Comprehensive learning TLBO with recursive precedence-based solution construction and multilevel local search for the linear ordering problem

The linear ordering problem (LOP) is a difficult permutation-based optimization task with a multitude of practical applications in different areas. The objective of the LOP is to maximize the total of the benefits associated with the pairwise precedence relations between the permuted items. Since it is NP-hard, several approximate methods have been developed to quickly produce acceptable solutions. We aim to design a specialized teaching–learning-based optimization (TLBO) method that exploits the permutation structure of the LOP. TLBO is a modern population-based metaheuristic that mimics the conventional process of transmitting knowledge and skills in a classroom. Here we extend and improve TLBO by employing a comprehensive learning strategy. In this strategy, a selected group of learners from the current class are employed as exemplars to generate new solutions. The key component of our comprehensive learning TLBO (CL-TLBO) is a recursive permutation construction procedure. It is an effective pivot-based partitioning algorithm that focuses on the pairwise precedences between permutation items in exemplar solutions to generate new candidate solutions. For better performance, we investigate different ways of selecting the pivot item at each partitioning step. Furthermore, we offer a multilevel local search technique to refine the solutions of sub-problems that are constructed during the recursive partitioning process. The experimental evaluation demonstrates a very competitive performance of the developed CL-TLBO method when compared with various well-established techniques.