A review on estimation of distribution algorithms in permutation-based combinatorial optimization problems

Abstract

Estimation of Distribution Algorithms (EDAs) are a set of algorithms that belong to the field of Evolutionary Computation. Characterized by the use of probabilistic models to represent the solutions and the dependencies between the variables of the problem, these algorithms have been applied to a wide set of academic and real-world optimization problems, achieving competitive results in most scenarios. Nevertheless, there are some optimization problems, whose solutions can be naturally represented as permutations, for which EDAs have not been extensively developed. Although some work has been carried out in this direction, most of the approaches are adaptations of EDAs designed for problems based on integer or real domains, and only a few algorithms have been specifically designed to deal with permutation-based problems. In order to set the basis for a development of EDAs in permutation-based problems similar to that which occurred in other optimization fields (integer and real-value problems), in this paper we carry out a thorough review of state-of-the-art EDAs applied to permutation-based problems. Furthermore, we provide some ideas on probabilistic modeling over permutation spaces that could inspire the researchers of EDAs to design new approaches for these kinds of problems.

RK-EDA: A Novel Random Key Based Estimation of Distribution Algorithm

“…These problems include Flow Shop Scheduling Problem (FSSP), Linear Ordering Problem (LOP), Quadratic Assignment Problem (QAP) and Travelling Salesman Problem (TSP). These are formerly defined in [3], we have used the same objective function as presented in the review paper and is summarised in Table 1. Note that we also consider the more recently used Total Flow Time (TFT) criteria for further experiments on the FSSP.…”

“…EDAs applied to permutations have been categorised into ad hoc approaches with varying strategies, integer space based and continuous space based [3]. One of the common continuous representations for solving permutations in EAs is the well-known Random Key (RK).…”

“…RK based EDAs have however been considered the poorest [3] of the EDAs designed for permutation problems. RK representation has not been sufficiently adapted to benefit from the operation of EDA.…”

“…RK representation has not been sufficiently adapted to benefit from the operation of EDA. It contains some inherent redundancy as a result of several RKs producing the same ordering thereby introducing plateaux to the search space [3], [2], [13]. Also, variability in the values that capture the same priority across solutions of a population limits the information captured by the probabilistic model.…”

Negative Correlation Learning in the Estimation of Distribution Algorithms for Combinatorial Optimization

“…In a problem with a single solution, using templates will help the algorithms to converge faster and obtain better solutions [4], [42]. In some situations, templates are used as a local search operator that helps to prevent premature convergence [4], [6].…”