X. Yao, Y. Liu, and G. Lin, "Evolutionary programming made faster," IEEE Trans. on Evolutionary Computation, vol. 3, no. 2, pp. 82--102, July 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....# i controls the size of the neighborhood along x i . Similarly, we characterize cn (#) by vector #, where # i denotes the maximum possible perturbation along # i . 4. 2 Generation of Trial Points Three general distributions used in SA to generate trial points include uniform [49] Gaussian [45, 222], and Cauchy [51] Examples of other methods are logarithmic explorations [50] and tree annealing [33, 32] that organize neighborhoods in a tree. Such methods only work well for problems with specific objective or constraint forms and may not work for general problems. Here we test the three ....

....being 1 and the other components being 0, and i is randomly generated from , n . There are three possible choices for # i : a) uniform, where # i is generated uniformly in [ # i , # i ] 49] b) Gaussian, where # i is generated from a Gaussian distribution with zero mean and variance # i [222]; and c) Cauchy, where # i is generated from a Cauchy density [51, 222] f d (x) i x . The major advantage [51, 222] of using a Cauchy distribution lies in its long flat tail. In addition to generating samples close to the current point, there is also a high probability of sampling ....

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X. Yao, Y. Liu, and G. Lin. Evolutionary programming made faster. IEEE Trans. on Evolutionary Computation, 3(2):82--102, 1999.

....distinguish it from Fogel s Classical EP(CEP) They found Cauchy mutation more effective for multimodal problems than Gaussian mutation, although no significant differences were observed for unimodal problems. Inspired by this, several types of combinations of Cauchy and Gaussian have been proposed[5, 18, 23, 24]. In these EPs, the mutation size of object variables is adjusted by it s own self adaptive property, derived from strategy parameters. However, EP still suffers from premature convergence, i.e. EP often converges before finding the global optimum, even when optimizing unimodal functions. ....

....contrast to the directional and deterministic changes caused by natural selection. We examined it s performance using static test functions and found that REP is free from the lower bound problem and more effective than conventional EP. The computational steps of the EPs are based on notations in [24] and [14] CEP, FEP and REP stand for Fogel s EP, Yao and Liu s EP and our extended EP, respectively. 2.1 Classical Evolutionary Programming CEP is implemented as follows in this study. 1. Generate an initial population of individuals, and set g = 1. Each individual is taken as a pair of ....

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X. Yao, Y. Liu and G. Lin (1999), " Evolutionary Programming Made Faster", IEEE Transactions on Evolutionary Computation, Vol. 3, No. 2, pp.82-102.

....objective function takes f = F over the search space (excluding points sampled already) can be expressed as: gF (x) c n X i=1 w i kr i (k 2 r 2 i (F Gamma i ) 2 ) n X i=1 s i t i (r i ) 10) 644 Table 1. Experimental results on evaluating 23 benchmark functions by EA [6], SQP [5] SIMANN [2] and SABS. Avg. best solution represents the average best solutions in the last generation of EP over 50 runs. SQP was run 100 times if the objective function was differentiable, and SA and SABS were each run 10 times. CPU times were measured by averaging the results of ....

....package [5] for solving nonlinear programming problems, and traditional SA implemented by SIMANN [2] SABS was built by replacing pure random sampling in SIMANN by our Bayesian sampling procedure. Table 1 shows the results of applying these algorithms on 23 optimization benchmarks collected in [6]: f 1 to f 7 are unimodal functions, f 8 to f 13 are multimodal functions with many local minima, and f 14 to f 23 have a few local minima. For comparison, we also list the results evaluated by evolutionary programming (EP) 6] Our results show that SABS performs the best in terms of both ....

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Xin Yao. Evolutionary programming made faster. IEEE Tran. on Evolutionary Computation, 3(2):82--102, July 1999. 646

....others being 0, and i is randomly generated from f1; 2; Delta Delta Delta ; ng. There are three possible choices for i : a) uniform, where i is generated uniformly in [ Gammaoe i ; oe i ] 6] b) Gaussian, where i is generated from a Gaussian distribution with zero mean and variance oe i [29]; and c) Cauchy, where i is generated from a Cauchy density f d (x) 1 oe i oe 2 i x 2 [7, 29] The major advantage [7, 29] of using a Cauchy distribution lies in its long flat tail. In addition to generating samples close to the current point, there is also a high probability of ....

.... choices for i : a) uniform, where i is generated uniformly in [ Gammaoe i ; oe i ] 6] b) Gaussian, where i is generated from a Gaussian distribution with zero mean and variance oe i [29] and c) Cauchy, where i is generated from a Cauchy density f d (x) 1 oe i oe 2 i x 2 [7, 29]. The major advantage [7, 29] of using a Cauchy distribution lies in its long flat tail. In addition to generating samples close to the current point, there is also a high probability of sampling remote points, making it easy to escape from local minima, especially when temperatures are low and ....

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X. Yao, Y. Liu, and G. Lin. Evolutionary programming made faster. IEEE Trans. on Evolutionary Computation, 3(2):82--102, 1999.

....frictional constraint. Nakamura et al. solve the problem as a nonlinear programming problem using Lagrange multipliers [3] Fukuda et al. proposed a method to plan the grasping points and the forces by using Evolutionary Computation [4] In this paper, an evolutionary computation technique [6] 7][8] is applied to the position force planning for grasping an object by multi fingered robot hand. The main feature of the problem is that not only the contact positions of the fingers but the contact forces, too, are used on the planning level. The contact points and forces should be specified in ....

....component values x i are modified as: x i (j) x i (j) j i0 (j)ffi ij (24) where we called j i0 (j) active strategy parameters, and j il (j) inactive strategy parameters which are no effect of creating x i . The computational procedure of REP can be described in the same manner as FEP [8], as follows: 1. Generate the initial population of individuals, and set g = 1. 2. Evaluate the objective value for each individual X i , 8i 2 f1; 2; g of the population based on the objective function f(x i ) 3. Each parent X i ,i = 1; 2; reproduces offspring X i . 4. ....

X. Yao, Y. Liu and G. Lin , " Evolutionary Programming Made Faster", IEEE Transactions on Evolutionary Computation, Vol. 3, No. 2, pp.82-102, 1999.

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X. Yao, Y. Liu, and G. Lin, "Evolutionary programming made faster," IEEE Trans. on Evolutionary Computation, vol. 3, no. 2, pp. 82--102, July 1999.

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X. Yao, Y. Liu, and G. Lin, "Evolutionary programming made faster," IEEE Trans. Evol. Comput., vol. 3, pp. 82--102, July 1999.

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Yao, X., Liu, Y., and Lin, G. (1999) "Evolutionary programming made faster," IEEE Transactions on Evolutionary Computation, vol. 3, no. 2, pp.82--102.

....(such as crossover and mutation) determine different neighbourhood and step sizes. This paper analyses the efficiency of various mutations in evolutionary programming (EP) by examining their neighbourhood and step sizes. It shows analytically when and why Cauchy mutation based fast EP (FEP) [1, 2] is better than Gaussian mutation based classical EP (CEP) It also studies the relationship between the optimality of the solution and the time used to find the solution. Based on the theoretical analysis, an improved FEP (IFEP) is proposed, which combines the advantages of both Cauchy and ....

....computation is not as strong as the applications. It is still very difficult to explain why an EA works for a particular problem, or why it does not. This paper analyses one particular class of EAs evolutionary programming (EP) and explains why and when Cauchy mutation based fast EP [1, 2] is faster than Gaussian mutation based classical EP (CEP) 1.1 Classical Evolutionary Programming A global minimisation problem can be formalised as a pair (S; f) where S R is a bounded set on R and f : S 7 R is an n dimensional real valued function. The problem is to find a point ....

X. Yao, Y. Liu, and G. Lin, "Evolutionary programming made faster," IEEE Transactions on Evolutionary Computation, 1996. Submitted.

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Yao, X., Liu, Y. and Lin, G., "Evolutionary programming made faster," IEEE Trans. Evolutionary Computation, Vol. 3, No. 2, pp. 82-102, 1999.

....the framework of generate and test search, different search algorithms investigated in artificial intelligence, operations research, computer science, and evolutionary computation can be unified together. The analysis of EAs will also be easier to understand using the generate and test framework [1, 2]. Figure 2 shows the two major steps of the generate and test search. 1. Generate the initial solution at random and denote it as the current solution; 2. Generate the next solution from the current one by perturbation; 3. Test whether the newly generated solution is acceptable; a) Accepted ....

....strategic parameters (i.e. the variances of the Gaussian distribution used in generating offspring) Usually, the means are 0, while the variances are represented as part of an individual and subject to evolution. Recently, new mutation based on Cauchy random numbers has been proposed [1, 2]. The new mutation operator has been shown to be significantly better than the Gaussian mutation for a number of benchmark problems. Figure 7 gives the detailed algorithm of the new EP fast EP (FEP) 1, 2] FEP is the same as CEP except for Eq. 2) 2.2.2 Selection Selection in EP is normally ....

[Article contains additional citation context not shown here]

X. Yao, Y. Liu, and G. Lin, "Evolutionary programming made faster," IEEE Transactions on Evolutionary Computation, p. Submitted, 1996.

....(such as crossover and mutation) determine different neighbourhood and step sizes. This paper analyses the efficiency of various mutations in evolutionary programming (EP) by examining their neighbourhood and step sizes. It shows analytically when and why Cauchy mutation based fast EP (FEP) [1, 2] is better than Gaussian mutation based classical EP (CEP) It also studies the relationship between the optimality of the solution and the time used to find the solution. Based on the theoretical analysis, an improved FEP (IFEP) is proposed, which combines the advantages of both Cauchy and ....

....computation is not as strong as the applications. It is still very difficult to explain why an EA works for a particular problem, or why it does not. This paper analyses one particular class of EAs evolutionary programming (EP) and explains why and when Cauchy mutation based fast EP [1, 2] is faster than Gaussian mutation based classical EP (CEP) 1.1 Classical Evolutionary Programming A global minimisation problem can be formalised as a pair (S; f) where S R n is a bounded set on R n and f : S 7 R is an n dimensional real valued function. The problem is to find a point ....

X. Yao, Y. Liu, and G. Lin, "Evolutionary programming made faster," IEEE Transactions on Evolutionary Computation, 1996. Submitted.

....crossover under the same binary chromosome encoding scheme due to its larger search step size. It is, however, important to note that the benefit of a large search step size is not unconditional. It is beneficial only when the current search points are suffciently far away from the global optimum [7]. This implies that a large search step size would be most useful in the initial stage of GA s search since the initial population is usually generated at random and is far away from the global optimum. As the GA search progresses, the current search points are expected to improve and move closer ....

....the distance between a parent and its offspring in the phenotype space. It is reversely proportional to E(l) i.e. it increases as E(l) decreases and vice versa. Since it has been shown that a large step size is better than a smaller one when the search points are far away from the global optimum [7], the analytical results in this section imply that the ranking of the performance of the four different crossover operators, from the best to the worst, should be n Gamma 1 point, uniform, two point and one point crossover. The next two sections present a set of experiments which demonstrate ....

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X. Yao, Y. Liu, and G. Lin, "Evolutionary programming made faster," Submitted to IEEE Trans. on Evolutionary Computation, 1996.

....the main factor which causes the difference between FES and CES. Cauchy function s long tail gives FES a higher probability of jumping out of a local minimum, but its smaller central part makes it weaker than CES at fine grained local search. Recent analytical results and further empirical studies [18] support the preliminary analyses presented in this paper. The future work of this research includes studying FES with recombination and a different order of mutating object variables (x s) and strategy parameters (j s) According to recent work on analysing EAs using step sizes of search ....

X. Yao, Y. Liu, and G. Lin, "Evolutionary programming made faster," IEEE Transactions on Evolutionary Computation, 1996. Submitted.

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X. Yao, Y. Liu and G. Lin, "Evolutionary programming made faster", IEEE Transaction on Evolutionary Computation, pp. 82-102, IEEE Press, 1999.

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X. Yao, Y. Liu, and G. Lin, "Evolutionary Programming Made Faster", IEEE Transaction on Evolutionary Computation, pp. 82-102, 1999.

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Yao, X., Liu, Y., & Lin, G. (1999). Evolutionary programming made faster. IEEE Trans. Evol. Comp., 3, 82--102.

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Yao, X., Liu, Y., & Lin, G. (1999). Evolutionary programming made faster. IEEE Trans. Evol. Comp., 3, 82--102.

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X. Yao, Y. Liu, and G. Lin, `Evolutionary Programming Made Faster', IEEE Transactions on Evolutionary Computation, 3(2), 82-- 102, (1999).

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X. Yao, Y. Liu, and G. Lin, "Evolutionary programming made faster," IEEE Trans. Evol. Comput., vol. 3, pp. 82--102, July 1999.

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X. Yao, Y. Liu, and G. Lin, "Evolutionary programming made faster," IEEE Transactions on Evolutionary Computation, Vol. 3:2, pp. 82-102, 1999.

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X. Yao, Y. Liu, and G. Lin, "Evolutionary programming made faster," IEEE Transactions on Evolutionary Computation, Vol. 3:2, pp. 82-102, 1999.

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