Self Adaptive Hybrid Evolutionary Algorithm

In this section, the proposed hybrid evolutionary algorithm (HEA) is introduced.

Recently, many efforts to enhance the traditional GAs have been made ([98]). Among them, one category focuses on modifying the structure of a population or the role an individual plays in it ([85]-[87] and [95]-[100]), such as the coevolutionary algorithms ([85]-[87]), distributed GA ([99]), cellular GA ([100]), and symbiotic evolution ([95]-[97]).

In a traditional evolution algorithm, the number of rules in a model must be predefined.

The length of individuals (chromosomes) in a population is the same and is defined by the population must be predefined. In the second se

based symbiotic evolution (SAGC-SE) is proposed for the population in the HEA. In the final section, a evolution using FP-growth algorithm (SAG-SEFA) is d based symbiotic evolution (SAGC-SE) is proposed for based symbiotic evolution (SAGC-SE) is proposed for the population must be predefined. In the second se based symbiotic evolution (SAGC-SE) is proposed for the population in the HEA. In the final section, a based symbiotic evolution (SAGC-SE) is proposed for the population in the HEA. In the final section, a based symbiotic evolution (SAGC-SE) is proposed for the population in the HEA. In the final section, a based symbiotic evolution (SAGC-SE) is proposed for the population in the HEA. In the final section, a the population in the HEA. In the final section, a based symbiotic evolution (SAGC-SE) is proposed for based symbiotic evolution (SAGC-SE) is proposed for the population in the HEA. In the final section, a the population in the HEA. In the final section, a based symbiotic evolution (SAGC-SE) is proposed for based symbiotic evolution (SAGC-SE) is proposed for based symbiotic evolution (SAGC-SE) is proposed for based symbiotic evolution (SAGC-SE) is proposed for the population in the HEA. In the final section, a the population in the HEA. In the final section, a based symbiotic evolution (SAGC-SE) is proposed for the population in the HEA. In the final section, a

trail-and-error testing. Therefore, for different control problem, the length of an individual (chromosome) must be redefined. For solving this problem, the hybrid evolutionary algorithm (HEA) is proposed to decide the number of fuzzy rules automatically.

The proposed HEA combines the modified compact genetic algorithm (MCGA) and the modified variable-length genetic algorithm (MVGA). In the MVGA, the initial length of each individual may be different from each other, depending on the total number of rules encoded in it. Thus, the number of rules does not need to be predefined. In HEA, individuals with an equal number of rules constitute the same group. Initially, there are several groups in a population. Unlike the traditional variable-length genetic algorithm (VGA), Bandyopadhyay et. al. ([30]) used “#” to mean, “does not care”. In the HEA, the variable two-part crossover (VTC) and variable two-part mutation (VTM) are adopted to make the traditional crossover and mutation operators applicable to different lengths of chromosomes. Therefore, using “#”

means that “does not care” is not needed in the VTC and VTM.

In the HEA, a chromosome is divided into two parts. The first part of the chromosome gives the antecedent parameters of a TSK-type neuro-fuzzy controller while the second part of the chromosome gives the consequent parameters of a TSK-type neuro-fuzzy controller. Each part of the chromosome can be performed using the VTC on the overlapping genes of two chromosomes. In the traditional VGA, Bandyopadhyay et. al. ([30]) only evaluated the performance of each chromosome in a population. The performance of the number of rules was not evaluated ([30]). In HEA, the elite-based reproduction strategy is proposed to keep the best group with the same length chromosomes. Therefore, the best group can be reproduced many times for each generation. The elite-based reproduction strategy is similar to the maturing phenomenon in society, where individuals become more suitable to the environment as they acquire knowledge from society.

In the proposed HEA, the modified compact genetic algorithm (MCGA) is proposed to and mutation operators applicable to different leng

means that “does not care” is not needed in the VTC and VTM.

In the HEA, a chromosome is divided into two parts.

gives the antecedent parameters of a TSK-type neuro means that “does not care” is not needed in the VTC means that “does not care” is not needed in the VTC and mutation operators applicable to different leng means that “does not care” is not needed in the VTC

In the HEA, a chromosome is divided into two parts.

means that “does not care” is not needed in the VTC

In the HEA, a chromosome is divided into two parts.

means that “does not care” is not needed in the VTC

In the HEA, a chromosome is divided into two parts.

means that “does not care” is not needed in the VTC

In the HEA, a chromosome is divided into two parts.

In the HEA, a chromosome is divided into two parts.

means that “does not care” is not needed in the VTC means that “does not care” is not needed in the VTC

In the HEA, a chromosome is divided into two parts.

In the HEA, a chromosome is divided into two parts.

means that “does not care” is not needed in the VTC means that “does not care” is not needed in the VTC means that “does not care” is not needed in the VTC means that “does not care” is not needed in the VTC

In the HEA, a chromosome is divided into two parts.

In the HEA, a chromosome is divided into two parts.

means that “does not care” is not needed in the VTC

In the HEA, a chromosome is divided into two parts.

(CGA) ([101]) represents a population as a probability distribution over the set of solutions and is operationally equivalent to the order-one behavior of the simple GA ([102]). The advantage of the CGA is that it processes each gene independently and requires less memory than the normal GA. In the proposed MCGA, the building blocks (BBs) in the MCGA represent the suitable lengths of the chromosomes and reproduce the individuals according to the BBs. The coding scheme consists of the coding done by the MVGA and the MCGA. The MVGA codes the adjustable parameters of a TSK-type neuro-fuzzy controller (TNFC) into an individual (chromosome), as shown in Fig. 3.1; where MS_j represents the parameters of the antecedentof the jth rule in the TNFC, Wj represents the parameters of the consequent of the jth rule, w is the corresponding parameter of the consequent part with the jth rule and ith _ij input variable, and Rk represents that there are Rk fuzzy rules in a TNFC. In Fig. 3.2, the MCGA codes the probability vector into the building blocks (BBs), where each probability vector represents the suitability of the number of fuzzy rules in a TNFC. In MCGA, the maximum number of rules (R_max) and minimum number of rules (R_min) must be predefined to prevent the number of fuzzy rules to generate beyond a certain bound (i.e., [R_min, R_max]).

m₁₁ σ₁₁

MS1 MS2 ... MSj ... W1 W2 ... Wj ...

m₂₁ σ₂₁ ... m_i1 σ_i1 ... m_n1 Ξ w^0j ... w_ij ... w_nj

Rk

k W

MSR

Figure 3.1: Coding the adjustable parameters of a TNFC into a chromosome in the MVGA.

Rmin

V

VR_min+1 … V_Rk … VR_max−1

Rmax

V

Figure 3.2: Coding the probability vector into the building blocks (BBs) in the MCGA.

The learning process of the HEA involves six major operators: initializing, evaluating, MCGA codes the probability vector into the building

vector represents the suitability of the number of

) and minimum number of rules ( vector represents the suitability of the number of

vector represents the suitability of the number of vector represents the suitability of the number of MCGA codes the probability vector into the building MCGA codes the probability vector into the building vector represents the suitability of the number of

) and minimum number of rules ( vector represents the suitability of the number of

) and minimum number of rules ( vector represents the suitability of the number of

vector represents the suitability of the number of MCGA codes the probability vector into the building MCGA codes the probability vector into the building MCGA codes the probability vector into the building

) and minimum number of rules ( ) and minimum number of rules (

mutation. Figure 3.3 shows the flowchart of the learning process. The whole learning process

Figure 3.3: Flowchart of the parameter learning in the HEA.

1. Initializing:

The initializing step sets initial values of the MVGA and MCGA. In the MVGA, individuals should be generated randomly to construct an initial population. The initial values of MVGA are generated randomly within a fixed range. The following formulations show how to generate the initial chromosomes:

min max Figure 3.3: Flowchart of the parameter learning in

Figure 3.3: Flowchart of the parameter learning in Figure 3.3: Flowchart of the parameter learning in Figure 3.3: Flowchart of the parameter learning in Figure 3.3: Flowchart of the parameter learning in Figure 3.3: Flowchart of the parameter learning in Figure 3.3: Flowchart of the parameter learning in Figure 3.3: Flowchart of the parameter learning in

represents the pth gene in a Chrc; and [σ_min , σ_max ], [ m_min , m_max ], and ]

,

[w_min w_max represent the predefined range.

In order to keep the same number of rules in a TNFC, the number of the rules of each chromosome needs to be generated η chromosomes. That is, the number of chromosomes generated of each group (η) must be predefined. Therefore, the population size Nc is set to η*(R_max-R_min +1). In the MCGA, the probability vectors of the BBs are set to 0.5 initially.

2. Evaluating:

The evaluating step is to evaluate each chromosome in a population. The goal of the HEA is to maximize the fitness value. The higher a fitness value, the better the fitness. The fitness function is used by a reinforcement signal defined in Chapter 4 will be introduced later.

3. Sorting:

After the evaluating step, the chromosomes in the population are sorted. After sorting the whole population, chromosomes in the top half of population are also sorted in each group. The sorting step can help performing the reproduction step because of the best chromosome in each group can be stayed. After sorting the chromosomes in the population, the algorithm goes to next step.

4. Elite-Based Reproduction Strategy (ERS):

Reproduction is a process in which individual strings are copied according to their fitness value. In the HEA, an elite-based reproduction strategy (ERS) is proposed to mimic the maturing phenomenon in society, where individuals become more suitable to the environment as they acquire more knowledge from society. The MCGA uses the BBs to represent the suitable length of the chromosomes and reproduces the chromosomes according to the probability vector in the BBs. The best

After the evaluating step, the chromosomes in the p sorting the whole population, chromosomes in the to

After the evaluating step, the chromosomes in the p After the evaluating step, the chromosomes in the p After the evaluating step, the chromosomes in the p After the evaluating step, the chromosomes in the p After the evaluating step, the chromosomes in the p After the evaluating step, the chromosomes in the p After the evaluating step, the chromosomes in the p After the evaluating step, the chromosomes in the p After the evaluating step, the chromosomes in the p After the evaluating step, the chromosomes in the p

the ERS. According to the results of the ERS, using the crossover and the mutation generate the other half individuals. After the ERS, the suitable length of chromosomes will be preserved and the unsuitable length of chromosomes will be removed. The detailed of the ERS is shown as follows:

Step 1. Update the probability vectors of the BBs according to the following chromosomes in the group with R_k rules in a population; λ is a predefined threshold value; Avg represents the average fitness value in the whole population; Nc is the population size;

Rk

N represents that there are

Rk

N chromosomes in the group that

individuals with Rk rules; fitp is the fitness value of the pth chromosome in all Nc populations; _Rq

fit k is the fitness value of the qth chromosome in the group with Rk

rules; and

Max _ ≥Avg, then the suitable chromosomes in the group with Rk

rules should be increased. On the other hand, if

sum of the fitness values of the chromosomes in the group with R_k rules.

Step 2. Determine the reproduction number according to the probability vectors of the BBs as follows:

where Nc represents the population size; Rp

Rk is the recorder, and a chromosome has Rk rules for constructing a TNFC.

Step 3. After step 2, the reproduction number of each group in the top half of a population is obtained. Then

Rk

Rp chromosomes in each group are generated using the roulette-wheel selection method ([72]).

Step 4. In the proposed ERS, for avoiding suitable number of fuzzy rules may fall in the local optima solution, the two different actions to update the

Rk

V are adopted.

The two deferent actions are defined according to the following equations:

In the proposed ERS, for avoiding suitable number o the local optima solution, the two different action

In the proposed ERS, for avoiding suitable number o In the proposed ERS, for avoiding suitable number o In the proposed ERS, for avoiding suitable number o the roulette-wheel selection method ([72]).

the roulette-wheel selection method ([72]).

In the proposed ERS, for avoiding suitable number o the local optima solution, the two different action

In the proposed ERS, for avoiding suitable number o In the proposed ERS, for avoiding suitable number o In the proposed ERS, for avoiding suitable number o the roulette-wheel selection method ([72]).

the roulette-wheel selection method ([72]).

the roulette-wheel selection method ([72]).

the local optima solution, the two different action

represents the best fitness value of the best combination of chromosomes in current generations. Eqs. 3.10-3.12 represent that if the best fitness is not changed for a sufficient generations, the suitable number of fuzzy rules may fall in the local optima solution.

5. Variable two-part crossover:

Although the ERS operation can search for the best existing individuals, it does not create any new individuals. In nature, an offspring has two parents and inherits genes from both. The main operator working on the parents is the crossover operator, the operation of which occurs for a selected pair with a crossover rate. In the HEA, the variable two-part crossover (VTC) is proposed to perform this step. In the VTC, the parents are selected from the enhanced elites. In the VTC, two parents are selected by using the roulette-wheel selection method ([72]). The two parents may be selected from the same or different groups. Performing crossover on the selected parents creates the offspring. Since the parents may be of different lengths, the misalignment of individuals must be avoided in the crossover operation. Therefore, a variable two-part crossover is proposed to solve this problem. The first part of the chromosome gives the antecedent parameters of a TNFC while the second part of the chromosome gives the consequent parameters of a TNFC. The two-point crossover ([76]) is adopted in each part of the chromosome. Thus, new individuals are created by exchanging the site’s values between the selected sites of the parents’ individuals.

To avoid the misalignment of individuals in the crossover, in the VTC, the selection of the crossover points in each part will not exceed the shortest length chromosome of two parents. Two individuals of different lengths using the variable two-part crossover operation are shown in Fig. 3.4. MSj represents the parameters of the antecedent part of the jth rule in the TNFC, Wj represents the parameters of the selected by using the roulette-wheel selection meth

selected from the same or different groups. Perform parents creates the offspring. Since the parents ma misalignment of individuals must be avoided in the selected from the same or different groups. Perform selected from the same or different groups. Perform selected by using the roulette-wheel selection meth selected from the same or different groups. Perform parents creates the offspring. Since the parents ma selected from the same or different groups. Perform parents creates the offspring. Since the parents ma selected from the same or different groups. Perform parents creates the offspring. Since the parents ma selected from the same or different groups. Perform parents creates the offspring. Since the parents ma parents creates the offspring. Since the parents ma selected from the same or different groups. Perform selected from the same or different groups. Perform parents creates the offspring. Since the parents ma parents creates the offspring. Since the parents ma selected from the same or different groups. Perform selected from the same or different groups. Perform selected from the same or different groups. Perform selected from the same or different groups. Perform parents creates the offspring. Since the parents ma parents creates the offspring. Since the parents ma selected from the same or different groups. Perform parents creates the offspring. Since the parents ma

in a TNFC. After the VTC, the individuals with poor performance are replaced by the new offspring.

Rk

MS

Rk

W

Rk

MS WR_k

Figure 3.4: The variable two-part crossover operation in the HEA.

6. Variable two-part mutation:

Although the ERS and the VTC produce many new strings; these strings do not provide any new information to every population at the site of an individual. Mutation can randomly alter the allele of a gene. In the HEA, the variable two-part mutation (VTM) is proposed to perform the mutation operation. The proposed VTM is different from the traditional mutation and is applicable to chromosomes of different length.

The first and second parts of the chromosome are the same as the VTC. In each part of a chromosome, uniform mutation ([84]) is adopted, and the mutated gene is drawn randomly from the domain of the corresponding variable. The VTM operation of each individual is shown in Fig. 3.5.

Rk

MS

Rk

W

Rk

k W

MSR ^new

Wj

MS₂new

Figure 3.5: The variable two-part mutation operation in the HEA.

provide any new information to every population at can randomly alter the allele of a gene. In the HEA (VTM) is proposed to perform the mutation operation from the traditional mutation and is applicable to can randomly alter the allele of a gene. In the HEA can randomly alter the allele of a gene. In the HEA provide any new information to every population at can randomly alter the allele of a gene. In the HEA (VTM) is proposed to perform the mutation operation can randomly alter the allele of a gene. In the HEA (VTM) is proposed to perform the mutation operation can randomly alter the allele of a gene. In the HEA (VTM) is proposed to perform the mutation operation can randomly alter the allele of a gene. In the HEA (VTM) is proposed to perform the mutation operation (VTM) is proposed to perform the mutation operation can randomly alter the allele of a gene. In the HEA can randomly alter the allele of a gene. In the HEA (VTM) is proposed to perform the mutation operation (VTM) is proposed to perform the mutation operation can randomly alter the allele of a gene. In the HEA can randomly alter the allele of a gene. In the HEA can randomly alter the allele of a gene. In the HEA

provide any new information to every population at can randomly alter the allele of a gene. In the HEA (VTM) is proposed to perform the mutation operation from the traditional mutation and is applicable to can randomly alter the allele of a gene. In the HEA can randomly alter the allele of a gene. In the HEA provide any new information to every population at can randomly alter the allele of a gene. In the HEA (VTM) is proposed to perform the mutation operation can randomly alter the allele of a gene. In the HEA (VTM) is proposed to perform the mutation operation can randomly alter the allele of a gene. In the HEA (VTM) is proposed to perform the mutation operation can randomly alter the allele of a gene. In the HEA (VTM) is proposed to perform the mutation operation (VTM) is proposed to perform the mutation operation can randomly alter the allele of a gene. In the HEA can randomly alter the allele of a gene. In the HEA (VTM) is proposed to perform the mutation operation (VTM) is proposed to perform the mutation operation can randomly alter the allele of a gene. In the HEA can randomly alter the allele of a gene. In the HEA can randomly alter the allele of a gene. In the HEA

在文檔中 以改良安全性增強式學習為基礎的自我適應進化演算法應用於模糊類神經控制器設計之研究 (頁 45-54)