carlos A. Conceição António ()
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Arcílio Carlos Ferreira Peixoto: Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal
Carlos A. Conceição António: Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal

Mathematics, 2025, vol. 13, issue 3, 1-30

Abstract: The science of biogeography was described through mathematical equations in 1967 by Robert MacArthur and Edward Wilson. In 2008, Dan Simon presented an algorithm called biogeography-based optimization, or BBO, which used some of the principles and definitions described in MacArthur and Wilson’s book. The objectives of this work were to study the behavior of the BBO method when it is hybridized with other evolutionary search methods and to analyze the effect of its application to some examples of mechanical engineering systems. The operators considered in the hybridization study are genetic recombination (crossover) and local search, aiming to overcome the limitations and difficulties that arise when using the original BBO. The results of the original BBO were promising in the context of a global search. However, there is a diversity problem that does not allow for good quality increments in the final phase of the evolutionary process. The additional modifications included, such as the concept of blending in migration, the cycle of mutations and the replacement of the worst solutions by injection of new ones, all show positive effects on the method’s performance. However, the biggest increase happened with the implementation of the hybridization processes. Crossover improved the speed and diversity of the population in some cases, while local search helped the algorithm in later generations, allowing it to quickly reach the optimum point. With this mentioned, it is important to note that the best results were all obtained with the fully modified algorithm. Statistical tests were implemented to validate the significance of changes due to modifications included in the original proposal of BBO.

Keywords: memetic algorithms; biogeography-based optimization; multi-objective optimization; population-based algorithms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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