scholarly journals Design and Analysis of Schemes for Adapting Migration Intervals in Parallel Evolutionary Algorithms

2015 ◽  
Vol 23 (4) ◽  
pp. 559-582 ◽  
Author(s):  
Andrea Mambrini ◽  
Dirk Sudholt
Keyword(s):  
Evolutionary Algorithms ◽  
Dynamic Behaviour ◽  
Upper Bounds ◽  
Expected Number ◽  
Running Time ◽  
Fundamental Parameters ◽  
Island Models ◽  
Parallel Evolutionary Algorithms ◽  
Adaptive Schemes

The migration interval is one of the fundamental parameters governing the dynamic behaviour of island models. Yet, there is little understanding on how this parameter affects performance, and how to optimally set it given a problem in hand. We propose schemes for adapting the migration interval according to whether fitness improvements have been found. As long as no improvement is found, the migration interval is increased to minimise communication. Once the best fitness has improved, the migration interval is decreased to spread new best solutions more quickly. We provide a method for obtaining upper bounds on the expected running time and the communication effort, defined as the expected number of migrants sent. Example applications of this method to common example functions show that our adaptive schemes are able to compete with, or even outperform, the optimal fixed choice of the migration interval, with regard to running time and communication effort.

scholarly journals General Upper Bounds on the Runtime of Parallel Evolutionary Algorithms*

2014 ◽  
Vol 22 (3) ◽  
pp. 405-437 ◽  
Author(s):  
Jörg Lässig ◽  
Dirk Sudholt
Keyword(s):  
Evolutionary Algorithms ◽  
Upper Bounds ◽  
Constant Factor ◽  
Structured Populations ◽  
Fitness Level ◽  
Performance Guarantees ◽  
Parallel Evolutionary Algorithms ◽  
Spatially Structured Populations ◽  
Boolean Optimization ◽  
General Method

We present a general method for analyzing the runtime of parallel evolutionary algorithms with spatially structured populations. Based on the fitness-level method, it yields upper bounds on the expected parallel runtime. This allows for a rigorous estimate of the speedup gained by parallelization. Tailored results are given for common migration topologies: ring graphs, torus graphs, hypercubes, and the complete graph. Example applications for pseudo-Boolean optimization show that our method is easy to apply and that it gives powerful results. In our examples the performance guarantees improve with the density of the topology. Surprisingly, even sparse topologies such as ring graphs lead to a significant speedup for many functions while not increasing the total number of function evaluations by more than a constant factor. We also identify which number of processors lead to the best guaranteed speedups, thus giving hints on how to parameterize parallel evolutionary algorithms.

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