ABSTRACT
This chapter reviews several methods developed for the linear ordering problem (LOP) and explores the problem formally, discussing its complexity and some approximation algorithms. It presents exact, greedy, and local search methods developed for the LOP, followed by a summary of metaheuristics for the problem. The branch-and-cut, a method resulting from the combination of the branch-and-bound and the cutting plane methods, has its efficiency shown for many problems, including the LOP. The chapter provides some methods that build solutions for the LOP by inserting and changing the position of vertices in the permutation using different rules and measures to evaluate the vertices in relation to the position they should be allocated. There are several metaheuristic algorithms proposed for the LOP. The iterative part of the algorithm is as follows: form the current population, a number of crossovers and mutations is applied, choosing parents to be combined and individuals to be mutated using a uniform distribution.
