# 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:

## 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.

## 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

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

### 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 , and , respectively.

 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 , and and for the ones obtained by the multi-objective evolutionary algorithms, click the links , and .

 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)
 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 , and , respectively.

 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)