Josu Ceberio

A Distance-Based Ranking Model Estimation of Distribution Algorithm for the Flowshop Scheduling Problem

The aim of this paper is two-fold. First, we introduce a novel general estimation of distribution algorithm to deal with permutation-based optimization problems. The algorithm is based on the use of a probabilistic model for permutations called the generalized Mallows model. In order to prove the potential of the proposed algorithm, our second aim is to solve the permutation flowshop scheduling problem. A hybrid approach consisting of the new estimation of distribution algorithm and a variable neighborhood search is proposed. Conducted experiments demonstrate that the proposed algorithm is able to outperform the state-of-the-art approaches. Moreover, from the 220 benchmark instances tested, the proposed hybrid approach obtains new best known results in 152 cases. An in-depth study of the results suggests that the successful performance of the introduced approach is due to the ability of the generalized Mallows estimation of distribution algorithm to discover promising regions in the search space.

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

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.

Introducing the mallows model on estimation of distribution algorithms

Estimation of Distribution Algorithms are a set of algorithms that belong to the field of Evolutionary Computation. Characterized by the use of probabilistic models to learn the (in)dependencies between the variables of the optimization problem, these algorithms have been applied to a wide set of academic and real-world optimization problems, achieving competitive results in most scenarios. However, they have not been extensively developed for permutation-based problems. In this paper we introduce a new EDA approach specifically designed to deal with permutation-based problems. In this paper, our proposal estimates a probability distribution over permutations by means of a distance-based exponential model called the Mallows model. In order to analyze the performance of the Mallows model in EDAs, we carry out some experiments over the Permutation Flowshop Scheduling Problem (PFSP), and compare the results with those obtained by two state-of-the-art EDAs for permutation-based problems.

The linear ordering problem revisited

The Linear Ordering Problem is a popular combinatorial optimisation problem which has been extensively addressed in the literature. However, in spite of its popularity, little is known about the characteristics of this problem. This paper studies a procedure to extract static information from an instance of the problem, and proposes a method to incorporate the obtained knowledge in order to improve the performance of local search-based algorithms. The procedure introduced identifies the positions where the indexes cannot generate local optima for the insert neighbourhood, and thus global optima solutions. This information is then used to propose a restricted insert neighbourhood that discards the insert operations which move indexes to positions where optimal solutions are not generated. In order to measure the efficiency of the proposed restricted insert neighbourhood system, two state-of-the-art algorithms for the LOP that include local search procedures have been modified. Conducted experiments confirm that the restricted versions of the algorithms outperform the classical designs systematically when a maximum number of function evaluations is considered as the stopping criterion. The statistical test included in the experimentation reports significant differences in all the cases, which validates the efficiency of our proposal. Moreover, additional experiments comparing the execution times reveal that the restricted approaches are faster than their counterparts for most of the instances.

The Plackett-Luce ranking model on permutation-based optimization problems

Estimation of distribution algorithms are known as powerful evolutionary algorithms that have been widely used for diverse types of problems. However, they have not been extensively developed for permutation-based problems. Recently, some progress has been made in this area by introducing probability models on rankings to optimize permutation domain problems. In particular, the Mallows model and the Generalized Mallows model demonstrated their effectiveness when used with estimation of distribution algorithms. Motivated by these advances, in this paper we introduce a Thurstone order statistics model, called Plackett-Luce, to the framework of estimation of distribution algorithms. In order to prove the potential of the proposed algorithm, we consider two different permutation problems: the linear ordering problem and the flowshop scheduling problem. In addition, the results are compared with those obtained by the Mallows and the Generalized Mallows proposals. Conducted experiments demonstrate that the Plackett-Luce model is the best performing model for solving the linear ordering problem. However, according to the experimental results, the Generalized Mallows model turns out to be very robust obtaining very competitive results for both problems, especially for the permutation flowshop scheduling problem.

Extending Distance-based Ranking Models in Estimation of Distribution Algorithms

Recently, probability models on rankings have been proposed in the field of estimation of distribution algorithms in order to solve permutation-based combinatorial optimisation problems. Particularly, distance-based ranking models, such as Mallows and Generalized Mallows under the Kendalls-τ distance, have demonstrated their validity when solving this type of problems. Nevertheless, there are still many trends that deserve further study. In this paper, we extend the use of distance-based ranking models in the framework of EDAs by introducing new distance metrics such as Cayley and Ulam. In order to analyse the performance of the Mallows and Generalized Mallows EDAs under the Kendall, Cayley and Ulam distances, we run them on a benchmark of 120 instances from four well known permutation problems. The conducted experiments showed that there is not just one metric that performs the best in all the problems. However, the statistical test pointed out that Mallows-Ulam EDA is the most stable algorithm among the studied proposals.

Application of Micro-Genetic Algorithm for Task Based Computing

Pervasive computing calls for applications which are often composed from independent and distributed components using facilities from the environment. This paradigm has evolved into task based computing where the application composition relies on explicit user task descriptions. The composition of applications has to be performed at run-time as the environment is dynamic and heterogeneous due to e.g., mobility of the user. An algorithm that decides on a component set and allocates it onto hosts accordingly to user task preferences and the platform constraints plays a central role in the application composition process. In this paper we will describe an algorithm for task-based application allocation. The algorithm uses micro-genetic approach and is characterized by a very low computational load and good convergence properties. We will compare the performance and the scalability of our algorithm with a straightforward evolutionary algorithm. Besides, we will outline a system for task-based computing where our algorithm is used.

Kernels of Mallows Models for Solving Permutation-based Problems

Recently, distance-based exponential probability models, such as Mallows and Generalized Mallows, have demonstrated their validity in the context of estimation of distribution algorithms (EDAs) for solving permutation problems. However, despite their successful performance, these models are unimodal, and therefore, they are not flexible enough to accurately model populations with solutions that are very sparse with regard to the distance metric considered under the model. In this paper, we propose using kernels of Mallows models under the Kendalls-tau and Cayley distances within EDAs. In order to demonstrate the validity of this new algorithm, Mallows Kernel EDA, we compare its performance with the classical Mallows and Generalized Mallows EDAs, on a benchmark of 90 instances of two different types of permutation problems: the quadratic assignment problem and the permutation flowshop scheduling problem. Experimental results reveal that, in most cases, Mallows Kernel EDA outperforms the Mallows and Generalized Mallows EDAs under the same distance. Moreover, the new algorithm under the Cayley distance obtains the best results for the two problems in terms of average fitness and computational time.

A review of distances for the Mallows and Generalized Mallows estimation of distribution algorithms

The Mallows (MM) and the Generalized Mallows (GMM) probability models have demonstrated their validity in the framework of Estimation of distribution algorithms (EDAs) for solving permutation-based combinatorial optimisation problems. Recent works, however, have suggested that the performance of these algorithms strongly relies on the distance used under the model. The goal of this paper is to review three common distances for permutations, Kendall’s-