Heuristics based on greedy randomized adaptive search and variable neighbourhood search for the minimum labelling spanning tree problem

This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-complete. A Greedy Randomized Adaptive Search Procedure (GRASP) and different versions of Variable Neighbourhood Search (VNS) are proposed. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics

Methods for evaluating Decision Problems with Limited Information

LImited Memory Influence Diagrams (LIMIDs) are general models of decision problems for representing limited memory policies (Lauritzen and Nilsson (2001)). The evaluation of LIMIDs can be done by Single Policy Updating that produces a local maximum strategy in which no single policy modification can increase the expected utility. This paper examines the quality of the obtained local maximum strategy and proposes three different methods for evaluating LIMIDs. The first algorithm, Temporal Policy Updating, resembles Single Policy Updating. The second algorithm, Greedy Search, successively updates the policy that gives the highest expected utility improvement. The final algorithm, Simulating Annealing, differs from the two preceeding by allowing the search to take some downhill steps to escape a local maximum. A careful comparison of the algorithms is provided both in terms of the quality of the obtained strategies, and in terms of implementation of the algorithms including some considerations of the computational complexity

Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem

This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-hard. A Greedy Randomized Adaptive Search Procedure (GRASP) and a Variable Neighbourhood Search (VNS) are proposed in this paper. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics

VNS-BASED ALGORITHMS FOR THE CENTROID-BASED CLUSTERING PROBLEM

The k-means algorithm with the corresponding problem formulation is one of the first methods that researchers use when solving a new automatic grouping (clus-tering) problem. Its improvement, modification and combination with other algorithms are described in the works of many researchers. In this research, we propose new al-gorithms of the Greedy Heuristic Method, which use an idea of the search in variable neighborhoods for solving the classical cluster analysis problem, and allows us to obtain a more accurate and stable result of solving in comparison with the known algorithms. Our computational experiments show that the new algorithms allow us to obtain re-sults with better values of the objective function value (sum of squared distances) in comparison with classical algorithms such as k-means, j-means and genetic algorithms on various practically important datasets. In addition, we present the first results for the GPU realization of the Greedy Heuristic Method

A robust experimental evaluation of automated multi-label classification methods

Automated Machine Learning (AutoML) has emerged to deal with the selection and configuration of algorithms for a given learning task. With the progression of AutoML, several effective methods were introduced, especially for traditional classification and regression problems. Apart from the AutoML success, several issues remain open. One issue, in particular, is the lack of ability of AutoML methods to deal with different types of data. Based on this scenario, this paper approaches AutoML for multi-label classification (MLC) problems. In MLC, each example can be simultaneously associated to several class labels, unlike the standard classification task, where an example is associated to just one class label. In this work, we provide a general comparison of five automated multi-label classification methods - two evolutionary methods, one Bayesian optimization method, one random search and one greedy search - on 14 datasets and three designed search spaces. Overall, we observe that the most prominent method is the one based on a canonical grammar-based genetic programming (GGP) search method, namely Auto-MEKAGGP. Auto-MEKAGGP presented the best average results in our comparison and was statistically better than all the other methods in different search spaces and evaluated measures, except when compared to the greedy search method

A memetic algorithm with adaptive hill climbing strategy for dynamic optimization problems

Copyright @ Springer-Verlag 2008Dynamic optimization problems challenge traditional evolutionary algorithms seriously since they, once converged, cannot adapt quickly to environmental changes. This paper investigates the application of memetic algorithms, a class of hybrid evolutionary algorithms, for dynamic optimization problems. An adaptive hill climbing method is proposed as the local search technique in the framework of memetic algorithms, which combines the features of greedy crossover-based hill climbing and steepest mutation-based hill climbing. In order to address the convergence problem, two diversity maintaining methods, called adaptive dual mapping and triggered random immigrants, respectively, are also introduced into the proposed memetic algorithm for dynamic optimization problems. Based on a series of dynamic problems generated from several stationary benchmark problems, experiments are carried out to investigate the performance of the proposed memetic algorithm in comparison with some peer evolutionary algorithms. The experimental results show the efficiency of the proposed memetic algorithm in dynamic environments.This work was supported by the National Nature Science Foundation of China (NSFC) under Grant Nos. 70431003 and 70671020, the National Innovation Research Community Science Foundation of China under Grant No. 60521003, and the National Support Plan of China under Grant No. 2006BAH02A09 and the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/01

Optimize Planning Heuristics to Rank, not to Estimate Cost-to-Goal

In imitation learning for planning, parameters of heuristic functions are optimized against a set of solved problem instances. This work revisits the necessary and sufficient conditions of strictly optimally efficient heuristics for forward search algorithms, mainly A* and greedy best-first search, which expand only states on the returned optimal path. It then proposes a family of loss functions based on ranking tailored for a given variant of the forward search algorithm. Furthermore, from a learning theory point of view, it discusses why optimizing cost-to-goal \hstar\ is unnecessarily difficult. The experimental comparison on a diverse set of problems unequivocally supports the derived theory.Comment: 10 page