NICGAR: a Niching Genetic Algorithm to Mine a Diverse Set of Interesting Quantitative Association Rules

This Website contains complementary material to the paper:

D. Martín, J. Alcalá-Fdez, A. Rosete and F.Herrera, NICGAR: a Niching Genetic Algorithm to Mine a Diverse Set of Interesting Quantitative Association Rules. Information Sciences 355-356 (2016) 208-228. DOI: 10.1016/j.ins.2016.03.039

Summary:

  1. Flowchart of the algorithm
  2. Experimental Framework
    1. Data-sets used in the paper
    2. Algorithms analyzed
  3. Results obtained
    1. Results obtained in the comparison with other NGAs
    2. Results obtained in the comparison with mono-objective and multi-objective evolutionary approaches
    3. Comparison with classical algorithms

 

 

Flowchart of the algorithm

NICGAR can be summarized as follows:

  • Input: Population size N, number of evaluations nTrials, probability of mutation Pmut, factor of amplitude for each attribute of the dataset ρ, difference threshold α, niching threshold NichMin, quality threshold EvMin.
  • Output: External population (EP)
  1. Initialize
    1. Generate the initial population (Pt) with N chromosomes.
    2. Evaluate the initial population.
  2. Generate the offspring population (Qt) as follows.
    1. Two parent individuals x1 and x2 are selected by binary tournament selection using the fitness function.
    2. Generate two offspring applying the crossover operator on the individuals x1 and x2. Next, the offspring are mutated and repaired using the appropriate operators.
    3. The offspring is evaluated.
    4. If the EP is not empty, the punishment mechanism is applied to each new individual if they belong to a niche from the EP and their fitness is lower than its corresponding solution of the EP.
  3. Join the parents with their offspring and select the best N individuals to take part in the next population (Pt+1).
  4. If the difference between the current population and the previous population is less than α%:
    1. Update the EP, based on the niches from Pt+1.
    2. Restart the population and apply the punishment mechanism to the new individuals that have been created in the restarting process.
  5. If the maximum number of evaluations is not reached, go to Step 2.
  6. Update the EP, based on the niches from the last population.
  7. The EP is returned.

A scheme of this algorithm is shown in the Figure 1.

 

Figure 1. Scheme of the algorithm NICGAR.

Scheme of the algorithm NICGAR

 

Experimental Framework

 

Data-sets used in the paper

Table 1 describes the 27 real-world datasets that have been used in this experimental study, where "Attributes(R/I/N)" is the number of attributes (Real/Integer/Nominal) in the data, "Examples" is the number of examples and "Download" contains a link for downloading each data-set in the KEEL format. You may also download all data-sets by clicking here. Moreover, the datasets are available in the repository KEEL-dataset, where they can be downloaded (available at KEEL-dataset Repository).

 

Table 1: Summary of the datasets considered for the experimental study

Dataset Attributes(R/I/N) Examples Download
Balance Scale 5 (5/0/0) 625 >Balance file
Basketball 5 (3/2/0) 96 Basketball file
Bolts 8 (2/6/0) 40 Bolts file
Coil2000 86 (0/86/0) 9822 Coil2000 file
Fars 29 (5/0/24) 100968 Farsfile
House_16H 17 (10/7/0) 22784 House16H file
Ionosphere 34 (32/1/1) 351 Ionosphere file
Letter 16 (0/16/0) 20000 Letter file
Magic 11(10/0/1) 19020 Magic file
Movement Libras 91 (90/0/1) 360 Movement_libras file
Optdigits 65 (0/65/0) 5620 Optdigits file
Penbased 16 (0/16/0) 10992 Penbased file
Pollution 16 (16/0/0) 60 Pollution file
Quake 4 (3/1/0) 2178 Quake file
Satimage 37 (0/37/0) 6435 Satimage file
Segment 20 (19/1/0) 2310 Segment file
Sonar 61 (60/0/1) 208 Sonar file
Spambase 58 (57/1/0) 4597 Spambase file
Spectfheart 45 (0/45/0) 267 Spectfheart file
Stock Price 10 (10/0/0) 950 Stock file
Stulong 5 (5/0/0) 1419 Stulong file
Texture 41 (40/1/0) 5500 Texture file
Thyroid 22 (6/16/0) 7200 Thyroid file
Vehicle 19 (0/18/1) 846 Vehicle file
Wdbc 31 (30/0/1) 569 Wdbc file
Wine 14 (13/1/0) 178 Wine file
Vowel 14 (10/4/0) 990 Vowel file

 

Algorithms analyzed

In these experiments, we compare the proposed approach with seven other algorithms, which are available from the KEEL software tool. A brief description of these algorithms follows.

  • Clearing: This Niching Genetic Algorithm is one of the most popular niching techniques used in conjunction with the evolutionary computation community. This method is based on limited the resources within subpopulations of similar individuals, where only the best individuals of each niche will survive since the fitness of the rest of them will be reset to zero. This process is applied after evaluation process and before the selection.
  • Adaptive Species Conservation Genetic Algorithm (ASCGA): This algorithm is based on the species conservation approach (SCGA) proposed by Li, it divides the population into several species according to their similarity and each of these species is built around a dominating individual, commonly referred to as a species seed. This method automatically adjust species parameters and allow the species to adapt to an optimization problem.
  • Evolutionary Association Rules Mining with Genetic Algorithm (EARMGA): This algorithm uses a GA to identify QARs. Each chromosome encodes a generalized k-rule, where k indicates the desired length. The most interesting rules are returned according to the interestingness measure defined by the fitness function, which is based on the support of the rule and its antecedent and consequent support. The proposed GA performs a dataset-independent approach that does not rely upon the minSup threshold.
  • GENetic Association Rules(GENAR): This algorithm uses a GA to mine association rules in numeric datasets. Each chromosome encodes an association rule, containing maximum and minimum intervals of each numeric attribute. The length of the rules is always fixed to the number of attributes, only the last attribute forms the consequent. The objective function considers the number of records covered by the rule and penalizes those which have already covered the same records in the dataset.
  • Genetic Association Rules (GAR): This algorithm is an extension of GENAR, which searches for frequent itemsets in numeric datasets without needing to discretize the attributes. Each chromosome is a k-itemset, in which each gene represents the maximum and minimum values of the attributes that belong to the k-itemset. This algorithm finds frequent itemsets, and it is therefore necessary to run another procedure afterwards in order to generate association rules.
  • Genetic algorithm for automated mining of both positive and negative quantitative association rules (Alatasetal): This algorithm designs a GA, which does not require a user-specified the minSup and minConf thresholds, to simultaneously search for intervals of quantitative attributes and to discover PNQARs that these intervals conform to in a single run. The chromosomes represent rules, in which each gene has four parts.
  • QAR-CIP-NSGA-II: This method mines a set of QARs with a good trade-off between interpretability and accuracy, which maximizes three objectives: comprehensibility, interestingness and performance, understanding by performance the product of Certainty Factor (CF) and support. This algorithm extends the well-known MOEA NSGA-II to perform an evolutionary learning of the intervals of the attributes and a condition selection for each rule.
  • MOPNAR: This algorithm extends the MOEA based on decomposition MOEA/D-DE to obtain a reduced set of PNQARs with a good trade-off between the number of rules, support and coverage of the dataset. It performs a condition selection and an evolutionary learning of the intervals of the attributes for each rule, maximizing three objectives: comprehensibility; interestingness and performance.
  • Apriori: Apriori follows a breadth-first strategy. It generates candidate itemsets for the current iteration by means of itemsets considered to be frequent in the previous iteration. It then enumerates all the subsets for each transaction and increments the support of candidates matching them. Then, those that have the user-specified minSup are marked as frequent for the next iteration. This process is repeated until all frequent itemsets have been found. Finally, Apriori uses the frequent itemsets to generate positive rules with confidence greater than minimum confidence.
  • Eclat: Eclat employs a depth-first strategy. It generates candidates by extending the prefixes of an itemset until an infrequent one is found. In such cases, it simply backtracks to the previous prefix and then recursively applies the above procedure. Unlike Apriori, for all the items in a dataset, it first constructs a list of all the transaction identifiers (tid-list) containing that item. Then it counts the support by merely intersecting two or more tid-lists to check whether they have items in common. If so, the support is equal to the size of the resulting set. The process for generating the positive rules is the same as Apriori.

Results obtained

This section is divided into three parts: the first part provides the results of the comparison with two NGAs extended to extract PNQARs. Next, the second part shows the results of the comparison with other mono-objective and multi-objective evolutionary approaches. Finally, in the third part, the performance results of our algorithm again two classical algorithms can be found.

Results obtained in the comparison with other NGAs

In this section, we present the performance results obtained of our algorithm against Clearing and ASCGA. Table 2 shows the average results obtained of 5 runs for each dataset.

Moreover, this performance results are available for download in xls, pdf and tex files by clicking the links iconExcel.jpg, PDF Icon and iconZip.png, respectively.

Table 2: Results for all datasets in the comparison with NGAs
Algorithm  #R  AvSup(s)  AvConf(s)  AvLift (s)  AvConv  AvCF (s)  AvNetconf(s)  AvYulesQ (s)  AvAmp (s)  AvDiv (s) %Trans (s)
 Balance
Clearing   24.20   0.08 (0.05)   0.82 (0.10)   2.74 (1.15)   8   0.68 (0.21)   0.49 (0.18)   0.73 (0.17)   3.47 (0.94)   0.73 (0.04)   89.48 (10.20) 
  ASCGA   21.20  0.09 (0.03)   0.73 (0.05)   2.30 (0.44)    8    0.54 (0.07)   0.39 (0.08)   0.62 (0.09)  3.34 (0.24)   0.74 (0.05)   75.01 (21.02) 
  NICGAR  26.40  0.06 (0.02)  0.92 (0.03)  4.25 (0.44)    8   0.86 (0.04)  0.69 (0.03)  0.91 (0.02)   3.81 (0.18)  0.82 (0.02)  89.96 (2.19) 
 Basketball
Clearing  57.00   0.03 (0.01)   0.98 (0.02)   32.87 (9.48)   8   0.97 (0.03)  0.91 (0.03)  0.99 (0.01)  2 (0.01)  0.99 (0.00)   84.17 (8.12) 
  ASCGA   10.00  0.09 (0.07)   0.97 (0.03)   14.81 (11.66)    8    0.94 (0.05)   0.83 (0.07)   0.98 (0.02)   2.04 (0.05)   0.81 (0.16)   35.84 (9.84) 
  NICGAR   49.80   0.04 (0.01)  0.99 (0.01)   9.43 (2.53)    8   0.98 (0.02)   0.80 (0.04)  0.99 (0.01)   2.15 (0.09)   0.95 (0.01)  91.67 (4.04) 
Bolts
Clearing  21.80  0.13 (0.07)   0.96 (0.04)   9.50 (4.16)   8   0.94 (0.05)   0.84 (0.05)   0.98 (0.02)   2.06 (0.10)  0.87 (0.06)   99.00 (1.37) 
  ASCGA   15.60   0.18 (0.04)   0.96 (0.03)   4.91 (2.43)    8    0.93 (0.05)   0.82 (0.06)   0.97 (0.03)   2.42 (0.29)   0.74 (0.10)   89.00 (16.73) 
  NICGAR   9.80  0.30 (0.04)  0.98 (0.02)   5.51 (1.66)    8    0.98 (0.02)  0.93 (0.03)  1 (0.00)  2 (0.00)   0.82 (0.02)  100.00 (0.00) 
   Coil2000
Clearing   18.60   0.23 (0.10)   0.80 (0.06)  5.93 (5.20)   8   0.69 (0.08)   0.63 (0.05)   0.85 (0.06)   2.08 (0.12)   0.75 (0.04)    99.81 (0.36) 
  ASCGA  29.00  0.22 (0.07)   0.63 (0.02)   4.21 (5.46)    8    0.38 (0.05)   0.32 (0.05)   0.54 (0.04)   2.71 (0.26)   0.81 (0.03)    99.62 (0.82) 
  NICGAR   25.40  0.28 (0.03)  0.93 (0.02)   3.65 (0.51)    8   0.89 (0.03)  0.86 (0.03)  0.98 (0.01)  2.04 (0.04)  0.82 (0.03)   99.96 (0.10) 
  Fars
Clearing   21.60   0.30 (0.07)   0.93 (0.02)  12.92 (16.92)   8   0.87 (0.04)   0.85 (0.04)   0.93 (0.05)   2.20 (0.04)   0.68 (0.04)   92.87 (15.06) 
  ASCGA  22.60   0.22 (0.05)   0.78 (0.09)   8.11 (8.17)    8    0.61 (0.12)   0.56 (0.11)   0.71 (0.14)   2.51 (0.21)   0.79 (0.02)   99.48 (1.17) 
  NICGAR   12.60  0.31 (0.05)  0.99 (0.00)   5.67 (0.58)    8   0.99 (0.01)   0.98 (0.02)  1 (0.00)  2.02 (0.04)   0.81 (0.04)  100.00 (0.00) 
  House16H
 Clearing  24.60   0.09 (0.06)   0.81 (0.05)   13.12 (8.20)   8   0.74 (0.04)   0.69 (0.06)   0.55 (0.22)   2.09 (0.07)   0.72 (0.09)   83.41 (21.75) 
  ASCGA   11.60   0.14 (0.06)   0.75 (0.13)  14.42 (24.64)    8    0.63 (0.19)   0.57 (0.20)   0.70 (0.07)   2.27 (0.31)   0.70 (0.08)   68.69 (16.64) 
  NICGAR   6.00   0.24 (0.04)  0.92 (0.00)   3.67 (0.71)   15.00  0.88 (0.01)   0.83 (0.01)  0.98 (0.00)   2 (0.00)   0.86 (0.02)   82.18 (13.91) 
 Ionosphere
Clearing  41.00  0.07 (0.02)   0.94 (0.02)  55.85 (25.71)   8   0.91 (0.03)  0.86 (0.05)   0.98 (0.01)  2.01 (0.02)  0.92 (0.03)   92.03 (4.34) 
  ASCGA   13.00   0.18 (0.04)   0.78 (0.07)   3.13 (0.64)    8    0.67 (0.11)   0.59 (0.09)   0.88 (0.08)   2.43 (0.13)   0.82 (0.07)   82.51 (17.39) 
  NICGAR   24.80  0.20 (0.02)   0.85 (0.01)   3.77 (0.59)    8    0.78 (0.02)   0.74 (0.02)   0.96 (0.00)  2.01 (0.02)   0.88 (0.01)   99.83 (0.15) 
  Letter
Clearing   17.40   0.16 (0.03)   0.87 (0.03)  7.28 (1.87)   8   0.77 (0.03)   0.72 (0.05)   0.93 (0.01)   2.11 (0.08)   0.81 (0.04)  98.26 (1.59)
  ASCGA   15.00  0.18 (0.09)   0.74 (0.06)   4.61 (0.76)    8    0.59 (0.08)   0.57 (0.09)   0.82 (0.07)   2.40 (0.25)   0.76 (0.07)   85.47 (24.98) 
  NICGAR  18.80   0.15 (0.02)  0.89 (0.02)   5.94 (1.31)    8   0.84 (0.03)  0.76 (0.04)  0.96 (0.01)  2.01 (0.02)  0.87 (0.01)   98.17 (1.62) 
Magic
Clearing  9.80  0.34 (0.18)   0.93 (0.01)   2.81 (0.64)   10.38   0.79 (0.24)  0.85 (0.03)  0.99 (0.01)   2.01 (0.02)   0.77 (0.16)  99.55 (0.32) 
  ASCGA   9.20   0.22 (0.09)   0.89 (0.06)   2.88 (0.35)   14.25   0.82 (0.08)   0.72 (0.05)   0.92 (0.07)   2.02 (0.05)   0.57 (0.18)   69.57 (15.76)
  NICGAR   6.60   0.26 (0.01)  0.94 (0.01)  3.00 (0.06)   15.30   0.91 (0.02)  0.85 (0.01)  0.99 (0.01)  2 (0.00)  0.85 (0.01)   94.87 (4.93) 
Movement Libras
Clearing   23.60   0.24 (0.01)   0.94 (0.03)  5.11 (2.50)   8   0.90 (0.04)   0.88 (0.04)   0.98 (0.02)  2 (0.00)  0.87 (0.01)    99.95 (0.12) 
  ASCGA   20.80   0.21 (0.06)   0.82 (0.11)   2.81 (0.65)    8    0.70 (0.18)   0.63 (0.21)   0.83 (0.15)   2.57 (0.51)   0.84 (0.05)   94.73 (11.34) 
  NICGAR  27.80 0.27 (0.01)   0.98 (0.00)   3.64 (0.05)    8   0.97 (0.01)  0.95 (0.01)  1.00 (0.00)  2 (0.00)   0.86 (0.00)  100.00 (0.00) 
Optdigits
Clearing   17.80   0.22 (0.12)   0.84 (0.06)  5.05 (3.47)   8   0.69 (0.14)   0.65 (0.07)   0.84 (0.05)   2.07 (0.16)   0.76 (0.07)   96.82 (4.63) 
  ASCGA   23.80   0.23 (0.07)   0.67 (0.04)   2.07 (0.55)    8    0.40 (0.08)   0.37 (0.04)   0.60 (0.07)   2.44 (0.14)   0.80 (0.03)   98.99 (1.06) 
  NICGAR  28.80 0.28 (0.02)   0.87 (0.02)   3.24 (0.40)    8   0.75 (0.05)   0.71 (0.01)  0.95 (0.01)  2.05 (0.04)  0.82 (0.02)  100.00 (0.00)
Penbased
Clearing   16.80   0.15 (0.04)   0.82 (0.05)   4.22 (2.14)   8   0.73 (0.08)   0.63 (0.08)   0.87 (0.05)  2.06 (0.06)   0.84 (0.02)   98.08 (1.10) 
  ASCGA  19.80   0.22 (0.04)   0.76 (0.02)   2.20 (0.31)    8    0.60 (0.05)   0.53 (0.04)   0.82 (0.05)   2.12 (0.06)   0.66 (0.20)   94.04 (6.20) 
  NICGAR   15.00   0.18 (0.02)   0.89 (0.01)   3.64 (0.77)    8    0.83 (0.02)   0.73 (0.03)  0.95 (0.01)  2.06 (0.10)  0.88 (0.02)  98.64 (0.92) 
Pollution
Clearing   48.60   0.05 (0.01)   0.98 (0.03)   18.68 (3.55)   8  0.97 (0.04)   0.90 (0.04)   0.99 (0.03)   2.01 (0.02)   0.96 (0.01)   90.34 (8.53) 
  ASCGA   13.00  0.13 (0.07)   0.95 (0.05)   9.54 (3.87)    8    0.92 (0.06)   0.83 (0.06)   0.98 (0.03)   2.16 (0.23)   0.85 (0.10)   72.67 (22.69) 
  NICGAR   57.80  0.08 (0.01)   0.98 (0.01)   8.35 (1.33)    8   0.97 (0.01)   0.84 (0.02)   1.00 (0.00)   2.07 (0.05)   0.93 (0.01)   100.00 (0.00) 
Quake
Clearing   33.20  0.03 (0.03)   0.86 (0.08)   38.81 (28.61)   8  0.84 (0.09)  0.76 (0.11)   0.84 (0.13)  2 (0.00)  0.88 (0.06)   75.42 (14.14) 
  ASCGA   4.60   0.28 (0.13)   0.84 (0.06)   3.39 (2.64)   5.64   0.72 (0.12)   0.66 (0.07)   0.87 (0.08)   2.08 (0.18)   0.62 (0.12)   72.51 (25.18) 
  NICGAR   3.60   0.28 (0.05)   0.90 (0.01)   2.51 (0.80)   11.40   0.81 (0.02)   0.72 (0.02)   0.95 (0.01)  2 (0.00)   0.75 (0.03)   83.15 (1.70) 
 Satimage
 Clearing   15.20   0.25 (0.03)  0.92 (0.02)   5.00 (3.32)   8   0.86 (0.03)   0.80 (0.03)   0.98 (0.01)   2.01 (0.03)  0.82 (0.01)   96.34 (6.91) 
  ASCGA   30.60  0.37 (0.04)   0.83 (0.05)   2.69 (0.10)    8    0.66 (0.05)   0.66 (0.06)   0.93 (0.01)   2.39 (0.15)   0.71 (0.02)  100.00 (0.00) 
  NICGAR   24.00   0.24 (0.01)  0.92 (0.01)   3.83 (0.31)   12.27  0.88 (0.01)  0.85 (0.01)  0.99 (0.00)  2 (0.00)  0.82 (0.01)   93.94 (2.29) 
Segment
Clearing   11.80   0.20 (0.01)   0.93 (0.05)   4.41 (0.80)   8   0.91 (0.07)   0.88 (0.08)   0.94 (0.09)   2.02 (0.04)   0.86 (0.03)   98.09 (3.04) 
  ASCGA  16.00  0.25 (0.06)   0.86 (0.05)   3.38 (0.69)    8    0.79 (0.05)   0.74 (0.10)   0.88 (0.08)   2.25 (0.18)   0.77 (0.05)   98.76 (1.42) 
  NICGAR   12.60   0.22 (0.01)   0.99 (0.01)   4.91 (0.43)    8    0.98 (0.01)   0.97 (0.01)   1.00 (0.00)  2 (0.00)  0.88 (0.01)   99.76 (0.26) 
   Sonar
Clearing   51.40   0.06 (0.03)   0.96 (0.02)   57.68 (14.37)   8   0.93 (0.03)   0.91 (0.03)   0.99 (0.01)  2 (0.00)  0.94 (0.03)   87.02 (22.84) \\
  ASCGA   18.20   0.20 (0.06)   0.77 (0.11)   4.12 (2.92)    8    0.58 (0.19)   0.51 (0.18)   0.74 (0.17)   2.57 (0.43)   0.85 (0.04)   95.48 (6.32) \\
  NICGAR   22.80   0.26 (0.03)   0.89 (0.02)   7.56 (5.59)    8    0.81 (0.02)   0.77 (0.02)   0.97 (0.01)   2.01 (0.02)   0.84 (0.02)  100.00 (0.00) 
Spambase
 Clearing   32.40  0.09 (0.12)   0.89 (0.05)  115.83 (93.33)   8   0.83 (0.09)   0.81 (0.10)   0.88 (0.09)   2.03 (0.04)  0.84 (0.14)   85.01 (23.67) 
  ASCGA   20.20   0.19 (0.03)   0.75 (0.06)   20.22 (20.15)    8    0.59 (0.04)   0.45 (0.10)   0.72 (0.08)   2.72 (0.33)   0.78 (0.04)  95.85 (6.84) 
  NICGAR   11.20   0.12 (0.02)   0.95 (0.02)   73.02 (28.16)    8    0.90 (0.03)   0.87 (0.04)  0.98 (0.01)  2 (0.00)   0.84 (0.05)   76.75 (31.96) 
Spectfheart
Clearing   39.00   0.12 (0.08)   0.97 (0.02)   61.20 (11.76)   8   0.91 (0.06)  0.94 (0.03)   0.99 (0.01)  2.01 (0.01)   0.86 (0.06)   86.22 (30.82) 
  ASCGA   12.60  0.37 (0.10)   0.89 (0.03)   18.04 (10.86)    8    0.68 (0.10)   0.80 (0.07)   0.95 (0.03)   2.17 (0.19)   0.71 (0.11)   99.25 (1.09) 
  NICGAR  72.20   0.13 (0.01)   0.98 (0.00)   29.01 (4.73)    8    0.92 (0.00)   0.92 (0.02)   1.00 (0.00)   2.03 (0.05)  0.89 (0.02)  100.00 (0.00) 
Stock
Clearing  14.60   0.21 (0.07)   0.91 (0.05)   16.56 (18.61)   8   0.86 (0.07)   0.78 (0.04)   0.96 (0.04)  2.06 (0.10)   0.84 (0.05)  99.41 (0.98) 
  ASCGA   8.00   0.28}(0.09)   0.90 (0.06)   2.70 (0.46)    8    0.85 (0.09)   0.79 (0.11)   0.95 (0.05)   2.18 (0.24)   0.70 (0.13)   81.04 (11.23) 
  NICGAR   9.20   0.28}(0.02)  0.95 (0.01)   3.01 (0.18)    8   0.93 (0.02)   0.87 (0.01)  0.99 (0.00)   2.07 (0.07)  0.86 (0.02)   99.41 (0.23) 
Stulong
Clearing   10.60  0.23 (0.12)   0.87 (0.02)  29.51 (43.04)   8   0.68 (0.10)  0.75 (0.11)   0.94 (0.04)   2.10 (0.14)   0.72 (0.10)   97.20 (1.52) 
  ASCGA   7.40   0.16 (0.03)   0.79 (0.01)   9.08 (7.99)   3.44   0.71 (0.02)   0.65 (0.01)   0.92 (0.01)  2 (0.00)   0.45 (0.05)   44.93 (23.77) 
  NICGAR   4.20   0.26 (0.07)   0.79 (0.03)   16.82 (19.90)    8    0.62 (0.08)   0.64 (0.06)   0.90 (0.03)   2.04 (0.09)  0.78 (0.06)   84.99 (7.01) 
Texture
Clearing   15.20   0.29 (0.04)   0.93 (0.02)   3.14 (0.32)   19.47   0.89 (0.03)   0.86 (0.04)   0.98 (0.02)   2.01 (0.03)   0.83 (0.02)   97.26 (5.77) 
  ASCGA   16.40   0.29 (0.04)   0.90 (0.04)    35.96 (56.31)   8   0.81 (0.07)   0.75 (0.06)   0.93 (0.06)   2.37 (0.28)   0.76 (0.09)   98.23 (2.05) 
  NICGAR   17.40   0.27 (0.02)   0.97 (0.00)   3.72 (0.39)    8    0.95 (0.00)   0.92 (0.01)   1.00 (0.00)  2 (0.00)   0.82 (0.02)   95.85 (4.66) 
Thyroid
Clearing   27.00   0.11 (0.16)   0.87 (0.08)   16.05 (9.81)   8   0.76 (0.21)   0.77 (0.08)   0.81 (0.10)   2.48 (0.38)   0.73 (0.12)   72.81 (40.62) 
  ASCGA   20.20   0.17 (0.07)   0.74 (0.06)   6.14 (4.15)    8    0.53 (0.11)   0.38 (0.16)   0.56 (0.16)   2.64 (0.43)   0.71 (0.09)   88.64 (13.24) 
  NICGAR   6.20   0.23 (0.07)   0.93 (0.02)   14.29 (9.46)    8    0.80 (0.07)   0.85 (0.02)   0.95 (0.05)   2.02 (0.05)   0.79 (0.05)   98.16 (2.30) 
 Wdbc
Clearing   18.80  0.19 (0.05)   0.92 (0.04)   48.87 (36.99)   8   0.88 (0.06)   0.84 (0.07)   0.97 (0.03)  2 (0.00)   0.86 (0.01)     99.51 (0.62) 
  ASCGA   13.80   0.26 (0.04)   0.81 (0.08)   3.18 (1.52)    8    0.68 (0.14)   0.62 (0.17)   0.81 (0.13)   2.37 (0.35)   0.78 (0.10)   97.62 (2.44) 
  NICGAR   13.60   0.27 (0.03)   0.96 (0.02)   3.49 (0.39)    8    0.93 (0.04)   0.90 (0.03)   0.99 (0.01)  2 (0.00)   0.84 (0.01)   98.53 (2.10) 
Vehicle
Clearing   13.00   0.26 (0.05)   0.96 (0.02)  5.21 (3.69)   8   0.93 (0.04)   0.89 (0.04)   0.97 (0.04)  2 (0.00)   0.84 (0.03)    99.95 (0.10) 
  ASCGA   13.80   0.25 (0.03)   0.92 (0.05)   3.35 (0.57)    8    0.87 (0.07)   0.84 (0.08)   0.96 (0.04)   2.08 (0.08)   0.76 (0.05)   96.86 (2.81) 
  NICGAR   12.80  0.27 (0.03)   0.97 (0.01)   3.46 (0.26)    8    0.95 (0.02)  0.92 (0.01)   1.00 (0.00)  2 (0.00)  0.86 (0.02)    99.98 (0.05) 
Wine
Clearing  23.20   0.14 (0.10)   0.94 (0.07)   19.43 (18.27)   8  0.91 (0.09)   0.83 (0.11)   0.97 (0.05)   2.02 (0.03)   0.92 (0.09)   93.49 (7.39) 
  ASCGA   8.40   0.25 (0.04)   0.88 (0.06)   3.70 (2.98)    8    0.79 (0.11)   0.73 (0.11)   0.92 (0.07)   2.17 (0.25)   0.78 (0.07)   83.71 (21.15) 
  NICGAR   6.60   0.28 (0.01)   0.94 (0.01)   2.79 (0.18)    8    0.90 (0.02)   0.84 (0.02)  0.99 (0.01)  2 (0.00)   0.86 (0.00)  94.61 (0.85) 
   Vowel
Clearing   51.60  0.23 (0.40)   0.96 (0.02)   92.68 (69.98)   8   0.78 (0.33)   0.91 (0.04)   0.50 (0.15)   2.02 (0.02)   0.81 (0.21)   92.10 (8.89) 
  ASCGA   15.40   0.19 (0.07)   0.79 (0.07)   4.41 (3.00)    8    0.68 (0.12)   0.59 (0.12)   0.81 (0.11)   2.40 (0.22)   0.77 (0.08)   92.89 (12.00) 
  NICGAR   8.40   0.27 (0.11)   0.95 (0.05)   5.81 (2.57)    8   0.92 (0.07)   0.89 (0.08)    0.95 (0.09)   2.02 (0.05)  0.85 (0.01)  100.00 (0.00) 

Results obtained in the comparison with mono-objective and multi-objective evolutionary approaches

In this section, we present the results obtained by our algorithm against four mono-objective evolutionary algorithms (EARMGA, GAR, GENAR and Alatasetal) and two multi-objective evolutionary algorithms (QAR-CIP-NSGA-II and MOPNAR). Table 3 and Table 4 show the average results obtained by the mono-objectives and the multi-objectives evolutionary approaches of 5 runs for each dataset, respectively.

Moreover, this performance results are available for download in xls, pdf and tex files. To download the results obtained by the mono-objective evolutionary algoritmhs, click the links by clicking the links iconExcel.jpg, PDF Icon and iconZip.png and for the ones obtained by the multi-objective evolutionary algorithms, click the links iconExcel.jpg, PDF Icon and iconZip.png.

Table 3: Results for all datasets in the comparison with mono-objective evolutionary approaches
Algorithm #R AvSup (σ) AvConf (σ) AvLift (σ) AvConv AvCF (σ) AvNetconf (σ) AvYulesQ (σ) AvAmp (σ) AvDiv (σ) %Trans (σ)
Balance
EARMGA 100 0.5 (0.04) 1 (0) 1 (0) 1 0 (0) 0 (0) 0 (0) 2 (0) 0.46 (0.02) 100 (0)
  GENAR 30 0.13 (0) 0.94 (0.01) 2.04 (0.02) 31.04 0.89 (0.01) 0.55 (0.01) 0.92 (0.01) 5 (0) 0.6 (0.01) 85.64 (0.96)
  GAR 0 -    -    -    - -    -    -    -    -    -   
  Alatasetal 24.4 0.31 (0.07) 1 (0) 1.1 (0.12) 0.06 (0.05) 0.03 (0.02) 0.05 (0.05) 4.35 (0.49) 0.48 (0.04) 100 (0)
  NICGAR 26.4 0.06 (0.02) 0.92 (0.03) 4.25 (0.44) 0.86 (0.04) 0.69 (0.03) 0.91 (0.02) 3.81 (0.18) 0.82 (0.02) 89.96 (2.19)
Basketball
EARMGA 100 0.27 (0.04) 1 (0) 1.02 (0.02) 0.06 (0.08) 0.01 (0.01) 0.05 (0.05) 2 (0) 0.55 (0.02) 100 (0)
  GENAR 30 0.3 (0.01) 0.97 (0.01) 1.12 (0.01) 0.7 (0.03) 0.13 (0) 0.67 (0.03) 5 (0) 0.3 (0.02) 91.04 (2.81)
  GAR 2 0.75 (0.01) 0.88 (0) 1.02 (0) 1.12 0.11 (0.01) 0.11 (0.01) 0.36 (0.04) 2 (0) 0 (0) 96.88 (0)
  Alatasetal 8.6 0.98 (0.01) 1 (0) 1 (0) 1 -0.01 (0.01) -0.01 (0.01) 0 (0) 3.2 (0.09) 0.09 (0.09) 100 (0)
  NICGAR 49.8 0.04 (0.01) 0.99 (0.01) 9.43 (2.53) 0.98 (0.02) 0.8 (0.04) 0.99 (0.01) 2.15 (0.09) 0.95 (0.01) 91.67 (4.04)
Bolts
EARMGA 100 0.34 (0.07) 1 (0) 1.05 (0.05) 0.15 (0.16) 0.03 (0.04) 0.15 (0.16) 2 (0) 0.57 (0.04) 100 (0)
  GENAR 30 0.13 (0) 1 (0) 1.62 (0.07) 1 (0) 0.42 (0.01) 1 (0) 8 (0) 0.27 (0.05) 44 (5.48)
  GAR 43 0.21 (0.03) 0.99 (0.01) 4.14 (0.3) 0.97 (0.01) 0.88 (0.03) 1 (0.01) 3.31 (0.51) 0.44 (0.07) 81.5 (18.08)
  Alatasetal 21 0.95 (0.09) 1 (0) 1.04 (0.08) 0.14 (0.31) 0.14 (0.31) 0.14 (0.31) 3.64 (0.43) 0.02 (0.02) 95 (8.66)
  NICGAR 9.8 0.3 (0.04) 0.98 (0.02) 5.51 (1.66) 0.98 (0.02) 0.93 (0.03) 1 (0) 2 (0) 0.82 (0.02) 100 (0)
Coil2000
EARMGA 77 0.42 (0.17) 1 (0) 1.01 (0) 0.05 (0.04) 0.01 (0) 0 (0) 2 (0) 0.55 (0.09) 100 (0)
  GENAR 30 0.01 (0) 0.96 (0) 1.02 (0.01) 0.34 (0.04) 0.02 (0) 0.01 (0.01) 86 (0) 0.53 (0) 14.48 (0.6)
  GAR 197 0.94 (0.01) 0.97 (0.01) 1.01 (0) 0.04 (0.01) 0.03 (0.01) 0.08 (0.04) 2.08 (0.03) 0.37 (0.02) 100 (0)
  Alatasetal 0 -    -    -    -    -    -    -    -    -   
  NICGAR 25.4 0.28 (0.03) 0.93 (0.02) 3.65 (0.51) 0.89 (0.03) 0.86 (0.03) 0.98 (0.01) 2.04 (0.04) 0.82 (0.03) 99.96 (0.1)
Fars
EARMGA 86.40 0.23 (0.05) 1 (0) 1.01 (0) 0.03 (0.06) 0.00 (0.00) 0.01 (0.01) 2 (0) 0.67 (0.03)   99.89 (0.25)   
  GAR 202.60    0.86   (0.00) 0.95 (0.00) 1.05 (0.01) 0.34 (0.04) 0.32 (0.04) 0.35 (0.05) 2.07 (0.03) 0.31 (0.02) 100 (0)
  GENAR 24.20 0.01 (0.00) 0.87 (0.00) 4.38 (0.01) 10.01 0.84 (0.00) 0.67 (0.01) 0.83 (0.06) 30.00 (0.00) 0.44 (0.01) 1.84 (0.15)   
  Alatasetal 61.33 0.13 (0.20) 1 (0) 2.67 (2.75) 0.91 (0.16) 0.20 (0.22) 0.32 (0.09) 8.42 (2.24) 0.39 (0.13) 39.68 (47.05)   
  NICGAR 12.60 0.31 (0.05) 0.99 (0.00)   5.67   (0.58) 0.99   (0.01) 0.98   (0.02) 1 (0) 2.02 (0.04) 0.81   (0.04) 100 (0)
House16
EARMGA 75.6 0.3 (0.1) 1 (0) 1 (0.01) 0.05 (0.08) 0 (0.01) 0 (0) 2.2 (0.45) 0.54 (0.09) 99.95 (0.12)
  GENAR 30 0.45 (0) 1 (0.01) 1.01 (0) 2.56 0.52 (0.02) 0.02 (0) 0.5 (0.02) 17 (0) 0.14 (0.01) 86.94 (0.32)
  GAR 112.8 0.77 (0.01) 0.9 (0) 1.03 (0) 1.33 0.2 (0) 0.17 (0.01) 0.49 (0.02) 2.01 (0.01) 0.28 (0.02) 99.98 (0.01)
  Alatasetal 91 0.19 (0.01) 0.99 (0.01) 1.03 (0.02) 0.58 (0.16) 0.03 (0.01) 0.41 (0.15) 8.75 (1.39) 0.51 (0.03) 98.24 (1.18)
  NICGAR 6 0.24 (0.04) 0.92 (0) 3.67 (0.71) 15 0.88 (0.01) 0.83 (0.01) 0.98 (0) 2 (0) 0.86 (0.02) 82.18 (13.91)
Ionosphere
EARMGA 100 0.4 (0.1) 1 (0) 1 (0) 1 0 (0) 0 (0) 0 (0) 2 (0) 0.59 (0.06) 100 (0)
  GENAR 30 0.3 (0) 0.99 (0) 1.55 (0.01) 0.97 (0) 0.5 (0) 0.98 (0) 34 (0) 0.04 (0) 34.99 (0.42)
  GAR 37.6 0.21 (0.01) 0.92 (0.01) 1.68 (0.04) 0.81 (0.02) 0.44 (0.01) 0.84 (0.01) 2 (0) 0.44 (0.04) 81.26 (1.5)
  Alatasetal 96 0.79 (0.02) 1 (0.01) 1.01 (0.5) 0.43 (0.02) 0.03 (0.02) 0.49 (0.01) 9.69 (0.02) 0.05 (0.06) 99.44 (1.4)
  NICGAR 24.8 0.2 (0.02) 0.85 (0.01) 3.77 (0.59) 0.78 (0.02) 0.74 (0.02) 0.96 (0) 2.01 (0.02) 0.88 (0.01) 99.83 (0.15)
Letter
EARMGA 100 0.36 (0.07) 1 (0) 1 (0) 0 (0.01) 0 (0) 0 (0.01) 2 (0) 0.6 (0.03) 100 (0)
  GENAR 30 0.02 (0) 0.27 (0.03) 6.9 (0.66) 1.92 0.24 (0.03) 0.25 (0.03) 0.82 (0.02) 17 (0) 0.63 (0.01) 72.76 (1.23)
  GAR 13.4 0.6 (0.05) 0.85 (0.01) 1.15 (0.04) 1.55 0.29 (0.06) 0.25 (0.05) 0.49 (0.06) 2 (0) 0.37 (0.12) 99.95 (0.06)
  Alatasetal 35.33 0.21 (0.18) 0.99 (0.01) 4.93 (6.73) 0.76 (0.22) 0.22 (0.28) 0.36 (0.3) 7 (2.66) 0.42 (0.19) 54.28 (46.04)
  NICGAR 18.8 0.15 (0.02) 0.89 (0.02) 5.94 (1.31) 0.84 (0.03) 0.76 (0.04) 0.96 (0.01) 2.01 (0.02) 0.87 (0.01) 98.17 (1.62)
Magic
EARMGA 96 0.33 (0.09) 1 (0) 1 (0) 0.01 (0.02) 0 (0) 0 (0.01) 2 (0) 0.58 (0.06) 100 (0)
  GENAR 30 0.43 (0) 0.81 (0) 1.25 (0) 1.85 0.46 (0) 0.34 (0) 0.66 (0) 11 (0) 0.04 (0) 62.81 (0.76)
  GAR 64.2 0.67 (0.01) 0.91 (0.01) 1.11 (0.01) 2.32 0.49 (0.02) 0.35 (0.02) 0.74 (0.02) 2.11 (0.06) 0.18 (0.02) 97.47 (0.93)
  Alatasetal 11 0.47 (0.09) 1 (0.01) 1.26 (0.06) 956.59 0.88 (0.02) 0.34 (0.02) 0.91 (0.02) 4.73 (0.06) 0.05 (0.06) 89.9 (0.9)
  NICGAR 6.6 0.26 (0.01) 0.94 (0.01) 3 (0.06) 15.3 0.91 (0.02) 0.85 (0.01) 0.99 (0.01) 2 (0) 0.85 (0.01) 94.87 (4.93)
Movement Libras
EARMGA 100 0.4 (0.03) 1 (0) 1 (0) 1 0 (0) 0 (0) 0 (0) 2 (0) 0.62 (0.03) 100 (0)
  GENAR 30 0.03 (0) 0.91 (0.01) 13.5 (0.1) 0.9 (0.01) 0.87 (0.01) 0.99 (0) 91 (0) 0.68 (0.01) 55.23 (1.34)
  GAR 3 0.31 (0.2) 0.89 (0.03) 3.69 (1.93) 6.52 0.83 (0.03) 0.83 (0.03) 0.99 (0.01) 2 (0) 0.29 (0.33) 49.31 (23.1)
  Alatasetal 0 -    -    -    - -    -    -    -    -    -   
  NICGAR 27.8 0.27 (0.01) 0.98 (0) 3.64 (0.05) 0.97 (0.01) 0.95 (0.01) 1 (0) 2 (0) 0.86 (0) 100 (0)
Optdigits
EARMGA 97.8 0.41 (0.17) 1 (0) 1 (0.01) 0.03 (0.04) 0 (0.01) 0 (0.01) 2 (0) 0.59 (0.08) 100 (0)
  GENAR 17 0.01 (0) 1 (0) 10.1 (0.01) 1 (0) 0.91 (0) 0.89 (0.04) 63 (0) 0.56 (0.01) 2.11 (0.34)
  GAR 63.6 0.71 (0.02) 0.97 (0) 1.02 (0.02) 0.17 (0.03) 0.04 (0.03) 0.1 (0.08) 2.01 (0.03) 0.49 (0.01) 100 (0)
  Alatasetal 0 -    -    -    - -    -    -    -    -    -   
  NICGAR 28.8 0.28 (0.02) 0.87 (0.02) 3.24 (0.4) 0.75 (0.05) 0.71 (0.01) 0.95 (0.01) 2.05 (0.04) 0.82 (0.02) 100 (0)
Penbased
EARMGA 100 0.42 (0.12) 1 (0) 1 (0) 1 0 (0) 0 (0) 0 (0) 2 (0) 0.58 (0.06) 100 (0)
  GENAR 30 0.05 (0) 0.96 (0.01) 9.56 (0.13) 0.96 (0.01) 0.91 (0.01) 1 (0) 17 (0) 0.62 (0.02) 46.29 (1.2)
  GAR 2 0.72 (0) 0.87 (0) 1.04 (0) 1.22 0.18 (0) 0.18 (0) 0.48 (0) 2 (0) 0 (0) 94.95 (0)
  Alatasetal 0 -    -    -    - -    -    -    -    -    -   
  NICGAR 15 0.18 (0.02) 0.89 (0.01) 3.64 (0.77) 0.83 (0.02) 0.73 (0.03) 0.95 (0.01) 2.06 (0.1) 0.88 (0.02) 98.64 (0.92)
  Pollution
EARMGA 100 0.21 (0.09) 1 (0) 1.08 (0.06) 0.16 (0.12) 0.03 (0.02) 0.14 (0.1) 2 (0) 0.7 (0.05) 100 (0)
  GENAR 30 0.23 (0.01) 1 (0) 1.23 (0.01) 0.99 (0.01) 0.24 (0.01) 0.98 (0.02) 16 (0) 0.15 (0.02) 47.33 (5.22)
  GAR 61.4 0.67 (0.03) 0.92 (0.01) 1.17 (0.02) 0.56 (0.05) 0.46 (0.05) 0.78 (0.05) 2 (0) 0.19 (0.02) 100 (0)
  Alatasetal 15.4 0.59 (0.52) 1 (0) 6.86 (8.43) 0.43 (0.52) 0.39 (0.51) 0.43 (0.52) 3.32 (0.94) 0.01 (0.01) 59.67 (52.98)
  NICGAR 57.8 0.08 (0.01) 0.98 (0.01) 8.35 (1.33) 0.97 (0.01) 0.84 (0.02) 1 (0) 2.07 (0.05) 0.93 (0.01) 100 (0)
Quake
EARMGA 100 0.3 (0.04) 1 (0) 1 (0) 1 0 (0) 0 (0) 0 (0) 2 (0) 0.45 (0.03) 100 (0)
  GENAR 30 0.55 (0) 0.95 (0) 1.01 (0) 1.09 0.09 (0.01) 0.01 (0.01) 0.1 (0) 4 (0) 0.07 (0.01) 81.89 (0.06)
  GAR 1 0.45 (0.02) 0.85 (0.02) 0.99 (0) 0.91 -0.02 (0) -0.03 (0.01) -0.13 (0.07) 2 (0) 0 (0) 53.26 (1.13)
  Alatasetal 4.25 0.67 (0.18) 1 (0.01) 1.01 (0.01) 0.1 (0.11) 0 (0.01) 0 (0.08) 2.08 (0.17) 0.2 (0.19) 98.06 (3.39)
  NICGAR 3.6 0.28 (0.05) 0.9 (0.01) 2.51 (0.8) 11.4 0.81 (0.02) 0.72 (0.02) 0.95 (0.01) 2 (0) 0.75 (0.03) 83.15 (1.7)
   Satimage
EARMGA 88.8 0.38 (0.1) 1 (0) 1 (0.01) 0.01 (0.02) 0 (0.01) 0 (0) 2 (0) 0.56 (0.03) 100 (0)
  GENAR 30 0.22 (0) 0.31 (0.01) 1.42 (0.09) 0.1 (0.01) 0.3 (0.01) 0.97 (0.01) 37 (0) 0.25 (0.03) 99.98 (0.03)
  GAR 206.6 0.91 (0.01) 0.97 (0) 1.04 (0.01) 2.22 0.39 (0.02) 0.37 (0.03) 0.76 (0.05) 2.1 (0.05) 0.42 (0.01) 100 (0)
  Alatasetal 0 -    -    -    - -    -    -    -    -    -   
  NICGAR 24 0.24 (0.01) 0.92 (0.01) 3.83 (0.31) 12.27 0.88 (0.01) 0.85 (0.01) 0.99 (0) 2 (0) 0.82 (0.01) 93.94 (2.29)
Segment
EARMGA 99.4 0.39 (0.22) 1 (0) 1.05 (0.04) 0.07 (0.03) 0.03 (0.01) 0.06 (0.03) 2 (0) 0.58 (0.11) 100 (0)
  GENAR 30 0.08 (0) 0.77 (0.03) 5.37 (0.19) 0.73 (0.03) 0.7 (0.03) 0.93 (0.01) 20 (0) 0.53 (0.02) 85.13 (2.93)
  GAR 20.6 0.4 (0.08) 0.89 (0.01) 2.16 (0.3) 3.45 0.52 (0.08) 0.4 (0.05) 0.64 (0.09) 2 (0) 0.4 (0.08) 97.18 (1.6)
  Alatasetal 63 0.49 (0.25) 0.96 (0.05) 1.04 (0.03) 0.32 (0.16) 0.03 (0.06) 0.25 (0.21) 4.26 (0.54) 0.36 (0.18) 99.96 (0.06)
  NICGAR 12.6 0.22 (0.01) 0.99 (0.01) 4.91 (0.43) 0.98 (0.01) 0.97 (0.01) 1 (0) 2 (0) 0.88 (0.01) 99.76 (0.26)
  Sonar
EARMGA 100 0.33 (0.08) 1 (0) 1.03 (0.05) 0.03 (0.03) 0.01 (0.02) 0.02 (0.02) 2 (0) 0.62 (0.04) 100 (0)
  GENAR 30 0.04 (0) 0.94 (0.01) 1.81 (0.03) 0.87 (0.03) 0.44 (0.02) 0.88 (0.03) 61 (0) 0.47 (0.03) 30.96 (1.06)
  GAR 7.2 0.38 (0.05) 0.83 (0.01) 1.3 (0.05) 2.05 0.45 (0.03) 0.29 (0.03) 0.59 (0.04) 2 (0) 0.21 (0.17) 69.62 (21.6)
  Alatasetal 0 -    -    -    - -    -    -    -    -    -   
  NICGAR 22.8 0.26 (0.03) 0.89 (0.02) 7.56 (5.59) 0.81 (0.02) 0.77 (0.02) 0.97 (0.01) 2.01 (0.02) 0.84 (0.02) 100 (0)
    Spambase
EARMGA 61.2 0.25 (0.16) 1 (0) 1.01 (0) 0.35 (0.36) 0.01 (0) 0 (0) 2 (0) 0.63 (0.13) 81.46 (41.45)
  GENAR 30 0.45 (0) 0.62 (0) 1.03 (0.01) 1.05 0.05 (0.01) 0.06 (0.01) 0.12 (0.02) 58 (0) 0.06 (0) 86.21 (0.24)
  GAR 10.6 0.55 (0) 0.9 (0) 1.09 (0.01) 1.74 0.41 (0.02) 0.19 (0.01) 0.55 (0.03) 2 (0) 0.02 (0.01) 60.59 (0)
  Alatasetal 0 -    -    -    - -    -    -    -    -    -   
  NICGAR 11.2 0.12 (0.02) 0.95 (0.02) 73.02 (28.16) 0.9 (0.03) 0.87 (0.04) 0.98 (0.01) 2 (0) 0.84 (0.05) 76.75 (31.96)
   Spectfheart
EARMGA 100 0.36 (0.1) 1 (0) 1.01 (0.02) 0.02 (0.04) 0.01 (0.01) 0.02 (0.03) 2 (0) 0.6 (0.06) 100 (0)
  GENAR 30 0.25 (0) 0.68 (0.01) 0.91 (0.01) 0.68 -0.13 (0.01) -0.17 (0.01) -0.45 (0.02) 45 (0) 0.14 (0) 60.15 (0.42)
  GAR 33.4 0.7 (0.02) 0.89 (0.01) 1.09 (0.01) 1.69 0.35 (0.03) 0.32 (0.04) 0.67 (0.05) 2 (0) 0.42 (0.05) 99.85 (0.33)
  Alatasetal 0 -    -    -    - -    -    -    -    -    -   
  NICGAR 72.2 0.13 (0.01) 0.98 (0) 29.01 (4.73) 0.92 (0) 0.92 (0.02) 1 (0) 2.03 (0.05) 0.89 (0.02) 100 (0)
  Stock
EARMGA 100 0.38 (0.09) 1 (0) 1.01 (0.01) 0.01 (0.01) 0.01 (0.01) 0.01 (0.01) 2 (0) 0.57 (0.05) 100 (0)
  GENAR 30 0.3 (0.01) 0.92 (0.01) 1.64 (0.04) 0.81 (0.03) 0.52 (0.02) 0.88 (0.02) 10 (0) 0.24 (0.01) 87.54 (1.44)
  GAR 2 0.52 (0.11) 0.88 (0.05) 1.52 (0.18) 3.74 0.72 (0.04) 0.72 (0.04) 0.95 (0.02) 2 (0) 0 (0) 65.9 (8.3)
  Alatasetal 7 0.11 (0.2) 0.99 (0.01) 76.82 (135.96) 0.89 (0.24) 0.71 (0.37) 0.75 (0.29) 2.57 (0.93) 0.06 (0.13) 20.45 (43.84)
  NICGAR 9.2 0.28 (0.02) 0.95 (0.01) 3.01 (0.18) 0.93 (0.02) 0.87 (0.01) 0.99 (0) 2.07 (0.07) 0.86 (0.02) 99.41 (0.23)
Stulong
EARMGA 94 0.3 (0.06) 1 (0) 1.01 (0) 0.06 (0.07) 0.01 (0) 0 (0) 2 (0) 0.5 (0.05) 100 (0)
  GENAR 30 0.89 (0) 0.99 (0) 1.01 (0) 1.02 0.02 (0) 0.01 (0) 0.06 (0.01) 5 (0) 0.02 (0) 95.12 (0.35)
  GAR 161.6 0.78 (0.02) 0.93 (0.01) 1.03 (0.01) 1.62 0.3 (0.02) 0.2 (0.01) 0.61 (0.03) 2.98 (0.06) 0.04 (0.01) 99.94 (0.03)
  Alatasetal 7.67 0.72 (0.17) 1 (0.01) 1.48 (0.47) 0.23 (0.16) 0.08 (0.04) 0.11 (0.41) 2.96 (0.34) 0.08 (0.08) 99.25 (0.7)
  NICGAR 4.2 0.26 (0.07) 0.79 (0.03) 16.82 (19.9) 0.62 (0.08) 0.64 (0.06) 0.9 (0.03) 2.04 (0.09) 0.78 (0.06) 84.99 (7.01)
  Texture
EARMGA 100 0.24 (0.05) 1 (0) 1.17 (0.33) 0.08 (0.1) 0.03 (0.03) 0.07 (0.1) 2 (0) 0.63 (0.06) 100 (0)
  GENAR 30 0.09 (0) 0.68 (0.02) 7.49 (0.2) 0.65 (0.02) 0.68 (0.02) 0.99 (0) 41 (0) 0.48 (0.03) 98.25 (0.17)
  GAR 43.8 0.71 (0) 0.93 (0.01) 1.24 (0.02) 0.69 (0.02) 0.66 (0.02) 0.93 (0.01) 2.01 (0.03) 0.38 (0.03) 97.85 (0.8)
  Alatasetal 0 -    -    -    - -    -    -    -    -    -   
  NICGAR 17.4 0.27 (0.02) 0.97 (0) 3.72 (0.39) 0.95 (0) 0.92 (0.01) 1 (0) 2 (0) 0.82 (0.02) 95.85 (4.66)
  Thyroid
EARMGA 88 0.57 (0.11) 1 (0) 1 (0.01) 0.01 (0.01) 0 (0.01) 0 (0.01) 2 (0) 0.48 (0.04) 100 (0)
  GENAR 30 0.69 (0) 0.93 (0) 1.01 (0) 1.05 0.05 (0.01) 0.02 (0.01) 0.07 (0.01) 22 (0) 0.04 (0) 95.5 (0.57)
  GAR 191.2 0.82 (0.01) 0.92 (0) 1.02 (0) 1.17 0.13 (0.01) 0.13 (0.01) 0.45 (0.02) 2.01 (0.02) 0.03 (0) 99.91 (0.08)
  Alatasetal 86.5 0.26 (0.1) 0.97 (0.03) 1.02 (0.01) 0.58 (0.07) 0.05 (0.02) 0.22 (0.12) 16.75 (3.22) 0.43 (0.02) 89.92 (5.28)
  NICGAR 6.2 0.23 (0.07) 0.93 (0.02) 14.29 (9.46) 0.8 (0.07) 0.85 (0.02) 0.95 (0.05) 2.02 (0.05) 0.79 (0.05) 98.16 (2.3)
  Vehicle
EARMGA 100 0.32 (0.07) 1 (0) 1.08 (0.07) 0.11 (0.08) 0.04 (0.04) 0.09 (0.07) 2 (0) 0.61 (0.04) 100 (0)
  GENAR 30 0.09 (0.01) 0.67 (0.02) 2.62 (0.06) 2.6 0.56 (0.02) 0.48 (0.02) 0.76 (0.02) 19 (0) 0.42 (0.01) 66.39 (1.9)
  GAR 26.4 0.67 (0.04) 0.94 (0.01) 1.25 (0.14) 0.42 (0.07) 0.3 (0.09) 0.74 (0.09) 2.02 (0.05) 0.21 (0.08) 100 (0)
  Alatasetal 22.4 0.01 (0) 1 (0) 77.37 (120.38) 1 (0) 0.79 (0.15) 0.61 (0.26) 4.27 (1.01) 0.16 (0.22) 0.24 (0.12)
  NICGAR 12.8 0.27 (0.03) 0.97 (0.01) 3.46 (0.26) 0.95 (0.02) 0.92 (0.01) 1 (0) 2 (0) 0.86 (0.02) 99.98 (0.05)
Wdbc
EARMGA 100 0.27 (0.12) 1 (0) 1.09 (0.16) 0.06 (0.09) 0.03 (0.06) 0.05 (0.08) 2 (0) 0.61 (0.09) 100 (0)
  GENAR 30 0.44 (0.01) 0.94 (0) 1.53 (0.01) 6.42 0.84 (0.01) 0.6 (0) 0.94 (0) 31 (0) 0.08 (0) 72.03 (1.52)
  GAR 90.4 0.54 (0.01) 0.86 (0) 1.18 (0.02) 2.35 0.35 (0.03) 0.29 (0.03) 0.45 (0.04) 2 (0) 0.09 (0.02) 99.13 (1.23)
  Alatasetal 0 -    -    -    - -    -    -    -    -    -   
  NICGAR 13.6 0.27 (0.03) 0.96 (0.02) 3.49 (0.39) 0.93 (0.04) 0.9 (0.03) 0.99 (0.01) 2 (0) 0.84 (0.01) 98.53 (2.1)
Wine
EARMGA 100 0.4 (0.14) 1 (0) 1.01 (0.01) 0.03 (0.03) 0.01 (0.01) 0.02 (0.03) 2 (0) 0.58 (0.08) 100 (0)
  GENAR 30 0.2 (0.01) 1 (0) 3.02 (0.02) 1 (0) 0.83 (0.01) 1 (0) 14 (0) 0.28 (0.03) 66.41 (1.84)
  GAR 7.6 0.21 (0.01) 0.98 (0.03) 2.83 (0.16) 0.96 (0.04) 0.79 (0.04) 0.99 (0.02) 2 (0) 0.54 (0.09) 45.29 (4.32)
  Alatasetal 27 0.27 (0.34) 1 (0) 40.9 (55.02) 0.81 (0.28) 0.47 (0.48) 0.78 (0.33) 4.34 (1.34) 0.1 (0.11) 40.23 (53.29)
  NICGAR 6.6 0.28 (0.01) 0.94 (0.01) 2.79 (0.18) 0.9 (0.02) 0.84 (0.02) 0.99 (0.01) 2 (0) 0.86 (0) 94.61 (0.85)
Vowel
EARMGA 100 0.34 (0.11) 1 (0) 1 (0) 0 (0.01) 0 (0) 0 (0.01) 2 (0) 0.62 (0.06) 100 (0)
  GENAR 30 0.02 (0) 0.56 (0.02) 6.06 (0.28) 0.51 (0.03) 0.48 (0.03) 0.86 (0.01) 14 (0) 0.7 (0) 63.64 (1.78)
  GAR 1.67 0.68 (0.08) 0.86 (0.03) 1.04 (0.01) 1.23 0.18 (0.08) 0.17 (0.1) 0.44 (0.21) 2 (0) 0 (0) 86.74 (13.44)
  Alatasetal 91.8 0.13 (0.02) 1 (0) 72.54 (138.87) 0.76 (0.09) 0.17 (0.14) 0.62 (0.15) 8.36 (0.79) 0.56 (0.01) 94.47 (4.49)
  NICGAR 8.4 0.27 (0.11) 0.95 (0.05) 5.81 (2.57) 0.92 (0.07) 0.89 (0.08) 0.95 (0.09) 2.02 (0.05) 0.85 (0.01) 100 (0)
Table 4: Results for all datasets in the comparison with multi-objective evolutionary approaches
Algorithm #R AvSup (σ) AvConf (σ) AvLift (σ) AvConv AvCF (σ) AvNetconf (σ) AvYulesQ (σ) AvAmp (σ) AvDiv (σ) %Trans (σ)
Balance
QAR-CIP-NSGAII 132.20 0.04 (0.00) 0.92 (0.00) 6.37 (0.31) 0.88 (0.01) 0.68 (0.01) 0.93 (0.00) 3.97 (0.03) 0.83 (0.00) 91.72 (1.23)
MOPNAR 96.80 0.16 (0.01) 0.83 (0.02) 2.02 (0.09) 0.70 (0.02) 0.43 (0.00) 0.81 (0.01) 2.99 (0.07) 0.64 (0.01) 100.00 (0.00)
NICGAR 26.40 0.06 (0.02) 0.92 (0.03) 4.25 (0.44) 0.86 (0.04) 0.69 (0.03) 0.91 (0.02) 3.81 (0.18) 0.82 (0.02) 89.96 (2.19)
Basketball
QAR-CIP-NSGAII 200.60 0.03 (0.01) 0.99 (0.01) 82.09 (2.07) 0.98 (0.01) 0.96 (0.01) 1.00 (0.00) 2.10 (0.02) 0.95 (0.01) 96.67 (1.36)
MOPNAR 134.20 0.13 (0.01) 0.97 (0.01) 58.43 (4.03) 0.94 (0.01) 0.84 (0.02) 0.98 (0.01) 2.27 (0.04) 0.75 (0.02) 100.00 (0.00)
NICGAR 49.80 0.04 (0.01) 0.99 (0.01) 9.43 (2.53) 0.98 (0.02) 0.80 (0.04) 0.99 (0.01) 2.15 (0.09) 0.95 (0.01) 91.67 (4.04)
Bolts
QAR-CIP-NSGAII 174.00 0.08 (0.01) 1.00 (0.00) 30.19 (1.97) 1.00 (0.00) 0.99 (0.00) 1.00 (0.00) 2.10 (0.07) 0.91 (0.03) 100.00 (0.00)
MOPNAR 69.00 0.37 (0.12) 1.00 (0.00) 15.77 (5.69) 1.00 (0.00) 0.92 (0.04) 1.00 (0.00) 2.30 (0.12) 0.54 (0.15) 100.00 (0.00)
NICGAR 9.80 0.30 (0.04) 0.98 (0.02) 5.51 (1.66) 0.98 (0.02) 0.93 (0.03) 1.00 (0.00) 2.00 (0.00) 0.82 (0.02) 100.00 (0.00)
 Coil2000
QAR-CIP-NSGAII 58.60 0.26 (0.11) 0.93 (0.04) 127.77 (103.26) 0.93 (0.04) 0.80 (0.13) 0.86 (0.13) 3.33 (0.63) 0.72 (0.05) 100.00 (0.00)
MOPNAR 39.20 0.41 (0.04) 0.92 (0.08) 6.80 (3.63) 0.89 (0.08) 0.71 (0.04) 0.97 (0.01) 3.15 (0.17) 0.55 (0.07) 100.00 (0.00)
NICGAR 25.40 0.28 (0.03) 0.93 (0.02) 3.65 (0.51) 0.89 (0.03) 0.86 (0.03) 0.98 (0.01) 2.04 (0.04) 0.82 (0.03) 99.96 (0.10)
Fars
QAR-CIP-NSGAII 109.40 0.22 (0.02) 0.95 (0.01) 544.76 (220.80) 0.95 (0.02) 0.75 (0.03) 0.84 (0.04) 3.33 (0.05) 0.78 (0.02) 100.00 (0.00)
MOPNAR 58.00 0.34 (0.02) 0.90 (0.05) 8.00 (1.79) 0.89 (0.05) 0.83 (0.05) 1.00 (0.00) 2.73 (0.12) 0.60 (0.04) 100.00 (0.00)
NICGAR 12.60 0.31 (0.05) 0.99 (0.00) 5.67 (0.58) 0.99 (0.01) 0.98 (0.02) 1.00 (0.00) 2.02 (0.04) 0.81 (0.04) 100.00 (0.00)
House16H
QAR-CIP-NSGAII 288.20 0.18 (0.02) 0.93 (0.00) 2549.17 (529.64) 0.91 (0.01) 0.71 (0.03) 0.84 (0.02) 2.98 (0.17) 0.76 (0.01) 99.81 (0.35)
MOPNAR 135.40 0.31 (0.07) 0.92 (0.05) 9.65 (3.06) 0.89 (0.05) 0.75 (0.03) 0.99 (0.00) 2.79 (0.21) 0.49 (0.14) 99.98 (0.02)
NICGAR 6.00 0.24 (0.04) 0.92 (0.00) 3.67 (0.71) 15.00 0.88 (0.01) 0.83 (0.01) 0.98 (0.00) 2.00 (0.00) 0.86 (0.02) 82.18 (13.91)
Ionosphere
QAR-CIP-NSGAII 125.20 0.10 (0.02) 0.96 (0.01) 143.56 (22.61) 0.94 (0.01) 0.90 (0.02) 0.99 (0.00) 2.67 (0.17) 0.87 (0.05) 87.70 (4.00)
MOPNAR 91.20 0.32 (0.04) 0.94 (0.02) 12.59 (3.57) 0.89 (0.02) 0.72 (0.04) 0.98 (0.01) 2.98 (0.06) 0.63 (0.05) 99.72 (0.64)
NICGAR 24.80 0.20 (0.02) 0.85 (0.01) 3.77 (0.59) 0.78 (0.02) 0.74 (0.02) 0.96 (0.00) 2.01 (0.02) 0.88 (0.01) 99.83 (0.15)
Letter
QAR-CIP-NSGAII 105.20 0.09 (0.01) 0.89 (0.01) 371.41 (84.60) 0.87 (0.01) 0.71 (0.03) 0.84 (0.05) 3.50 (0.17) 0.79 (0.04) 97.94 (1.87)
MOPNAR 75.60 0.28 (0.03) 0.91 (0.03) 7.63 (1.25) 0.87 (0.01) 0.64 (0.06) 0.98 (0.01) 3.33 (0.23) 0.39 (0.04) 99.94 (0.10)
NICGAR 18.80 0.15 (0.02) 0.89 (0.02) 5.94 (1.31) 0.84 (0.03) 0.76 (0.04) 0.96 (0.01) 2.01 (0.02) 0.87 (0.01) 98.17 (1.62)
Magic
QAR-CIP-NSGAII 210.80 0.22 (0.04) 0.95 (0.01) 4464.87 (614.11) 0.93 (0.00) 0.56 (0.04) 0.71 (0.05) 2.35 (0.05) 0.74 (0.03) 99.95 (0.03)
MOPNAR 115.20 0.37 (0.05) 0.91 (0.04) 8.72 (1.44) 0.89 (0.03) 0.70 (0.03) 0.99 (0.01) 2.58 (0.11) 0.52 (0.05) 99.98 (0.03)
NICGAR 6.60 0.26 (0.01) 0.94 (0.01) 3.00 (0.06) 15.30 0.91 (0.02) 0.85 (0.01) 0.99 (0.01) 2.00 (0.00) 0.85 (0.01) 94.87 (4.93)
Movement Libras
QAR-CIP-NSGAII 57.80 0.05 (0.01) 0.96 (0.02) 154.26 (26.59) 0.96 (0.02) 0.94 (0.02) 1.00 (0.00) 2.37 (0.15) 0.90 (0.03) 55.28 (14.04)
MOPNAR 84.20 0.26 (0.08) 0.98 (0.01) 24.01 (17.48) 0.97 (0.01) 0.91 (0.02) 1.00 (0.00) 2.62 (0.16) 0.62 (0.10) 99.34 (1.20)
NICGAR 27.80 0.27 (0.01) 0.98 (0.01) 3.64 (0.05) 0.97 (0.01) 0.95 (0.01) 1.00 (0.00) 2.00 (0.00) 0.86 (0.00) 100.00 (0.00)
Optdigits
QAR-CIP-NSGAII 94.60 0.19 (0.03) 0.87 (0.03) 40.21 (21.97) 0.84 (0.04) 0.58 (0.05) 0.85 (0.02) 3.46 (0.21) 0.69 (0.04) 100.00 (0.00)
MOPNAR 77.00 0.26 (0.07) 0.85 (0.05) 7.09 (2.53) 0.81 (0.05) 0.60 (0.05) 0.97 (0.01) 3.45 (0.40) 0.59 (0.02) 100.00 (0.00)
NICGAR 28.80 0.28 (0.02) 0.87 (0.02) 3.24 (0.40) 0.75 (0.05) 0.71 (0.01) 0.95 (0.01) 2.05 (0.04) 0.82 (0.02) 100.00 (0.00)
Penbased
QAR-CIP-NSGAII 108.40 0.07 (0.01) 0.89 (0.03) 243.31 (157.03) 0.87 (0.03) 0.68 (0.08) 0.82 (0.08) 3.23 (0.26) 0.85 (0.02) 95.58 (2.79)
MOPNAR 107.20 0.30 (0.07) 0.92 (0.01) 6.82 (1.69) 0.89 (0.02) 0.73 (0.02) 0.99 (0.00) 2.99 (0.14) 0.59 (0.01) 99.98 (0.03)
NICGAR 15.00 0.18 (0.02) 0.89 (0.01) 3.64 (0.77) 0.83 (0.02) 0.73 (0.03) 0.95 (0.01) 2.06 (0.10) 0.88 (0.02) 98.64 (0.92)
Pollution
QAR-CIP-NSGAII 249.40 0.05 (0.01) 1.00 (0.01) 51.75 (0.80) 0.99 (0.00) 0.97 (0.01) 1.00 (0.00) 2.09 (0.02) 0.95 (0.00) 100.00 (0.00)
MOPNAR 79.40 0.19 (0.03) 0.99 (0.01) 38.06 (3.84) 0.98 (0.01) 0.90 (0.03) 1.00 (0.00) 2.25 (0.07) 0.65 (0.11) 98.00 (2.74)
NICGAR 57.80 0.08 (0.01) 0.98 (0.01) 8.35 (1.33) 0.97 (0.01) 0.84 (0.02) 1.00 (0.00) 2.07 (0.05) 0.93 (0.01) 100.00 (0.00)
Quake
QAR-CIP-NSGAII 137.20 0.08 (0.01) 0.93 (0.01) 450.67 (46.72) 0.89 (0.01) 0.62 (0.03) 0.77 (0.02) 2.32 (0.06) 0.83 (0.02) 71.60 (2.25)
MOPNAR 49.20 0.32 (0.05) 0.91 (0.04) 8.70 (2.47) 0.86 (0.05) 0.57 (0.03) 0.95 (0.02) 2.32 (0.09) 0.52 (0.04) 100.00 (0.00)
NICGAR 3.60 0.28 (0.05) 0.90 (0.01) 2.51 (0.80) 11.40 0.81 (0.02) 0.72 (0.02) 0.95 (0.01) 2.00 (0.00) 0.75 (0.03) 83.15 (1.70)
Satimage
QAR-CIP-NSGAII 299.80 0.29 (0.02) 0.93 (0.01) 34.04 (34.62) 0.90 (0.01) 0.78 (0.02) 0.96 (0.02) 5.26 (0.36) 0.69 (0.02) 100.00 (0.00)
MOPNAR 172.80 0.32 (0.04) 0.95 (0.01) 7.55 (0.61) 0.93 (0.01) 0.80 (0.02) 1.00 (0.01) 3.74 (0.24) 0.63 (0.05) 100.00 (0.00)
NICGAR 24.00 0.24 (0.01) 0.92 (0.01) 3.83 (0.31) 12.27 0.88 (0.01) 0.85 (0.01) 0.99 (0.00) 2.00 (0.00) 0.82 (0.01) 93.94 (2.29)
Segment
QAR-CIP-NSGAII 176.60 0.18 (0.03) 1.00 (0.00) 451.22 (40.06) 0.99 (0.00) 0.71 (0.02) 0.79 (0.02) 2.46 (0.07) 0.83 (0.01) 100.00 (0.00)
MOPNAR 123.60 0.30 (0.01) 0.99 (0.01) 17.70 (2.35) 0.98 (0.01) 0.89 (0.05) 1.00 (0.00) 2.66 (0.13) 0.65 (0.04) 99.99 (0.02)
NICGAR 12.60 0.22 (0.01) 0.99 (0.01) 4.91 (0.43) 0.98 (0.01) 0.97 (0.01) 1.00 (0.00) 2.00 (0.00) 0.88 (0.01) 99.76 (0.26)
 Sonar
QAR-CIP-NSGAII 123.00 0.06 (0.02) 0.95 (0.02) 128.39 (15.96) 0.92 (0.03) 0.87 (0.04) 0.97 (0.01) 2.38 (0.10) 0.91 (0.04) 80.20 (12.03)
MOPNAR 71.00 0.32 (0.05) 0.93 (0.02) 13.38 (7.66) 0.89 (0.03) 0.71 (0.06) 0.98 (0.01) 2.74 (0.14) 0.64 (0.04) 99.14 (1.68)
NICGAR 22.80 0.26 (0.03) 0.89 (0.02) 7.56 (5.59) 0.81 (0.02) 0.77 (0.02) 0.97 (0.01) 2.01 (0.02) 0.84 (0.02) 100.00 (0.00)
Spambase
QAR-CIP-NSGAII 178.60 0.29 (0.03) 0.92 (0.02) 154.34 (19.12) 0.86 (0.03) 0.62 (0.01) 0.91 (0.02) 4.50 (0.26) 0.64 (0.03) 100.00 (0.00)
MOPNAR 83.40 0.37 (0.08) 0.86 (0.07) 6.79 (1.09) 0.79 (0.07) 0.58 (0.07) 0.94 (0.02) 4.17 (0.84) 0.58 (0.03) 100.00 (0.00)
NICGAR 11.20 0.12 (0.02) 0.95 (0.02) 73.02 (28.16) 0.90 (0.03) 0.87 (0.04) 0.98 (0.01) 2.00 (0.00) 0.84 (0.05) 76.75 (31.96)
Spectfheart
QAR-CIP-NSGAII 109.00 0.17 (0.02) 0.90 (0.02) 55.74 (9.50) 0.84 (0.03) 0.70 (0.04) 0.94 (0.01) 3.04 (0.19) 0.79 (0.02) 96.11 (1.53)
MOPNAR 55.80 0.42 (0.02) 0.92 (0.03) 12.27 (5.12) 0.86 (0.03) 0.64 (0.05) 0.96 (0.02) 2.70 (0.08) 0.60 (0.05) 99.70 (0.67)
NICGAR 72.20 0.13 (0.01) 0.98 (0.00) 29.01 (4.73) 0.92 (0.00) 0.92 (0.02) 1.00 (0.00) 2.03 (0.05) 0.89 (0.02) 100.00 (0.00)
Stock
QAR-CIP-NSGAII 107.60 0.08 (0.01) 0.94 (0.01) 91.91 (43.28) 0.93 (0.01) 0.90 (0.01) 1.00 (0.00) 2.97 (0.07) 0.83 (0.04) 73.75 (6.75)
MOPNAR 105.20 0.26 (0.02) 0.93 (0.01) 12.51 (1.32) 0.92 (0.01) 0.83 (0.02) 1.00 (0.00) 2.95 (0.14) 0.59 (0.03) 100.00 (0.00)
NICGAR 9.20 0.28 (0.02) 0.95 (0.01) 3.01 (0.18) 0.93 (0.02) 0.87 (0.01) 0.99 (0.00) 2.07 (0.07) 0.86 (0.02) 99.41 (0.23)
Stulong
QAR-CIP-NSGAII 153.80 0.19 (0.03) 0.82 (0.01) 39.32 (5.96) 0.74 (0.01) 0.58 (0.02) 0.92 (0.01) 2.90 (0.05) 0.60 (0.02) 99.94 (0.09)
MOPNAR 89.40 0.31 (0.03) 0.84 (0.02) 4.33 (0.38) 0.76 (0.02) 0.52 (0.02) 0.93 (0.01) 2.69 (0.14) 0.50 (0.03) 100.00 (0.00)
NICGAR 4.20 0.26 (0.07) 0.79 (0.03) 16.82 (19.90) 0.62 (0.08) 0.64 (0.06) 0.90 (0.03) 2.04 (0.09) 0.78 (0.06) 84.99 (7.01)
Texture
QAR-CIP-NSGAII 151.00 0.14 (0.03) 0.98 (0.01) 785.39 (104.79) 0.97 (0.01) 0.79 (0.02) 0.84 (0.02) 2.66 (0.16) 0.78 (0.03) 99.87 (0.14)
MOPNAR 117.60 0.29 (0.06) 0.97 (0.02) 14.26 (4.86) 0.96 (0.02) 0.90 (0.04) 1.00 (0.00) 2.83 (0.34) 0.62 (0.08) 100.00 (0.00)
NICGAR 17.40 0.27 (0.02) 0.97 (0.00) 3.72 (0.39) 0.95 (0.00) 0.92 (0.01) 1.00 (0.00) 2.00 (0.00) 0.82 (0.02) 95.85 (4.66)
Thyroid
QAR-CIP-NSGAII 216.60 0.29 (0.03) 0.93 (0.01) 163.67 (40.48) 0.88 (0.01) 0.63 (0.02) 0.92 (0.01) 3.30 (0.15) 0.57 (0.03) 100.00 (0.00)
MOPNAR 75.60 0.37 (0.07) 0.92 (0.03) 11.43 (0.97) 0.84 (0.02) 0.59 (0.04) 0.94 (0.01) 3.40 (0.56) 0.43 (0.06) 100.00 (0.01)
NICGAR 6.20 0.23 (0.07) 0.93 (0.02) 14.29 (9.46) 0.80 (0.07) 0.85 (0.02) 0.95 (0.05) 2.02 (0.05) 0.79 (0.05) 98.16 (2.30)
Wdbc
QAR-CIP-NSGAII 126.80 0.17 (0.02) 0.99 (0.00) 220.99 (35.03) 0.98 (0.00) 0.96 (0.01) 1.00 (0.00) 2.26 (0.07) 0.85 (0.03) 98.57 (1.24)
MOPNAR 85.00 0.33 (0.02) 0.98 (0.00) 15.45 (3.37) 0.97 (0.00) 0.91 (0.02) 1.00 (0.00) 2.56 (0.06) 0.58 (0.12) 99.58 (0.51)
NICGAR 13.60 0.27 (0.03) 0.96 (0.02) 3.49 (0.39) 0.93 (0.04) 0.90 (0.03) 0.99 (0.01) 2.00 (0.00) 0.84 (0.01) 98.53 (2.10)
Vehicle
QAR-CIP-NSGAII 131.80   0.16 (0.01) 0.99 (0.00) 107.11 (23.20) 0.98 (0.01) 0.96 (0.01) 1.00 (0.00) 2.35 (0.04) 0.83 (0.01) 100.00 (0.00)
MOPNAR 107.40 0.27 (0.03) 0.98 (0.01) 15.39 (2.89) 0.98 (0.01) 0.92 (0.02) 1.00 (0.00) 2.55 (0.09) 0.64 (0.05) 100.00 (0.00)
NICGAR 12.80 0.27 (0.03) 0.97 (0.01) 3.46 (0.26) 0.95 (0.02) 0.92 (0.01) 1.00 (0.00) 2.00 (0.00) 0.86 (0.02) 99.98 (0.05)
Wine
QAR-CIP-NSGAII 122.20  0.04 (0.00) 0.97 (0.01) 118.50 (4.75) 0.97 (0.01) 0.95 (0.01) 1.00 (0.00) 2.31 (0.09) 0.92 (0.02) 83.94 (9.20)
MOPNAR 71.60 0.26 (0.03) 0.95 (0.02) 19.42 (9.74) 0.93 (0.03) 0.81 (0.05) 1.00 (0.00) 2.83 (0.11) 0.59 (0.03) 100.00 (0.00)
NICGAR 6.60 0.28 (0.01) 0.94 (0.01) 2.79 (0.18) 0.90 (0.02) 0.84 (0.02) 0.99 (0.01) 2.00 (0.00) 0.86 (0.00) 94.61 (0.85)
Vowel
QAR-CIP-NSGAII 84.40  0.03 (0.00) 0.95 (0.02) 540.52 (58.59) 0.95 (0.02) 0.92 (0.02) 0.99 (0.01) 2.48 (0.12) 0.94 (0.01) 84.19 (9.37)
MOPNAR 50.20 0.18 (0.03) 0.91 (0.04) 16.29 (2.97) 0.90 (0.04) 0.75 (0.05) 0.99 (0.01) 3.21 (0.20) 0.58 (0.05) 99.72 (0.63)
NICGAR 8.40 0.27 (0.11) 0.95 (0.05) 5.81 (2.57) 0.92 (0.07) 0.89 (0.08) 0.95 (0.09) 2.02 (0.05) 0.85 (0.01) 100.00 (0.00)

Results obtained in the comparison with classical algorithms

In this section, we present the results obtained by our algorithm against two classical algorithms (Apriori and Eclat). Table 5 shows the average results obtained of 5 runs for each dataset. Notice that we only show the results obtained by the Apriori and Eclat algorithms over 15 datasets due to the fact that they present scalability problems and cannot run in all datasets.

Finally, this performance results are available for download in xls, pdf and tex files by clicking the links iconExcel.jpg, PDF Icon and iconZip.png, respectively.

Table 5: Results for all datasets in the comparison with the classical algorithms
Algorithm #R AvSup (σ) AvConf (σ) AvLift (σ) AvConv AvCF (σ) AvNetconf (σ) AvYulesQ (σ) AvAmp (σ) AvDiv (σ) %Trans (σ)
Balance
Apriori 2 0.14 (0) 0.86 (0) 6.25 (0) 5.77 0.83 (0) 0.86 (0) 1 (0) 3 (0) 1 (0) 27.2 (0)
Eclat 2 0.14 (0) 0.86 (0) 6.25 (0) 5.77 0.83 (0) 0.86 (0) 1 (0) 3 (0) 1 (0) 27.2 (0)
NICGAR 26.4 0.06 (0.02) 0.92 (0.03) 4.25 (0.44) 0.86 (0.04) 0.69 (0.03) 0.91 (0.02) 3.81 (0.18) 0.82 (0.02) 89.96 (2.19)
Basketball
Apriori 4 0.15 (0) 0.87 (0) 4.88 (0) 6.65 0.84 (0) 0.81 (0) 0.99 (0) 2.75 (0) 0.5 (0) 33.34 (0)
Eclat 4 0.15 (0) 0.87 (0) 4.88 (0) 6.65 0.84 (0) 0.81 (0) 0.99 (0) 2.75 (0) 0.5 (0) 33.34 (0)
NICGAR 49.8 0.04 (0.01) 0.99 (0.01) 9.43 (2.53) 0.98 (0.02) 0.8 (0.04) 0.99 (0.01) 2.15 (0.09) 0.95 (0.01) 91.67 (4.04)
Bolts
Apriori 1246 0.15 (0) 0.99 (0) 7.16 (0) 0.98 (0) 0.96 (0) 1 (0) 4.36 (0) 0.45 (0) 97.5 (0)
Eclat 1246 0.15 (0) 0.99 (0) 7.16 (0) 0.98 (0) 0.96 (0) 1 (0) 4.36 (0) 0.45 (0) 97.5 (0)
NICGAR 9.8 0.3 (0.04) 0.98 (0.02) 5.51 (1.66) 0.98 (0.02) 0.93 (0.03) 1 (0) 2 (0) 0.82 (0.02) 100 (0)
Coil2000
Apriori 0 - - - - - - - - - -
Eclat 0 - - - - - - - - - -
NICGAR 25.4 0.28 (0.03) 0.93 (0.02) 3.65 (0.51) 0.89 (0.03) 0.86 (0.03) 0.98 (0.01) 2.04 (0.04) 0.82 (0.03) 99.96 (0.1)
Fars
Apriori 0 - - - - - - - - - -
Eclat 0 - - - - - - - - - -
NICGAR 12.6 0.31 (0.05) 0.99 (0.00) 5.67 (0.58) 0.99 (0.01) 0.98 (0.02) 1 (0) 2.02 (0.04) 0.81 (0.04) 100 (0)
House16H
Apriori 1749917 0.22 (0) 0.97 (0) 2.19 (0) 0.83 (0) 0.45 (0) 0.76 (0) 8.65 (0) 0.28 (0) 100 (0)
Eclat 1749917 0.22 (0) 0.97 (0) 2.19 (0) 0.83 (0) 0.45 (0) 0.76 (0) 8.65 (0) 0.37 (0) 100 (0)
NICGAR 6 0.24 (0.04) 0.92 (0) 3.67 (0.71) 15 0.88 (0.01) 0.83 (0.01) 0.98 (0) 2 (0) 0.86 (0.02) 82.18 (13.91)
Inosphere
Apriori 211770656 0.12 (0) 0.98 (0) 4.4 (0) 0.97 (0) 0.72 (0) 1 (0) 10.79 (0) 0.03 (0) 100 (0)
Eclat 211770656 0.12 (0) 0.98 (0) 4.4 (0) 0.97 (0) 0.72 (0) 1 (0) 10.79 (0) 0.28 (0) 100 (0)
NICGAR 24.8 0.2 (0.02) 0.85 (0.01) 3.77 (0.59) 0.78 (0.02) 0.74 (0.02) 0.96 (0) 2.01 (0.02) 0.88 (0.01) 99.83 (0.15)
Letter
Apriori 3916 0.14 (0) 0.88 (0) 4.66 (0) 0.81 (0) 0.73 (0) 0.93 (0) 4.55 (0) 0.49 (0) 99.49 (0)
Eclat 3916 0.14 (0) 0.88 (0) 4.66 (0) 0.81 (0) 0.73 (0) 0.93 (0) 4.55 (0) 0.49 (0) 99.49 (0)
NICGAR 18.8 0.15 (0.02) 0.89 (0.02) 5.94 (1.31) 0.84 (0.03) 0.76 (0.04) 0.96 (0.01) 2.01 (0.02) 0.87 (0.01) 98.17 (1.62)
Magic
Apriori 9785 0.19 (0) 0.96 (0) 2.73 (0) 0.87 (0) 0.52 (0) 0.9 (0) 5.53 (0) 0.4 (0) 99.96 (0)
Eclat 9785 0.19 (0) 0.96 (0) 2.73 (0) 0.87 (0) 0.52 (0) 0.9 (0) 5.53 (0) 0.4 (0) 99.96 (0)
NICGAR 6.6 0.26 (0.01) 0.94 (0.01) 3 (0.06) 15.3 0.91 (0.02) 0.85 (0.01) 0.99 (0.01) 2 (0) 0.85 (0.01) 94.87 (4.93)
Movement Libras
Apriori 0 - - - - - - - - - -
Eclat 0 - - - - - - - - - -
NICGAR 27.8 0.27 (0.01) 0.98 (0) 3.64 (0.05) 0.97 (0.01) 0.95 (0.01) 1 (0) 2 (0) 0.86 (0) 100 (0)
Optdigits
Apriori 0 - - - - - - - - - -
Eclat 0 - - - - - - - - - -
NICGAR 28.8 0.28 (0.02) 0.87 (0.02) 3.24 (0.4) 0.75 (0.05) 0.71 (0.01) 0.95 (0.01) 2.05 (0.04) 0.82 (0.02) 100 (0)
Penbased
Apriori 1918 0.14 (0) 0.92 (0) 4.23 (0) 0.82 (0) 0.63 (0) 0.87 (0) 4.07 (0) 0.5 (0) 99.5 (0)
Eclat 1918 0.14 (0) 0.92 (0) 4.23 (0) 0.82 (0) 0.63 (0) 0.87 (0) 4.07 (0) 0.5 (0) 99.5 (0)
NICGAR 15 0.18 (0.02) 0.89 (0.01) 3.64 (0.77) 0.83 (0.02) 0.73 (0.03) 0.95 (0.01) 2.06 (0.1) 0.88 (0.02) 98.64 (0.92)
Pollution
Apriori 41510 0.13 (0) 0.95 (0) 5.84 (0) 0.93 (0) 0.86 (0) 0.98 (0) 5.88 (0) 0.38 (0) 100 (0)
Eclat 41510 0.13 (0) 0.95 (0) 5.84 (0) 0.93 (0) 0.86 (0) 0.98 (0) 5.88 (0) 0.38 (0) 100 (0)
NICGAR 57.8 0.08 (0.01) 0.98 (0.01) 8.35 (1.33) 0.97 (0.01) 0.84 (0.02) 1 (0) 2.07 (0.05) 0.93 (0.01) 100 (0)
Quake
Apriori 18 0.25 (0) 0.91 (0) 1 (0) 1.15 0.11 (0) -0.01 (0) 0.02 (0) 2.56 (0) 0.45 (0) 90.55 (0)
Eclat 18 0.25 (0) 0.91 (0) 1 (0) 1.15 0.11 (0) -0.01 (0) 0.02 (0) 2.56 (0) 0.45 (0) 90.55 (0)
NICGAR 3.6 0.28 (0.05) 0.9 (0.01) 2.51 (0.8) 11.4 0.81 (0.02) 0.72 (0.02) 0.95 (0.01) 2 (0) 0.75 (0.03) 83.15 (1.7)
Satimage
Apriori 0 - - - - - - - - - -
Eclat 0 - - - - - - - - - -
NICGAR 24 0.24 (0.01) 0.92 (0.01) 3.83 (0.31) 12.27 0.88 (0.01) 0.85 (0.01) 0.99 (0) 2 (0) 0.82 (0.01) 93.94 (2.29)
Segment
Apriori 3253152 0.14 (0) 0.98 (0) 2.99 (0) 0.85 (0) 0.48 (0) 0.84 (0) 8.57 (0) 0.33 (0) 100 (0)
Eclat 3253152 0.14 (0) 0.98 (0) 2.99 (0) 0.85 (0) 0.48 (0) 0.84 (0) 8.57 (0) 0.41 (0) 100 (0)
NICGAR 12.6 0.22 (0.01) 0.99 (0.01) 4.91 (0.43) 0.98 (0.01) 0.97 (0.01) 1 (0) 2 (0) 0.88 (0.01) 99.76 (0.26)
Sonar
Apriori 0 - - - - - - - - - -
Eclat 0 - - - - - - - - - -
NICGAR 22.8 0.26 (0.03) 0.89 (0.02) 7.56 (5.59) 0.81 (0.02) 0.77 (0.02) 0.97 (0.01) 2.01 (0.02) 0.84 (0.02) 100 (0)
Spambase
Apriori 0 - - - - - - - - - -
Eclat 0 - - - - - - - - - -
NICGAR 11.2 0.12 (0.02) 0.95 (0.02) 73.02 (28.16) 0.9 (0.03) 0.87 (0.04) 0.98 (0.01) 2 (0) 0.84 (0.05) 76.75 (31.96)
Spectfheart
Apriori 0 - - - - - - - - - -
Eclat 0 - - - - - - - - - -
NICGAR 72.2 0.13 (0.01) 0.98 (0) 29.01 (4.73) 0.92 (0) 0.92 (0.02) 1 (0) 2.03 (0.05) 0.89 (0.02) 100 (0)
Stock
Apriori 855 0.13 (0) 0.91 (0) 4.77 (0) 0.88 (0) 0.76 (0) 0.96 (0) 4.16 (0) 0.44 (0) 99.48 (0)
Eclat 855 0.13 (0) 0.91 (0) 4.77 (0) 0.88 (0) 0.76 (0) 0.96 (0) 4.16 (0) 0.44 (0) 99.48 (0)
NICGAR 9.2 0.28 (0.02) 0.95 (0.01) 3.01 (0.18) 0.93 (0.02) 0.87 (0.01) 0.99 (0) 2.07 (0.07) 0.86 (0.02) 99.41 (0.23)
Stulong
Apriori 89 0.31 (0) 0.93 (0) 1.22 (0) 0.43 (0) 0.14 (0) 0.29 (0) 3.26 (0) 0.43 (0) 99.86 (0)
Eclat 89 0.31 (0) 0.93 (0) 1.22 (0) 0.43 (0) 0.14 (0) 0.29 (0) 3.26 (0) 0.43 (0) 99.86 (0)
NICGAR 4.2 0.26 (0.07) 0.79 (0.03) 16.82 (19.9) 0.62 (0.08) 0.64 (0.06) 0.9 (0.03) 2.04 (0.09) 0.78 (0.06) 84.99 (7.01)
Texture
Apriori 0 - - - - - - - - - -
Eclat 0 - - - - - - - - - -
NICGAR 17.4 0.27 (0.02) 0.97 (0) 3.72 (0.39) 0.95 (0) 0.92 (0.01) 1 (0) 2 (0) 0.82 (0.02) 95.85 (4.66)
Thyroid
Apriori 0 - - - - - - - - - -
Eclat 0 - - - - - - - - - -
NICGAR 6.2 0.23 (0.07) 0.93 (0.02) 14.29 (9.46) 0.8 (0.07) 0.85 (0.02) 0.95 (0.05) 2.02 (0.05) 0.79 (0.05) 98.16 (2.3)
Wdbc
Apriori 0 - - - - - - - - - -
Eclat 0 - - - - - - - - - -
NICGAR 13.6 0.27 (0.03) 0.96 (0.02) 3.49 (0.39) 0.93 (0.04) 0.9 (0.03) 0.99 (0.01) 2 (0) 0.84 (0.01) 98.53 (2.1)
Vehicle
Apriori 141107 0.14 (0) 0.95 (0) 4.18 (0) 0.91 (0) 0.76 (0) 0.95 (0) 6.4 (0) 0.47 (0) 100 (0)
Eclat 141107 0.14 (0) 0.95 (0) 4.18 (0) 0.91 (0) 0.76 (0) 0.95 (0) 6.4 (0) 0.47 (0) 100 (0)
NICGAR 12.8 0.27 (0.03) 0.97 (0.01) 3.46 (0.26) 0.95 (0.02) 0.92 (0.01) 1 (0) 2 (0) 0.86 (0.02) 99.98 (0.05)
Wine
Apriori 1348 0.13 (0) 0.91 (0) 5.97 (0) 0.87 (0) 0.82 (0) 0.97 (0) 4.07 (0) 0.68 (0) 100 (0)
Eclat 1348 0.13 (0) 0.91 (0) 5.97 (0) 0.87 (0) 0.82 (0) 0.97 (0) 4.07 (0) 0.68 (0) 100 (0)
NICGAR 6.6 0.28 (0.01) 0.94 (0.01) 2.79 (0.18) 0.9 (0.02) 0.84 (0.02) 0.99 (0.01) 2 (0) 0.86 (0) 94.61 (0.85)
Vowel
Apriori 235 0.14 (0) 0.98 (0) 2.97 (0) 0.96 (0) 0.69 (0) 0.97 (0) 3.48 (0) 0.7 (0) 100 (0)
Eclat 235 0.14 (0) 0.98 (0) 2.97 (0) 0.96 (0) 0.69 (0) 0.97 (0) 3.48 (0) 0.7 (0) 100 (0)
NICGAR 8.4 0.27 (0.11) 0.95 (0.05) 5.81 (2.57) 0.92 (0.07) 0.89 (0.08) 0.95 (0.09) 2.02 (0.05) 0.85 (0.01) 100 (0)

 

 

Page Maintained by D.Martín and J. Alcalá-Fdez