Expanding from Discrete Cartesian to Permutation Gene-pool Optimal Mixing Evolutionary Algorithms

The recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) family, which includes the Linkage Tree Genetic Algorithm (LTGA), has been shown to scale excellently on a variety of discrete, Cartesian-space, optimization problems. This paper shows that GOMEA can quite straightforwardly also be used to solve permutation optimization problems by employing the random keys encoding of permutations. As a test problem, we consider permutation flowshop scheduling, minimizing the total flow time on 120 different problem instances (Taillard benchmark). The performance of GOMEA is compared with the recently published generalized Mallows estimation of distribution algorithm (GM-EDA). Statistical tests show that results of GOMEA variants are almost always significantly better than results of GM-EDA. Moreover, even without using local search, the new GOMEA variants obtained the best-known solution for 30 instances in every run and even new upper bounds for several instances. Finally, the time complexity per solution for building a dependency model to drive variation is an order of complexity less for GOMEA than for GM-EDA, altogether suggesting that GOMEA also holds much promise for permutation optimization.

[1]  Tian-Li Yu,et al.  Optimization by Pairwise Linkage Detection, Incremental Linkage Set, and Restricted / Back Mixing: DSMGA-II , 2015, GECCO.

[2]  Martin Pelikan,et al.  Scalable Optimization via Probabilistic Modeling , 2006, Studies in Computational Intelligence.

[3]  James C. Bean,et al.  Genetic Algorithms and Random Keys for Sequencing and Optimization , 1994, INFORMS J. Comput..

[4]  Pei-Chann Chang,et al.  A linkage mining in block-based evolutionary algorithm for permutation flowshop scheduling problem , 2015, Comput. Ind. Eng..

[5]  D. Goldberg,et al.  Escaping hierarchical traps with competent genetic algorithms , 2001 .

[6]  Jin-Kao Hao,et al.  GASAT: A Genetic Local Search Algorithm for the Satisfiability Problem , 2006, Evolutionary Computation.

[7]  Petros Koumoutsakos,et al.  Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) , 2003, Evolutionary Computation.

[8]  Alexander Mendiburu,et al.  A Distance-Based Ranking Model Estimation of Distribution Algorithm for the Flowshop Scheduling Problem , 2014, IEEE Transactions on Evolutionary Computation.

[9]  Shlomo Moran,et al.  Optimal implementations of UPGMA and other common clustering algorithms , 2007, Inf. Process. Lett..

[10]  Dirk Thierens,et al.  More concise and robust linkage learning by filtering and combining linkage hierarchies , 2013, GECCO '13.

[11]  Fernando G. Lobo,et al.  A parameter-less genetic algorithm , 1999, GECCO.

[12]  Dirk Thierens,et al.  Scalability Problems of Simple Genetic Algorithms , 1999, Evolutionary Computation.

[13]  Peter A. N. Bosman,et al.  Exploiting Linkage Information and Problem-Specific Knowledge in Evolutionary Distribution Network Expansion Planning , 2015, GECCO.

[14]  Dirk Thierens,et al.  Benchmarking Parameter-Free AMaLGaM on Functions With and Without Noise , 2013, Evolutionary Computation.

[15]  Éric D. Taillard,et al.  Benchmarks for basic scheduling problems , 1993 .

[16]  Dirk Thierens,et al.  Crossing the road to efficient IDEAs for permutation problems , 2001 .

[17]  Martin Pelikan,et al.  Scalable Optimization via Probabilistic Modeling: From Algorithms to Applications (Studies in Computational Intelligence) , 2006 .

[18]  Tom Schaul,et al.  Natural Evolution Strategies , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).