Permutation-based optimization problems are a class of combinatorial optimization problems that naturally arises in many real world applications and theoretical scenarios where an optimal ordering or ranking of items has to be found with respect to one or more objective criteria. Some popular examples are: flowshop scheduling problem, traveling salesman problem, quadratic assignment problem and linear ordering problem.

Since the first paper on the traveling salesman problem in 1985 by Goldberg, permutation problems have been recurrently addressed in the field of Evolutionary Computation (EC) from a wide variety of perspectives. Evolutionary algorithms, fitness landscape analysis, genotypic representations or probabilistic modeling on rankings are only a few of the topics that have been discussed in the literature.

In modern combinatorics, permutations are probably among the richest combinatorial structures. Motivated principally by their versatility - ordered set of items, collection of disjoint cycles, transpositions, matrices or graphs - permutations appear in a vast range of domains, thus making permutation problems a very special case where ideas and concepts originated from classical mathematic fields, such as algebra, geometry, and probability theory, can be exploited and used in the design of new metaheuristics and genetic operators.

All these aspects have recently motivated a strong and ongoing research interest towards permutation problems in EC. Therefore, this special session aims to highlight the most recent advances in the field and to bring together the EC researchers working in all the aspects of permutation problems.

Below, the papers presented in the second edition of the special session in IEEE WCCI 2018 are listed (names in bold correspond to the presenters in the special session):

A Meta-Learning Algorithm Selection Approach for the Quadratic Assignment Problem.

. Slides.**Augusto Dantas**and Aurora PozoHill-climbing algorithm: letâ€™s go for a walk before finding the optimum.

. Slides.**Leticia Hernando**, Alexander Mendiburu and Jose A. LozanoAn Analysis of Indirect Optimisation Strategies for Scheduling.

*Charles Neau, Olivier Regnier-Coudert and*. Slides.**John McCall**Algebraic Crossover Operators for Permutations.

*Marco Baioletti, Alfredo Milani and*. Slides.**Valentino Santucci**A Decomposition-based Local Search Algorithm for Multi-objective Sequence Dependent Setup Times Permutation Flowshop Scheduling.

. Slides.**Murilo Zangari**, Ademir Aparecido Constantino and Josu CeberioAre the artificially generated instances uniform in terms of difficulty?

. Slides.**Aritz Perez**, Josu Ceberio and Jose A. Lozano