Chapter 3 Self Adaptive Evolutionary Algorithms
3.3 Self adaptive Groups Based Symbiotic Evolution using FP-growth Algorithm
Although the SAGC-SE could solve the problem of the HEA that all the fuzzy rules are encoded into one chromosome. Moreover the SAGC-SE not only evaluates the fuzzy rule locally but also makes groups to cooperate with each other for generating the better chromosomes. However, in the SAGC-SE, how to select groups to choose individuals for constructing a TNFC with different number of rules is a major problem. Therefore, for determining the number of fuzzy rules automatically, the SAGC-SE selects different number of groups to construct complete solution. In this way, the SAGC-SE selects groups randomly.
It’s obvious that the performance of the SAGC-SE dependents on how to select individuals from groups.
In this section, the self adaptive groups based symbiotic evolution using FP-growth algorithm (SAG-SEFA) will be discussed. The SAG-SEFA is proposed for providing a
Self adaptive Groups Based Symbiotic Evolution using FP-growth Algorithm
Self adaptive Groups Based Symbiotic Evolution Self adaptive Groups Based Symbiotic Evolution Self adaptive Groups Based Symbiotic Evolution Self adaptive Groups Based Symbiotic Evolution Self adaptive Groups Based Symbiotic Evolution using FP-growth Algorithm
Self adaptive Groups Based Symbiotic Evolution using FP-growth Algorithm
Self adaptive Groups Based Symbiotic Evolution using FP-growth Algorithm
Self adaptive Groups Based Symbiotic Evolution using FP-growth Algorithm
using FP-growth Algorithm
Self adaptive Groups Based Symbiotic Evolution Self adaptive Groups Based Symbiotic Evolution Self adaptive Groups Based Symbiotic Evolution using FP-growth Algorithm
using FP-growth Algorithm
Self adaptive Groups Based Symbiotic Evolution Self adaptive Groups Based Symbiotic Evolution Self adaptive Groups Based Symbiotic Evolution Self adaptive Groups Based Symbiotic Evolution using FP-growth Algorithm
using FP-growth Algorithm
Self adaptive Groups Based Symbiotic Evolution
using FP-growth Algorithm
method of how to select groups to select individuals for constructing a TSK-type neuro-fuzzy controller (TNFC) with different number of rules in the SAGC-SE. Therefore, the SAG-SEFA is used to determine the suitable number of rules in a TNFC and the suitable groups used to perform the selection of groups. Moreover, the SAG-SEFA adopts a different way to select suitable groups to perform crossover steps.
The SAG-SEFA is proposed to improve the SAGC-SE. The purpose of the SAG-SEFA is to determine not only the suitable number of rules in a TNFC but also the suitable rules that are used to construct a TNFC. Therefore, the SAG-SEFA, as well as the SAGC-SE, consists of structure and parameter learning.
In structure learning, as well as SAGC-SE, the SAG-SEFA determines the number of fuzzy rules automatically and processes the variable length of a combination of chromosomes by using the TSSA.
In parameter learning, to solve the problem of the SAGC-SE that the chromosomes are selected randomly to perform selection step. The proposed SAG-SEFA determines which suitable groups should be selected the chromosomes that will form TNFCs with different rules and which suitable groups that should be selected to perform selected step. Furthermore, the SAG-SEFA also provides a different way to determine the suitable groups to perform crossover step. The SAG-SEFA proposes using the data mining based selection strategy (DMSS) and the data mining based crossover strategy (DMCS) to determine which groups should be used to select individuals to form a TNFC with each different rules and to determine which groups should be used to select individuals to perform crossover steps using the frequent pattern growth (FP-growth) ([50]) data mining method.
The goal of FP-growth is to find the frequent patterns that do not have candidate generation. In the proposed DMSS, the FP-growth is used to find from transactions the sets of groups that occur frequently. In SAG-SEFA, a “transaction” refers to the collection of groups
In parameter learning, to solve the problem of the selected randomly to perform selection step. The pr suitable groups should be selected the chromosomes
In parameter learning, to solve the problem of the In parameter learning, to solve the problem of the In parameter learning, to solve the problem of the selected randomly to perform selection step. The pr
In parameter learning, to solve the problem of the selected randomly to perform selection step. The pr
In parameter learning, to solve the problem of the selected randomly to perform selection step. The pr
In parameter learning, to solve the problem of the selected randomly to perform selection step. The pr selected randomly to perform selection step. The pr In parameter learning, to solve the problem of the In parameter learning, to solve the problem of the selected randomly to perform selection step. The pr selected randomly to perform selection step. The pr In parameter learning, to solve the problem of the In parameter learning, to solve the problem of the In parameter learning, to solve the problem of the In parameter learning, to solve the problem of the selected randomly to perform selection step. The pr selected randomly to perform selection step. The pr In parameter learning, to solve the problem of the selected randomly to perform selection step. The pr
the DMSS uses three actions to determine Rk groups that are used to select Rk chromosomes to form TNFCs with Rk rules. The three actions defined in the DMSS are normal, search, and exploration. In the normal action, as well as SAGC-SE, Rk groups that are used to select Rk chromosomes to form a TNFC are chosen randomly. In the search action, Rk groups are chosen from the set of frequently-occurring groups which chosen from the candidate sets of frequently-occurring groups. In the exploration action, Rk groups are chosen without using the set of frequently-occurring groups. As well as the DMSS, in the DMCS, the suitable groups used to select chromosomes to perform the crossover steps are decided based on the three actions (normal, search, or exploration). Compare with SAGC-SE, the SAG-SEFA provides a robust way to select groups to perform selection and crossover step. Therefore, the three actions (normal, search, or exploration) can improve the combination of solutions to avoid fall in the local optimal solution.
The structure of the chromosome in the SAG-SEFA, as well as SAGC-SE, is shown in Fig. 3.6. In the proposed SAG-SEFA, as well as the SAGC-SE, the coding structure of the chromosomes must be suitable for symbiotic evolution. The coding structure is shown in Fig.
3.8.
For determining the suitable number of fuzzy rules, the two-step self-adaptive algorithm (TSSA) proposed in SAGC-SE is adopted. As well as SAGC-SE, the building blocks (BBs) are used to represent the suitability of TNFCs with different number of fuzzy rules and to determine to the number of TNFCs with each different fuzzy rules should be selected to evaluate the chromosomes. The TSSA codes the probability vector into the building blocks (BBs) is shown in Fig. 3.7. In the TSSA, the maximum and minimum number of rules must be predefined to prevent the number of fuzzy rules from generating beyond a certain bound (i.e., [Rmin, Rmax]).
The learning process of the SAG-SEFA is shown in Fig. 3.11. As shown in Fig. 3.11, The structure of the chromosome in the SAG-SEFA, as
In the proposed SAG-SEFA, as well as the SAGC-SE, t chromosomes must be suitable for symbiotic evolutio
The structure of the chromosome in the SAG-SEFA, as The structure of the chromosome in the SAG-SEFA, as The structure of the chromosome in the SAG-SEFA, as
In the proposed SAG-SEFA, as well as the SAGC-SE, t The structure of the chromosome in the SAG-SEFA, as
In the proposed SAG-SEFA, as well as the SAGC-SE, t The structure of the chromosome in the SAG-SEFA, as
In the proposed SAG-SEFA, as well as the SAGC-SE, t The structure of the chromosome in the SAG-SEFA, as
In the proposed SAG-SEFA, as well as the SAGC-SE, t In the proposed SAG-SEFA, as well as the SAGC-SE, t The structure of the chromosome in the SAG-SEFA, as The structure of the chromosome in the SAG-SEFA, as
In the proposed SAG-SEFA, as well as the SAGC-SE, t In the proposed SAG-SEFA, as well as the SAGC-SE, t The structure of the chromosome in the SAG-SEFA, as The structure of the chromosome in the SAG-SEFA, as The structure of the chromosome in the SAG-SEFA, as The structure of the chromosome in the SAG-SEFA, as
In the proposed SAG-SEFA, as well as the SAGC-SE, t In the proposed SAG-SEFA, as well as the SAGC-SE, t The structure of the chromosome in the SAG-SEFA, as
In the proposed SAG-SEFA, as well as the SAGC-SE, t
(TSSA), data mining based selection strategy (DMSS), fitness assignment, sorting, elite-based reproduction strategy (ERS), data mining-based crossover strategy (DMCS), and the mutation strategy. In the SAG-SEFA, the operators of the initialization, two-step self-adaptive algorithm (TSSA), sorting, elite-based reproduction strategy (ERS), and the mutation strategy are same as the SAGC-SE introduced in Section 3.2. About this, the only three operators of the data mining based selection strategy (DMSS), fitness assignment, and data mining-based crossover strategy (DMCS) are described step-by-step as follows:
Figure 3.11: Learning process of the SAG-SEFA.
1. The data mining based selection strategy (DMSS):
After the TSSA, the selection times of the TNFCs with different rules are determined. The SAG-SEFA then performs the selection step. The selection step in the SAG-SEFA can be divided into the selection of groups and the selection of chromosomes. In the selection of groups, the data mining-based selection strategy (DMSS) is proposed to improve the selection of the SAGC-SE in which chromosomes are selected randomly to form TNFCs. In the DMSS, the groups are selected according to the groups that frequently obtain the best performance. To defend the groups that frequently obtain the best performance, the FP-growth ([50]) data mining method is adopted. The FP-growth was proposed by Han et al. ([50]).
The goal of FP-growth is to find the frequently-occurring patterns that do not have candidate generation. In the proposed DMSS, the FP-growth is used to find the frequently-occurring groups from transactions (in the SAG-SEFA, a transaction means a set of the groups that performs well). After the groups that occur frequently have been found, the DMSS selects the Rk groups that are used to select chromosomes to form TNFCs with Rk rules according to the frequently-occurring groups. To avoid the frequently-occurring groups that may fall in the local optimal solution, the DMSS uses three actions to select Rk groups. The three actions defined in this paper are normal, search, and exploration. The details of the DMSS are as follows:
Step 1. The transactions are built in the following equation:
candidate generation. In the proposed DMSS, the FP-frequently-occurring groups from transactions (in t means a set of the groups that performs well). Afte have been found, the DMSS selects the
frequently-occurring groups from transactions (in t frequently-occurring groups from transactions (in t candidate generation. In the proposed DMSS, the FP-frequently-occurring groups from transactions (in t means a set of the groups that performs well). Afte frequently-occurring groups from transactions (in t means a set of the groups that performs well). Afte frequently-occurring groups from transactions (in t means a set of the groups that performs well). Afte frequently-occurring groups from transactions (in t means a set of the groups that performs well). Afte means a set of the groups that performs well). Afte frequently-occurring groups from transactions (in t frequently-occurring groups from transactions (in t means a set of the groups that performs well). Afte means a set of the groups that performs well). Afte frequently-occurring groups from transactions (in t frequently-occurring groups from transactions (in t frequently-occurring groups from transactions (in t frequently-occurring groups from transactions (in t means a set of the groups that performs well). Afte means a set of the groups that performs well). Afte frequently-occurring groups from transactions (in t means a set of the groups that performs well). Afte
.
ThreadFitn is the predefined value; TransactionNum is the total number of transactions; Transactionj[i] represents the ith item in the jth transaction; and
] [ CRuleSet i
TNF Rk denotes the ith group of the selected Rk groups used to select chromosomes to form a TNFC with Rk rules. The transactions have the form shown in Table 3.1. As shown in Table 3.1, every transaction represents the Rk groups that form a TNFC with Rk rules. For example, as shown in Table 3.1, the first transaction of the transaction set means that the 3-rule TNFC that is selected from the first group, fourth group, and eighth group performs well. The step of building transactions continues in the normal, search, and exploration actions.
Table 3.1: Transactions in a FP-growth.
Transaction index Groups
After the transactions are built, the DMSS selects groups according to different action types. If the action type is normal, the DMSS selects the groups, using the chromosomes to form a TNFC with Rkk rules. The transactions have the form shown in Table 3.1. As shown in Table 3.1, every transact
rules. For example, as shown in Table 3.1, the fir of the transaction set means that the 3-rule TNFC t
in Table 3.1. As shown in Table 3.1, every transact in Table 3.1. As shown in Table 3.1, every transact chromosomes to form a TNFC with R
in Table 3.1. As shown in Table 3.1, every transact
rules. For example, as shown in Table 3.1, the fir in Table 3.1. As shown in Table 3.1, every transact
rules. For example, as shown in Table 3.1, the fir in Table 3.1. As shown in Table 3.1, every transact
rules. For example, as shown in Table 3.1, the fir in Table 3.1. As shown in Table 3.1, every transact
rules. For example, as shown in Table 3.1, the fir rules. For example, as shown in Table 3.1, the fir in Table 3.1. As shown in Table 3.1, every transact
in Table 3.1. As shown in Table 3.1, every transact
rules. For example, as shown in Table 3.1, the fir rules. For example, as shown in Table 3.1, the fir in Table 3.1. As shown in Table 3.1, every transact
in Table 3.1. As shown in Table 3.1, every transact in Table 3.1. As shown in Table 3.1, every transact in Table 3.1. As shown in Table 3.1, every transact
rules. For example, as shown in Table 3.1, the fir rules. For example, as shown in Table 3.1, the fir in Table 3.1. As shown in Table 3.1, every transact
rules. For example, as shown in Table 3.1, the fir
following equation:
Therefore, the groups that perform well will be stored in a transaction if the groups fit Eq. 3.36. If the best fitness value does not improve for a sufficient number of generations (NormalTimes), the DMSS selects the groups according to another action type (which go to the next steps).
Step 3. Find the groups that occur frequently:
If the action is the search or exploration action (the Accumulator exceeds the NormalTimes), the DMSS uses FP-growth to find the groups that occur frequently in transactions. The frequently-occurring groups are found according to the predefined Minimum_Support. Minimum_Support represents the minimum fraction of transactions that contain an item set. After Minimum_Support is defined, data mining using FP-growth will be performed. The FP-growth algorithm can be viewed as having two parts: construction of the FP-tree and FP-growth. The sample
Find the groups that occur frequently:
If the action is the search or exploration action ( action type (which go to the next steps).
action type (which go to the next steps).
), the DMSS selects the groups according to another action type (which go to the next steps).
Find the groups that occur frequently:
action type (which go to the next steps).
Find the groups that occur frequently:
action type (which go to the next steps).
Find the groups that occur frequently:
action type (which go to the next steps).
Find the groups that occur frequently:
Find the groups that occur frequently:
action type (which go to the next steps).
action type (which go to the next steps).
Find the groups that occur frequently:
Find the groups that occur frequently:
action type (which go to the next steps).
action type (which go to the next steps).
action type (which go to the next steps).
action type (which go to the next steps).
Find the groups that occur frequently:
Find the groups that occur frequently:
action type (which go to the next steps).
Find the groups that occur frequently:
represents the set of one group which has support counts bigger than Minimum_Suppor in transactions. The result is shown in Table 3.3. Then the retrieved frequently-occurring groups are ordered by descending order based on their supports, as shown in Table 3.4. The ordered list in Table 3.4 is called the F-list. After the F-list is obtained, the next step is to discard the infrequently-occurring groups and sort the remaining groups in the same order as in the F-list in each transaction. The result is shown in Table 3.5. The ordered transactions are then used to construct the FP-tree. The steps for constructing the FP-tree are illustrated in Fig. 3.12 (a). In Fig. 3.12 (a), formed by scanning the last transaction, the right-most chart is called the prefix-tree of the frequent 1-groupset. Each node of the prefix-tree is composed of one group, a count of the frequent 1-groupset, and a node frequently-occurring group link. Then the complete FP-tree is created by combining the prefix-tree of the 1-groupset and the header-table. An example of an FP-tree is shown in Fig. 3.12 (b). This FP-tree is constructed from the transactions shown in Table 3.2.
(2) FP-growth:
The FP-growth algorithm is done by following steps: construction of a conditional group base, construction of a corresponding conditional FP-tree, mining the frequently-occurring groups on the conditional FP-tree, and concatenation of the suffix group and the frequently-occurring groups on the conditional FP-tree.
First, select each frequent 1-groupset as a suffix group, and find the corresponding set of paths connecting to the root of the FP-tree. The set of prefix paths is called the conditional group base. Then accumulate the count for each group in the base to construct the conditional FP-tree of the corresponding the frequent 1-groupset, and a node frequently-occu
complete FP-tree is created by combining the prefix the header-table. An example of an FP-tree is shown FP-tree is constructed from the transactions shown complete FP-tree is created by combining the prefix complete FP-tree is created by combining the prefix the frequent 1-groupset, and a node frequently-occu complete FP-tree is created by combining the prefix the header-table. An example of an FP-tree is shown complete FP-tree is created by combining the prefix the header-table. An example of an FP-tree is shown complete FP-tree is created by combining the prefix the header-table. An example of an FP-tree is shown complete FP-tree is created by combining the prefix the header-table. An example of an FP-tree is shown the header-table. An example of an FP-tree is shown complete FP-tree is created by combining the prefix complete FP-tree is created by combining the prefix the header-table. An example of an FP-tree is shown the header-table. An example of an FP-tree is shown complete FP-tree is created by combining the prefix complete FP-tree is created by combining the prefix complete FP-tree is created by combining the prefix complete FP-tree is created by combining the prefix the header-table. An example of an FP-tree is shown the header-table. An example of an FP-tree is shown complete FP-tree is created by combining the prefix the header-table. An example of an FP-tree is shown
FP-tree, FP-growth data mining is completed by the concatenation of the suffix group with the generated frequently-occurring groups. The groups generated by the FP-growth, shown in Table 3.6, are then thrown into the pool that is called
FP-tree, FP-growth data mining is completed by the concatenation of the suffix group with the generated frequently-occurring groups. The groups generated by the FP-growth, shown in Table 3.6, are then thrown into the pool that is called