Decision trees for the algorithm selection problem : integer programming based approaches.

Programa de P?s-Gradua??o em Ci?ncia da Computa??o. Departamento de Ci?ncia da Computa??o, Instituto de Ci?ncias Exatas e Biol?gicas, Universidade Federal de Ouro Preto.Even though it is well known that for most relevant computational problems different algorithms may perform better on different classes of problem instances, most researchers still focus on determining a single best algorithmic configuration based on aggregate results such as the average. In this thesis, we propose Integer Programming based approaches to build decision trees for the Algorithm Selection Problem. These techniques allow the automation of three crucial decisions: (i) discerning the most important problem features to determine problem classes; (ii) grouping the problems into classes and (iii) select the best algorithm configuration for each class. We tested our approach from different perspectives: (i) univariate approach, where for each branch node, only one cutoff point of a feature is chosen and (ii) multivariate approach, where for each branch node, weights for multiple features are used (oblique decision trees). Considering the current scenario where the number of cores per machine has increased considerably, we also propose a new approach based on recommendation of concurrent algorithms. To evaluate our approaches, extensive computational experiments were executed using a dataset that considers the linear programming algorithms implemented in the COIN-OR Branch & Cut solver across a comprehensive set of instances, including all MIPLIB benchmark instances. We also conducted experiments with the scenarios/- datasets of the Open Algorithm Selection Challenge (OASC) held in 2017. Considering the first dataset and a 10-fold cross validation experiment, while selecting the single best solver across all instances decreased the total running time by 2%, our univariate approach decreased the total running time by 68% and using the multivariate approach, the total running time is decreased by 72%. An even greater performance gain can be obtained using concurrent algorithms, something not yet explored in the literature. For our experiments, using three algorithm configurations per leaf node, the total running time is decreased by 85%. These results indicate that our method generalizes quite well and does not overfit. Considering the results obtained using the scenarios of the OASC, the experimental results showed that our decision trees can produce better results than less interpretable models, such as random forest, which has been extensively used for algorithm recommendation

Optimal Decision Trees for the Algorithm Selection Problem: Integer Programming Based Approaches

Even though it is well known that for most relevant computational problems different algorithms may perform better on different classes of problem instances, most researchers still focus on determining a single best algorithmic configuration based on aggregate results such as the average. In this paper, we propose Integer Programming based approaches to build decision trees for the Algorithm Selection Problem. These techniques allow automate three crucial decisions: (i) discerning the most important problem features to determine problem classes; (ii) grouping the problems into classes and (iii) select the best algorithm configuration for each class. To evaluate this new approach, extensive computational experiments were executed using the linear programming algorithms implemented in the COIN-OR Branch & Cut solver across a comprehensive set of instances, including all MIPLIB benchmark instances. The results exceeded our expectations. While selecting the single best parameter setting across all instances decreased the total running time by 22%, our approach decreased the total running time by 40% on average across 10-fold cross validation experiments. These results indicate that our method generalizes quite well and does not overfit.Comment: International Transactions in Operational Research. 201

Algoritmos exatos e heurísticos para a resolução do problema da descoberta de cliques de peso máximo.

Programa de Pós-Graduação em Ciência da Computação. Departamento de Computação, Universidade Federal de Ouro Preto.O presente trabalho trata do projeto, implementação e avaliação de algoritmos exatos e heur ísticos, sequenciais e paralelos, para a resolu c~ao do problema da enumera c~ao de cliques com peso acima de um limiar (PECPL). Esse problema considera um grafo com vertices ponderados, onde o objetivo e encontrar todos os cliques maximais com peso acima de um limiar. Os algoritmos estudados neste trabalho são aplicados na separa ção de cortes no contexto de Programa ção Inteira. Encontrar todos os cliques acima de um dado peso e equivalente ao problema de encontrar todas as desigualdades violadas de clique. Foram desenvolvidas adapta ções em algoritmos conhecidos na literatura, para a resolução do problema. Para o algoritmo de Bron-Kerbosch, uma adapta c~ao foi realizada para resolver o PECPL. Al em disso, v arias melhorias foram propostas a m de melhorar a efi ciência na resolu ção das instâncias do problema. Foram propostas uma versão iterativa do algoritmo, originalmente recursivo, e uma versão paralela. O algoritmo de Ostergard e a heur stica busca tabu com multi-vizinhanças tamb ém foram implementados e modi ficados para re etir o problema abordado no presente trabalho. Por m, a metaheur stica Simulated Annealing foi proposta e desenvolvida utilizando-se das mesmas estruturas de vizinhan ca utilizadas na heur stica busca tabu com multivizinhanças. A diferen ça das duas t ecnicas est a na estrat égia de resolu ção do problema: enquanto a primeira utiliza-se do conceito de lista tabu, a ultima simula o processo de recozimento de metais. Nos experimentos computacionais, foram utilizadas 7292 instâncias, oriundas de quatro conjuntos referentes a separa ção de cortes em problemas formulados por meio do uso de programa c~ao inteira. Os experimentos foram conduzidos em duas partes: em um primeiro momento, as instâncias foram utilizadas para resolu ção do PECPL. Posteriormente, o foco foi a resolu ção do problema do clique de peso m áximo (PCPM). Quanto a resolu c~ao do PECPL, os resultados obtidos comprovam a efi ciência do algoritmo de Bron-Kerbosch, quando comparado aos demais algoritmos, ao encontrar a solu ção ótima para todas as instâncias e em um tempo consideravelmente menor do que as outras t ecnicas. Quando a an alise dos resultados foi direcionada a resolu c~ao do PCPM, todas as t écnicas implementadas obtiveram bons resultados, com destaque para a heur stica busca tabu com multi-vizinhan cas, a qual resolveu todas as instâncias de forma ótima, com o menor tempo computacional em rela c~ao as demais abordagens. Como trabalhos futuros, são sugeridos a ado c~ao de operadores l ogicos para a representa c~ao do grafo no algoritmo de Bron-Kerbosch, a melhoria da vers~ao paralela do algoritmo e o estudo do projeto das metaheurí sticas Simulated Annealing e busca tabu.This work deals with the design, implementation and evaluation of exact and heuristic algorithms, sequential and parallel to the resolution of clique enumeration problem with weight above a threshold (PECPL). This problem considers a graph with weighted vertices, where the goal is to nd all maximal cliques with weight above a threshold. The algorithms studied in this work are applied in the separation cuts in the context of Integer Programming. Find all clique above a certain weight is equivalent to the problem of nding all the inequalities violated clique. Adaptations were developed algorithms known in the literature, to solve the problem. For the Bron-Kerbosch algorithm, an adaptation was made to solve the PECPL. In addition, several improvements were proposed in order to improve e ciency in the resolution of problem instances. It has been proposed an iterative version of the algorithm, recursive originally, and a parallel version. The Ostergard algorithm and multi-neighborhoods tabu search heuristic were also implemented and modi ed to re ect the problem addressed in this paper. Finally, the Simulated Annealing metaheuristic was proposed and developed using the same neighborhood structures used in multi-neighborhoods tabu search heuristic. The di erence of the two techniques is in solving strategy problem: while the rst is used the concept of tabu list, the last simulates the process of annealing of metals. In the computational experiments, we used 7292 instances, belonging to four sets related to the separation cuts in problems formulated by using integer programming. The experiments were conducted in two parts: at rst, the instances were used for solving the PECPL. Later, the focus was on resolving the maximum weight clique problem (PCPM). As for the resolution of the PECPL, the results prove the e ciency of Bron-Kerbosch algorithm, when compared to other algorithms to nd the optimal solution for all instances and in a considerably shorter time than the other techniques. When analyzing the results was directed to resolving the PCPM, all techniques implemented performed well, particularly the multi-neighborhoods tabu search heuristic, which solved all instances optimally with less computational time compared to other approaches. As future work, it is suggested the adoption of logical operators for the representation of the graph in Bron-Kerbosch algorithm, improved parallel version of the algorithm and the study design of simulated annealing and tabu search metaheuristics

Optimal decision trees for the algorithm selection problem: integer programming based approaches

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NEOTROPICAL CARNIVORES: a data set on carnivore distribution in the Neotropics

Mammalian carnivores are considered a key group in maintaining ecological health and can indicate potential ecological integrity in landscapes where they occur. Carnivores also hold high conservation value and their habitat requirements can guide management and conservation plans. The order Carnivora has 84 species from 8 families in the Neotropical region: Canidae; Felidae; Mephitidae; Mustelidae; Otariidae; Phocidae; Procyonidae; and Ursidae. Herein, we include published and unpublished data on native terrestrial Neotropical carnivores (Canidae; Felidae; Mephitidae; Mustelidae; Procyonidae; and Ursidae). NEOTROPICAL CARNIVORES is a publicly available data set that includes 99,605 data entries from 35,511 unique georeferenced coordinates. Detection/non-detection and quantitative data were obtained from 1818 to 2018 by researchers, governmental agencies, non-governmental organizations, and private consultants. Data were collected using several methods including camera trapping, museum collections, roadkill, line transect, and opportunistic records. Literature (peer-reviewed and grey literature) from Portuguese, Spanish and English were incorporated in this compilation. Most of the data set consists of detection data entries (n = 79,343; 79.7%) but also includes non-detection data (n = 20,262; 20.3%). Of those, 43.3% also include count data (n = 43,151). The information available in NEOTROPICAL CARNIVORES will contribute to macroecological, ecological, and conservation questions in multiple spatio-temporal perspectives. As carnivores play key roles in trophic interactions, a better understanding of their distribution and habitat requirements are essential to establish conservation management plans and safeguard the future ecological health of Neotropical ecosystems. Our data paper, combined with other large-scale data sets, has great potential to clarify species distribution and related ecological processes within the Neotropics. There are no copyright restrictions and no restriction for using data from this data paper, as long as the data paper is cited as the source of the information used. We also request that users inform us of how they intend to use the data