jmlr jmlr2012 jmlr2012-31 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Félix-Antoine Fortin, François-Michel De Rainville, Marc-André Gardner, Marc Parizeau, Christian Gagné
Abstract: DEAP is a novel evolutionary computation framework for rapid prototyping and testing of ideas. Its design departs from most other existing frameworks in that it seeks to make algorithms explicit and data structures transparent, as opposed to the more common black-box frameworks. Freely available with extensive documentation at http://deap.gel.ulaval.ca, DEAP is an open source project under an LGPL license. Keywords: distributed evolutionary algorithms, software tools
Reference: text
sentIndex sentText sentNum sentScore
1 Its design departs from most other existing frameworks in that it seeks to make algorithms explicit and data structures transparent, as opposed to the more common black-box frameworks. [sent-17, score-0.191]
2 Introduction Evolutionary Computation (EC) is a sophisticated field with very diverse techniques and mechanisms, where even well designed frameworks can become quite complicated under the hood. [sent-23, score-0.158]
3 They thus strive to hide the implementation details as much as possible, by providing large libraries of high-level functionalities, often in many different flavours. [sent-24, score-0.028]
4 The more elaborate these boxes become, the more obscure they are, and the less likely the commoner is to ever take a peek under the hood to consider making changes. [sent-26, score-0.028]
5 But using EC to solve real-world problems most often requires the customization of algorithms. [sent-27, score-0.067]
6 The DEAP (Distributed Evolutionary Algorithms in Python) framework is built over the Python programming language that provides the essential glue for assembling sophisticated EC systems. [sent-28, score-0.028]
7 Its aim is to provide practical tools for rapid prototyping of custom evolutionary algorithms, where every step of the process is as explicit (pseudocode like) and easy to read and understand as possible. [sent-29, score-0.453]
8 Core Architecture DEAP’s core is composed of two simple structures: a creator and a toolbox. [sent-32, score-0.162]
9 The creator module is a meta-factory that allows the run-time creation of classes via both inheritance and composition. [sent-33, score-0.316]
10 Practically speaking, this allows the creation of genotypes and populations from any data structure such as lists, sets, dictionaries, trees, etc. [sent-36, score-0.038]
11 This creator concept is key to facilitating the implementation of any type of EA, including genetic algorithms (Mitchell, 1998), genetic programming (Banzhaf et al. [sent-37, score-0.308]
12 , 1998), evolution strategies (Beyer and Schwefel, 2002), covariance matrix adaptation evolution strategy (Hansen and Ostermeier, 2001), particle swarm optimization (Kennedy and Eberhart, 2001), and many more. [sent-38, score-0.251]
13 The toolbox is a container for the tools (operators) that the user wants to use in his EA. [sent-39, score-0.25]
14 The toolbox is manually populated by the user with selected tools. [sent-40, score-0.195]
15 For instance, if the user needs a crossover in his algorithm, but has access to several crossover types, he will choose the one best suited for his current problem, for example a uniform crossover “cxUniform”, and register it into the toolbox using a generic “mate” alias. [sent-41, score-0.654]
16 If he later decides that some other crossover is better suited, his algorithm will remain unchanged, he will only need to update the corresponding alias in the toolbox. [sent-43, score-0.342]
17 The core functionalities of DEAP are levered by several peripheral modules. [sent-44, score-0.157]
18 The algorithms module contains four classical EC algorithms: generational, (µ , λ), (µ + λ), and ask-and-tell (Collette et al. [sent-45, score-0.15]
19 These serve as a starting point for users to build their own custom EAs meeting their specific needs. [sent-47, score-0.071]
20 The tools module provides basic EC operators such as initializations, mutations, crossovers, and selections. [sent-48, score-0.269]
21 These operators can be directly added to a toolbox in order to be used in algorithms. [sent-49, score-0.174]
22 This module also contains a number of components that gather useful information regarding the evolution: fitness statistics, genealogy, hall-of-fame for the best individuals encountered so far, and checkpointing mechanisms to allow evolution restart. [sent-50, score-0.361]
23 A base module contains some data structures frequently used in EC, but not implemented in standard Python (e. [sent-51, score-0.183]
24 The last module named dtm, for Distributed Task Manager, offers distributed substitutes for common Python functions such as apply and map. [sent-54, score-0.15]
25 It even balances the workload among workers to optimize the distribution efficiency. [sent-56, score-0.095]
26 The individual is represented as a bit-string where each bit corresponds to a feature that can be selected or not. [sent-58, score-0.026]
27 On line 2, the relevant DEAP modules are first imported. [sent-61, score-0.033]
28 Next, an Individual class is derived from the Python list and composed with our newly created FitnessMulti object. [sent-69, score-0.029]
29 The toolbox register method accepts a variable number of arguments. [sent-71, score-0.203]
30 The first is the alias name, and the second the function that we want to associate with this alias. [sent-72, score-0.2]
31 All other arguments are passed to this function when the alias is called. [sent-73, score-0.228]
32 randint with arguments 0 and 1, and thus generate a random bit. [sent-76, score-0.028]
33 tion problem, this bit function is simply called n = 80 times repeatedly using the tools. [sent-79, score-0.026]
34 initRepeat method that accepts three arguments: a container, a function, and the number of times to repeat initialization. [sent-80, score-0.042]
35 Similarly, a population alias is defined to allow population initialization, in this case with n = 100 individuals. [sent-81, score-0.392]
36 Line 18 then proceeds with the allocation of a population of individuals that have their fitness evaluated on line 19 by mapping the evaluation function to every element of the population container. [sent-82, score-0.28]
37 Lines 20 and 21 replace the individuals fitness with their newly computed values. [sent-83, score-0.117]
38 Finally, lines 23 through 28 show the evolutionary loop that uses the µ + λ strategy, where µ = 100 parents (current population) are mixed with λ = 100 offspring (lambda line 24) for the selection process (NSGA-II) to produce the next generation of k = 100 parents (line 28). [sent-84, score-0.412]
39 The varOr algorithm loops until it has generated λ offspring using either crossover (mate alias) with probability cxpb, mutation (mutate alias) with probability mutpb, or reproduction. [sent-85, score-0.209]
40 Efficient distribution of specific parts of user algorithms is made possible by the dtm module. [sent-86, score-0.24]
41 The task manager distributes these sub-tasks across the worker nodes, and automatically balances the workload evenly among them. [sent-88, score-0.18]
42 Table 1 presents a comparison of the number of lines required by some of the most popular frameworks to define different components of a OneMax example (without distribution). [sent-92, score-0.261]
43 Columns respectively indicate how many lines are required to define the bit-string type, to configure the operators, to implement the generational algorithm and to execute the example. [sent-93, score-0.17]
44 DEAP is the only framework that allows the complete definition of the EA in less than one hundred lines of code. [sent-94, score-0.103]
45 Even though some frameworks may allow shorter expressions of standardized solutions, any needed customization of type or algorithm can also force the user to dig deep into the framework to modify perhaps hundreds of lines. [sent-95, score-0.265]
46 We therefore assert that DEAP is superior to previous frameworks for rapid prototyping of new algorithms and definition of custom types. [sent-96, score-0.396]
47 Conclusion Current major EC frameworks generally do a good job of offering generic tools to solve hard problems using EAs. [sent-98, score-0.234]
48 Even experts can become overwhelmed when trying to implement specific features. [sent-100, score-0.028]
49 The DEAP core is implemented in 6 program files (Python modules) with only 1653 lines of code. [sent-102, score-0.165]
50 To these core lines, the DTM module adds another 2073 lines for enabling the easy distribution of computationally intensive algorithm parts. [sent-103, score-0.315]
51 The framework also includes more than 35 application examples that add another 2448 lines of code, leading to an average ratio of core lines to example lines of 1. [sent-104, score-0.371]
52 In other words, DEAP implements the 15 examples of OpenBEAGLE plus 20 more with 10 times less lines of code. [sent-111, score-0.103]
53 Acknowledgments This work has been supported by the Fonds de recherche du Qu´ bec - Nature et technologies e (FQRNT) and by the Natural Sciences and Engineering Research Council of Canada (NSERC). [sent-112, score-0.085]
54 On object-oriented programming of optimizers – Examples in Scilab. [sent-135, score-0.028]
55 A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. [sent-146, score-0.09]
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Author: Ji Liu, Peter Wonka, Jieping Ye
Abstract: We consider the following sparse signal recovery (or feature selection) problem: given a design matrix X ∈ Rn×m (m ≫ n) and a noisy observation vector y ∈ Rn satisfying y = Xβ∗ + ε where ε is the noise vector following a Gaussian distribution N(0, σ2 I), how to recover the signal (or parameter vector) β∗ when the signal is sparse? The Dantzig selector has been proposed for sparse signal recovery with strong theoretical guarantees. In this paper, we propose a multi-stage Dantzig selector method, which iteratively refines the target signal β∗ . We show that if X obeys a certain condition, then with a large probability ˆ the difference between the solution β estimated by the proposed method and the true solution β∗ measured in terms of the ℓ p norm (p ≥ 1) is bounded as ˆ β − β∗ p ≤ C(s − N)1/p log m + ∆ σ, where C is a constant, s is the number of nonzero entries in β∗ , the risk of the oracle estimator ∆ is independent of m and is much smaller than the first term, and N is the number of entries of β∗ larger √ than a certain value in the order of O (σ log m). The proposed √ method improves the estimation √ bound of the standard Dantzig selector approximately from Cs1/p log mσ to C(s − N)1/p log mσ where the value N depends on the number of large entries in β∗ . When N = s, the proposed algorithm achieves the oracle solution with a high probability, where the oracle solution is the projection of the observation vector y onto true features. In addition, with a large probability, the proposed method can select the same number of correct features under a milder condition than the Dantzig selector. Finally, we extend this multi-stage procedure to the LASSO case. Keywords: multi-stage, Dantzig selector, LASSO, sparse signal recovery
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