On the impact of linkage learning, gene-pool optimal mixing, and non-redundant encoding on permutation optimization

Arthur Guijt,Ngoc Hoang Luong,Peter A.N Bosman,Mathijs De Weerdt

doi:10.1016/j.swevo.2022.101044

Abstract

Gene-pool Optimal Mixing Evolutionary Algorithms (GOMEAs) have been shown to achieve state-of-the-art results on various types of optimization problems with various types of problem variables. Recently, a GOMEA for permutation spaces was introduced by leveraging the random keys encoding, obtaining promising first results on permutation flow shop instances. A key cited strength of GOMEAs is linkage learning, i.e., the ability to determine and leverage, during optimization, key dependencies between problem variables. However, the added value of linkage learning was not tested in depth for permutation GOMEA. Here, we introduce a new version of permutation GOMEA, called qGOMEA, that works directly in permutation space, removing the redundancy of using random keys. We additionally consider various linkage information sources, including random noise, in both GOMEA variants, and compare performance with various classic genetic algorithms on a wider range of problems than considered before. We find that, although the benefits of linkage learning are clearly visible for various artificial benchmark problems, this is far less the case for various real-world inspired problems. Finally, we find that qGOMEA performs best, and is more applicable to a wider range of permutation problems.

Highlights

Permutation problems are among the most important real-world problems
In addition to the Gene-pool Optimal Mixing Evolutionary Algorithms (GOMEAs) – Permutation GOMEA (pGOMEA) and qGOMEA – with both Linkage Tree and Random Tree models, we evaluate the performance of standard permutation crossover operators – CX[17], PMX[16], OX[15], Edge Recombination (ER)[18] – and uniform crossover on Random Keys [9] in a simple-GA setup
One example of limitations regarding the number of configurations is that we only covered a configuration of qGOMEA using PMX-style repair once. We note that such modifications to qGOMEA can improve performance on various problems, and much like traditional crossover, provide significant performance benefits when the chosen repair matches the problem at hand

Summary

Introduction

Scheduling problems, such as Permutation Flowshop or Jobshop Scheduling, and routing problems, such as Traveling Salesperson, are permutation problems that can be used to model realworld optimization tasks. Significant scalability improvements have been made by linkage learning, i.e., the automatic accounting for dependencies between problem variables by deriving and exploiting them during optimization, for instance through the estimation of probability distributions as done in Estimation of Distribution Algorithms (EDAs) [3,4]. Of particular interest are the more recent Gene–pool Optimal Mixing Evolutionary Algorithms GOMEAs [5], which have been shown to be able to outperform EDAs on various benchmark problems for problems with discrete Cartesian variables as well as problems with real-valued variables by learning linkage more directly through information theoretic measures and by exploiting this information through more extensive solution mixing in each generation [5,6,7]

Methods

Results

Discussion

Conclusion