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On Easiest Functions for Mutation Operators in Bio-Inspired Optimisation.

Dogan Corus¹, Jun He², Thomas Jansen²

¹2Department of Computer Science, University of Sheffield, Sheffield, S1 4DP UK.

|February 28, 2020

Summary

This summary is machine-generated.

This study identifies MinBlocks as an easiest function for the (1+1) Evolutionary Algorithm with contiguous somatic hypermutation (CHM). Hybrid algorithms combining CHM and standard bit mutation (SBM) achieve optimal performance on easiest functions for individual operators.

Keywords:

Artificial immune systems Evolutionary algorithms Hybridisation Running time analysis Theory

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Area of Science:

Computer Science
Artificial Intelligence
Bio-inspired Computing

Background:

Analyzing algorithm performance requires understanding easy and hard function classes.
OneMax is known as an easiest function for (1+1) Evolutionary Algorithm with standard bit mutation (SBM), while Trap is a hardest function.

Purpose of the Study:

Extend the analysis of easiest function classes to the contiguous somatic hypermutation (CHM) operator.
Investigate hybrid algorithms combining CHM and SBM for improved performance.

Main Methods:

Define and analyze the MinBlocks function as an easiest function for (1+1) EA with CHM.
Conduct runtime and fixed budget analyses for MinBlocks.
Rigorously prove the performance of hybrid algorithms combining CHM and SBM.

Main Results:

MinBlocks is proven to be an easiest function for (1+1) EA with CHM.
Hybrid algorithms using CHM and SBM demonstrate optimal asymptotic performance on OneMax and MinBlocks.
Easiest functions for hybrid algorithms are not simple weighted combinations of individual operator easiest functions.

Conclusions:

Contiguous somatic hypermutation (CHM) has a distinct easiest function, MinBlocks.
Hybrid algorithms effectively leverage the strengths of multiple operators, achieving optimal performance on diverse function classes.
The design of easiest functions for hybrid algorithms requires a nuanced understanding beyond simple aggregation.