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## Micro-Differential Evolution with Extra Moves Along the Axes

### Citations

1893 |
A simple sequentially rejective multiple test procedure.
- Holm
- 1979
(Show Context)
Citation Context ... 1.03e + 03± 4.44e + 01 - In addition to the results presented above, the ranking among all the algorithms considered in this article has been performed by means of the Holm-Bonferroni procedure, see =-=[42]-=- and [43], for the 5 algorithms under study and the 76 problems under consideration. The Holm-Bonferroni procedure consists of the following. Considering the results in the tables above, the 5 algorit... |

1012 |
Individual comparisons by ranking method,”
- Wilcoxon
- 1945
(Show Context)
Citation Context ... fitness value ± standard deviation over the 100 available runs has been computed. In order to strengthen the statistical significance of the results, for each test problem the Wilcoxon Rank-Sum test =-=[41]-=- has been also applied, with a confidence level of 0.95. The proposed µDEA has been run with Spop = 5, F = 0.7, αe = 0.5, see eq. (2), Iter = 20, η = 0.25, and ρ = 0.4 of the width of the decision spa... |

443 |
Differential Evolution: A Practical Approach to Global Optimization.
- Price, Storn, et al.
- 2005
(Show Context)
Citation Context ...j the offspring should be generated. With F ∈ [0, 1 + [, it is meant here that the scale factor should be a positive value which cannot be much greater than 1 (i.e. is a small positive value), see =-=[22]-=-. While there is no theoretical upper limit for F , effective values are rarely greater than 1.0. The mutation scheme given in Equation (1) is also known as DE/rand/1. In literature many other mutatio... |

178 | Problem Definitions and Evaluation Criteria for the CEC
- Mallipeddi, Suganthan
- 2010
(Show Context)
Citation Context ...rowing area around the pivot solution xp. III. NUMERICAL RESULTS All the test problems included in the following four testbeds have been considered in this study. • The CEC2005 benchmark described in =-=[37]-=- in 30 dimensions (25 test problems) • The BBOB2010 benchmark described in [38] in 100 dimensions (24 test problems) • The CEC2008 benchmark described in [39] in 1000 dimensions (7 test problems) • Th... |

137 |
Micro-genetic algorithms for stationary and non-stationary function optimization.
- Krishnakumar
- 1989
(Show Context)
Citation Context ...based algorithm that use a small population, are indicated as micro algorithms and indicated by the prefix µ. An early implementation of micro algorithm is the micro Genetic Algorithm (µGA), see e.g. =-=[14]-=- and [15]. Over the latest years, micro algorithms have been employed in various engineering applications as they are proven to be lighter in terms of hardware requirements and thus are prone to their... |

129 |
Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems,”
- Brest, Greiner, et al.
- 2006
(Show Context)
Citation Context ...p) then xp = xs else compute xs[i] = xp[i] + ρ2 if f (xs) ≤ f (xp) then xp = xs end if end if end for end for end if end while Fig. 2. Pseudo code of the µDEA algorithm For example, the so called jDE =-=[26]-=- proposed a controlled randomization of the DE parameters. Another popular DE variant based on controlled randomization of the parameters has been proposed in [27]. The Self-Adaptive Differential Evol... |

125 | Differential evolution algorithm with strategy adaptation for global numerical optimization,”
- Qin, Huang, et al.
- 2009
(Show Context)
Citation Context ...ndomization of the DE parameters. Another popular DE variant based on controlled randomization of the parameters has been proposed in [27]. The Self-Adaptive Differential Evolution (SADE) proposed in =-=[28]-=- employs multiple mutation strategies and a randomized coordination scheme based on an initial learning. Another efficient coordination strategy for a multiple mutation structure has been proposed in ... |

109 |
Differential evolution: A survey of the stateof-the-art,”
- Das, Suganthan
- 2011
(Show Context)
Citation Context ...resentation of the Bin Packing Problem. This paper proposes a novel implementation of µDE, namely micro-Differential Evolution with Axis-moves (µDEA). The proposed µDEA is a DE/rand/1/exp scheme, see =-=[21]-=-, that employs a very small population. In addition, µDEA makes use of an extra refinement operator that perturbs the solution of the micro-population characterized by the highest performance. This re... |

80 | Formal analysis and random respectful reco~binatio~.". III R.K. I d L B B k (Eds ) Proc oFfiourth Int. Con/. on Genetic Algonthms. 1991, Be ew, an
- Radcliffe
- 1993
(Show Context)
Citation Context ...tors. Since most recombination operators have the property that, if both parents share the same value of a variable, then the offspring also has the same value in correspondence of that variable, see =-=[7]-=-, recombination has the power of exploring the part of the search space where individuals disagree. In contrast, mutation explores the entire search space. According to this analysis this mechanism of... |

67 |
A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability,”
- Garcıa, Fernandez, et al.
- 2009
(Show Context)
Citation Context ...03± 4.44e + 01 - In addition to the results presented above, the ranking among all the algorithms considered in this article has been performed by means of the Holm-Bonferroni procedure, see [42] and =-=[43]-=-, for the 5 algorithms under study and the 76 problems under consideration. The Holm-Bonferroni procedure consists of the following. Considering the results in the tables above, the 5 algorithms under... |

55 |
Accelerating differential evolution using an adaptive local search,”
- Noman, Iba
- 2008
(Show Context)
Citation Context ...arch moves. Thus, DE variants that include extra moves into the original framework, usually, lead to improved versions. The extra moves can be explicitly implemented within the DE framework, see e.g. =-=[33]-=- and [34], or can be implicitly contained in other perturbation mechanism. The randomization, as shown in [32] and [35], plays a very important role as it allows the generation of candidate solutions ... |

41 | A micro-genetic algorithm for multiobjective optimization. First international conference on evolutionary multi-criterion optimization
- Coello, A, et al.
- 2001
(Show Context)
Citation Context ...orithm that use a small population, are indicated as micro algorithms and indicated by the prefix µ. An early implementation of micro algorithm is the micro Genetic Algorithm (µGA), see e.g. [14] and =-=[15]-=-. Over the latest years, micro algorithms have been employed in various engineering applications as they are proven to be lighter in terms of hardware requirements and thus are prone to their use in e... |

41 | On stagnation of the differential evolution algorithm.
- Lampinen, Zelinka
- 2000
(Show Context)
Citation Context ... as it allows the generation of candidate solutions that would not be generated by standard mutation and crossover operations. The second reason is that DE can be excessively exploratory. As shown in =-=[36]-=-, a typical challenge in DE functioning is that the solutions in a population can be diverse and still unable to outperform the individual with the best performance (i.e. DE can easily suffers from st... |

28 |
Tasgetiren: Differential evolution algorithm with ensemble of parameters and mutation strategies,
- Mallipeddi, Suganthan, et al.
- 2011
(Show Context)
Citation Context ... employs multiple mutation strategies and a randomized coordination scheme based on an initial learning. Another efficient coordination strategy for a multiple mutation structure has been proposed in =-=[29]-=-. A modified selection strategy, based on the location within the population, for the individuals undergoing mutation has been proposed in [30]. Another example of efficient DE variant has been propos... |

27 |
Multiple trajectories search for large scale global optimization.
- LY, Chen
- 2008
(Show Context)
Citation Context ...ution along its n axes, i.e. separately perturbs each design variable. This operator can be seen as a modification of a classical hill-descend algorithm and employs the perturbation logic proposed in =-=[25]-=-. The implementation of this operator requires an additional solution, which will here be referred to as xs. The pivot individual xp is perturbed by computing, for each variable i: xs[i] = xp[i]− ρ, (... |

25 | Parameter tuning for configuring and analyzing evolutionary algorithms”,
- Eiben, Smit
- 2011
(Show Context)
Citation Context ... crucially important, if not the most important, parameter in algorithms that process multiple solutions, such as Evolutionary and Swarm Intelligence Algorithms (EAs and SIAs, respectively), see e.g. =-=[1]-=-. The tuning of this parameter is hard since, the success of a given problem can heavily depend on it. Looking at this issue from a complementary perspective, a robust algorithmic design might have a ... |

19 | Benchmark functions for the cec’2010 special session and competition on large-scale global optimization,”
- Tang, Li, et al.
- 2010
(Show Context)
Citation Context ...ms) • The BBOB2010 benchmark described in [38] in 100 dimensions (24 test problems) • The CEC2008 benchmark described in [39] in 1000 dimensions (7 test problems) • The CEC2010 benchmark described in =-=[40]-=- in 1000 dimensions (20 test problems) Thus, 76 test problems have been considered in this study. For each algorithm in this paper (see following subsections) 100 runs have been performed. Each run ha... |

16 |
Population size reduction for the differential evolution algorithm
- Brest, Maučec
- 2008
(Show Context)
Citation Context ... problem can heavily depend on it. Looking at this issue from a complementary perspective, a robust algorithmic design might have a variable population size. This variation can be deterministic as in =-=[2]-=- or self-adaptive as in [3], [4], and [5]. The topic whether a large, a small, or unitary population is preferable is a topic under discussion in computational intelligence community. In this regard, ... |

16 |
Scale factor local search in differential evolution,”
- Neri, Tirronen
- 2009
(Show Context)
Citation Context ...s. Thus, DE variants that include extra moves into the original framework, usually, lead to improved versions. The extra moves can be explicitly implemented within the DE framework, see e.g. [33] and =-=[34]-=-, or can be implicitly contained in other perturbation mechanism. The randomization, as shown in [32] and [35], plays a very important role as it allows the generation of candidate solutions that woul... |

15 |
A fast adaptive memetic algorithm for on-line and off-line control design of PMSM drives.
- Caponio, Cascella, et al.
- 2007
(Show Context)
Citation Context ... on it. Looking at this issue from a complementary perspective, a robust algorithmic design might have a variable population size. This variation can be deterministic as in [2] or self-adaptive as in =-=[3]-=-, [4], and [5]. The topic whether a large, a small, or unitary population is preferable is a topic under discussion in computational intelligence community. In this regard, an extensive study on popul... |

11 | Y.S.: An adaptive multimeme algorithm for designing hiv multidrug therapies.
- Neri, Toivanen, et al.
- 2007
(Show Context)
Citation Context ...t. Looking at this issue from a complementary perspective, a robust algorithmic design might have a variable population size. This variation can be deterministic as in [2] or self-adaptive as in [3], =-=[4]-=-, and [5]. The topic whether a large, a small, or unitary population is preferable is a topic under discussion in computational intelligence community. In this regard, an extensive study on population... |

11 | An Adaptive Differential Evolution Algorithm With Novel Mutation and Crossover Strategies for
- Islam, Das, et al.
- 2012
(Show Context)
Citation Context ...dified selection strategy, based on the location within the population, for the individuals undergoing mutation has been proposed in [30]. Another example of efficient DE variant has been proposed in =-=[31]-=- where a novel DE mutation is combined with a randomized fitness based selection of the individuals undergoing mutation. As highlighted in [23] and [32], the reasons behind the wide margin of improvem... |

8 | Using micro-genetic algorithms to improve localization in wireless sensor networks
- Tam, Cheng, et al.
- 2006
(Show Context)
Citation Context ...ickly achieve improvements during the early stages of the optimization process. This feature makes micro-algorithms especially useful in real-time applications when a quick answer is needed, see e.g. =-=[17]-=-. The effect of small populations is obviously different when applied to various search strategies, see [18]. Amongst the various micro algorithms proposed in literature, micro-Differential Evolution ... |

7 | On stability and convergence of the population-dynamics in differential evolution,
- Dasgupta, Das, et al.
- 2009
(Show Context)
Citation Context ...e [9]. On the other hand, in [10] and [11], it is shown that, if properly designed, a population-based algorithm with a very small population size can efficiently solve large scale problems, see also =-=[12]-=- and [13]. The latter kind of algorithms, i.e. population-based algorithm that use a small population, are indicated as micro algorithms and indicated by the prefix µ. An early implementation of micro... |

6 | Cooperative Micro-Differential Evolution for HighDimensional Problems
- Parsopoulos
- 2009
(Show Context)
Citation Context ...mework, but also about the proper sizing of the population. Some studies clearly suggest the usage of large populations in order to ensure the success of the algorithm, see [9]. On the other hand, in =-=[10]-=- and [11], it is shown that, if properly designed, a population-based algorithm with a very small population size can efficiently solve large scale problems, see also [12] and [13]. The latter kind of... |

6 |
Disturbed Exploitation compact Differential Evolution for Limited Memory Optimization Problems,”
- Neri, Iacca, et al.
- 2011
(Show Context)
Citation Context ...he DE/rand/1 mutation, the algorithm is referred to as DE/rand/1/exp (in our case µDE/rand/1/exp). For the sake of clarity the pseudo-code of the exponential crossover is shown in Fig. 1. As shown in =-=[24]-=-, it can easily be observed that for a given value of Cr, the meaning of the exponential crossover would change with the dimensionality of the problem. For low dimensionality problems the trial soluti... |

6 |
Compact Differential Evolution
- Mininno, Neri, et al.
- 2011
(Show Context)
Citation Context ...le of efficient DE variant has been proposed in [31] where a novel DE mutation is combined with a randomized fitness based selection of the individuals undergoing mutation. As highlighted in [23] and =-=[32]-=-, the reasons behind the wide margin of improvements for the original DE scheme are mainly two. The first reason is that DE scheme has a limited amount of search moves. Thus, DE variants that include ... |

6 |
Scale Factor Inheritance Mechanism in Distributed Differential Evolution,” Soft Computing - A Fusion of Foundations
- Weber, Tirronen, et al.
- 2010
(Show Context)
Citation Context ... The extra moves can be explicitly implemented within the DE framework, see e.g. [33] and [34], or can be implicitly contained in other perturbation mechanism. The randomization, as shown in [32] and =-=[35]-=-, plays a very important role as it allows the generation of candidate solutions that would not be generated by standard mutation and crossover operations. The second reason is that DE can be excessiv... |

4 |
Self-adaptive population sizing for a tune-free differential evolution,” Soft Computing – A Fusion of Foundations
- Teng, Teo, et al.
- 2009
(Show Context)
Citation Context ...g at this issue from a complementary perspective, a robust algorithmic design might have a variable population size. This variation can be deterministic as in [2] or self-adaptive as in [3], [4], and =-=[5]-=-. The topic whether a large, a small, or unitary population is preferable is a topic under discussion in computational intelligence community. In this regard, an extensive study on population-based al... |

4 |
Benefits of a population: Five mechanisms that advantage population-based algorithms
- Prügel-Bennett
- 2010
(Show Context)
Citation Context ...c under discussion in computational intelligence community. In this regard, an extensive study on population-based algorithms and their advantages over single solution algorithms has been reported in =-=[6]-=-. Five distinct mechanisms that would justify the superiority of population-based algorithms over schemes that perturb a single solution have been identified and studied. The first mechanism is that a... |

4 | A large population size can be unhelpful in evolutionary algorithms
- Chen, Tang, et al.
- 2012
(Show Context)
Citation Context ... within an optimization framework, but also about the proper sizing of the population. Some studies clearly suggest the usage of large populations in order to ensure the success of the algorithm, see =-=[9]-=-. On the other hand, in [10] and [11], it is shown that, if properly designed, a population-based algorithm with a very small population size can efficiently solve large scale problems, see also [12] ... |

4 |
Image thresholding using micro opposition-based differential evolution (micro-ode),” in Evolutionary Computation
- Rahnamayan, Tizhoosh
- 2008
(Show Context)
Citation Context ... when applied to various search strategies, see [18]. Amongst the various micro algorithms proposed in literature, micro-Differential Evolution (µDE) is a successfully applied scheme. For example, in =-=[19]-=- a µDE employing opposition-based mechanism has been proposed for image thresholding problems. In [20] a µDE apprach is proposed for evolving an indirect representation of the Bin Packing Problem. Thi... |

3 |
et al., “Real-Parameter BlackBox Optimization Benchmarking 2010: Noiseless Functions Definitions
- Hansen, Auger, et al.
- 2010
(Show Context)
Citation Context ...roblems included in the following four testbeds have been considered in this study. • The CEC2005 benchmark described in [37] in 30 dimensions (25 test problems) • The BBOB2010 benchmark described in =-=[38]-=- in 100 dimensions (24 test problems) • The CEC2008 benchmark described in [39] in 1000 dimensions (7 test problems) • The CEC2010 benchmark described in [40] in 1000 dimensions (20 test problems) Thu... |

2 |
Evolving bin packing heuristic using micro-differential evolution with indirect representation
- Sotelo-Figueroa, Soberanes, et al.
(Show Context)
Citation Context ... literature, micro-Differential Evolution (µDE) is a successfully applied scheme. For example, in [19] a µDE employing opposition-based mechanism has been proposed for image thresholding problems. In =-=[20]-=- a µDE apprach is proposed for evolving an indirect representation of the Bin Packing Problem. This paper proposes a novel implementation of µDE, namely micro-Differential Evolution with Axis-moves (µ... |

2 |
Recent advances in differential evolution: a review and experimental analysis,”
- Neri, Tirronen
- 2010
(Show Context)
Citation Context ...for F , effective values are rarely greater than 1.0. The mutation scheme given in Equation (1) is also known as DE/rand/1. In literature many other mutation variants have been proposed, see [21] and =-=[23]-=-. When the provisional offspring has been generated by mutation, a popular crossover, namely exponential crossover is applied to the parent solution xj and the provisional offspring x′off , see [22]. ... |

2 |
Differential Evolution with a Neighborhood-based Mutation Operator
- Das, Abraham, et al.
- 2009
(Show Context)
Citation Context ...y for a multiple mutation structure has been proposed in [29]. A modified selection strategy, based on the location within the population, for the individuals undergoing mutation has been proposed in =-=[30]-=-. Another example of efficient DE variant has been proposed in [31] where a novel DE mutation is combined with a randomized fitness based selection of the individuals undergoing mutation. As highlight... |

1 |
cooperative micro-particle swarm optimization: A master-slave model
- “Parallel
- 2012
(Show Context)
Citation Context ...ut also about the proper sizing of the population. Some studies clearly suggest the usage of large populations in order to ensure the success of the algorithm, see [9]. On the other hand, in [10] and =-=[11]-=-, it is shown that, if properly designed, a population-based algorithm with a very small population size can efficiently solve large scale problems, see also [12] and [13]. The latter kind of algorith... |

1 |
Abc: a micro artificial bee colony algorithm for large scale global optimization
- Rajasekhar, Das, et al.
(Show Context)
Citation Context ... the other hand, in [10] and [11], it is shown that, if properly designed, a population-based algorithm with a very small population size can efficiently solve large scale problems, see also [12] and =-=[13]-=-. The latter kind of algorithms, i.e. population-based algorithm that use a small population, are indicated as micro algorithms and indicated by the prefix µ. An early implementation of micro algorith... |

1 |
Design of fractional order controller for a servohydraulic positioning system with micro artificial bee colony algorithm
- Rajasekhar, Das, et al.
(Show Context)
Citation Context ...rs, micro algorithms have been employed in various engineering applications as they are proven to be lighter in terms of hardware requirements and thus are prone to their use in embedded systems, see =-=[16]-=-. In addition, algorithms that make use of small populations are more exploitative than the large ones and thus quickly achieve improvements during the early stages of the optimization process. This f... |

1 |
Empirical analysis of a micro-evolutionary algorithm for numerical optimization
- Viveros-Jimènez, Mezura-Montes, et al.
(Show Context)
Citation Context ...orithms especially useful in real-time applications when a quick answer is needed, see e.g. [17]. The effect of small populations is obviously different when applied to various search strategies, see =-=[18]-=-. Amongst the various micro algorithms proposed in literature, micro-Differential Evolution (µDE) is a successfully applied scheme. For example, in [19] a µDE employing opposition-based mechanism has ... |

1 |
JADE: Adaptive Differential Evolution with
- Zhang, Sanderson
(Show Context)
Citation Context ...rithm For example, the so called jDE [26] proposed a controlled randomization of the DE parameters. Another popular DE variant based on controlled randomization of the parameters has been proposed in =-=[27]-=-. The Self-Adaptive Differential Evolution (SADE) proposed in [28] employs multiple mutation strategies and a randomized coordination scheme based on an initial learning. Another efficient coordinatio... |