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Top1. Introduction
Estimation of Distribution Algorithms (EDAs) have been widely published in more than two decades. These algorithms have shown to be efficient to solve optimization problems. In addition, these algorithms have been used to tackle combinatorial problems. It can be considered that there are two classifications for the EDAs, i.e., pure EDAs and hybrid EDAs.
Pure EDAs base their performance on a probability model to find new solutions from previous solutions meanwhile hybrid EDAs base their performance on an interaction between a probability model and some another technique or method to generate offspring or to improve the performance of the algorithm. As hybrid EDAs is considered the Peña et al´s (2004) research for solving synthetic optimizations problems. The Zhang et al´s (2006) algorithm for the quadratic assignment problem. The Liu et al´s (2011) study for the permutation flow-shop scheduling problem. The Wang´s (2012) method for the flexible job-shop scheduling problem. The Fang et al´s (2015) algorithm for the stochastic resource-constrained project-scheduling problem, and the Wang et al´s (2016) research for the distributed permutation ñowshop scheduling problems under machine breakdown. The articles mentioned above are current and representative of this group of hybrid EDAs.
Both pure EDAs and hybrid EDAs have been widely used to solve combinatorial problems. The development of EDAs does not finish in this point. Recently, new EDAs have been published. These EDAs have a new characteristic. These utilize permutation of elements-based representation as a solution to solve combinatorial optimization problems. That is, these algorithms propose specific probability models to integrate solutions as permutation-based representation. This category is named distance-based ranking models. The proposed EDA by Ceberio et al (2014) for flow-shop scheduling problem, the Pérez-Rodríguez et al´s (2017) study for the school bus routing problem with bus stop selection, the Pérez-Rodríguez & Hernández-Aguirre´s (2018) algorithm for the flexible job-shop scheduling problem with process plan flexibility, and the Pérez-Rodríguez & Hernández-Aguirre´s (2019) technique for the vehicle routing problem with time windows, are currently published papers belonging to this category.
From the previous classification, it can be seen that recent authors have combined new and recognized methodologies to solve optimization problems such as the job-shop scheduling problem. Recently, other studies make comparisons between other algorithms, such as the genetic algorithm, the particle swarm optimization algorithm, multi-objective algorithms, and others. Currently, other researchers show the effectiveness and efficiency of the proposed methods as a part of their manuscripts. The published methods try to get new solutions to some benchmark problems. The cited methods carried out experiments on actual examples, i.e., actual data of real environments. Some examples of such methodologies are detailed below
Ning et al (2017) combines a permutation flow-shop scheduling problem and a non-permutation flow-shop scheduling problem with minimal and maximal time lag considerations. Sáenz-Alanís et al (2016) address a job-shop scheduling in the beer production context, where sequence-dependent setup times are related to the cleaning operations. Deep & Singh (2015) study cellular manufacture systems where machines are grouped in machine cells able to process multiple operations at the same time.
Phanden & Jain (2015) offer a simulation-based genetic algorithm approach to solve flexible job-shop scheduling problems with process plan flexibility. The authors assess the effect of flexible process plan of a part-type in a production order environment. The objective is to find the minimum makespan as a performance measure.
Li & Gao (2016) propose an effective hybrid algorithm that hybridizes the genetic algorithm and tabu search, for the flexible job-shop scheduling problems with the objective of minimizing the makespan.
Xu et al. (2017) establish a mathematical model for job-shop scheduling problems, and an improved bat algorithm is proposed to solve the mathematical model mentioned. The objective is to seek an appropriate schedule that costs minimum time to complete all operations.