6.4 Bee's representation

An important behavior of employed and onlooker bees is their capacity of sharing

A hybrid algorithm was proposed to make the ABC auto-adjustable during each iteration to decide the number of clusters by incorporating K-means and a Consensus method. In particular, K-means is used to select the elements inside each generated cluster to decide centroids for similarity calculations. The solution of the algorithm is represented as a vector of size n (number of Web services to cluster) where each position of the element in the vector is the group to which it belongs to.

The objective function of this hybrid algorithm is shown in Eq. (4):

Min ∑ C i ¼ 1 x∈ci y∈ci

empty, and there should be no intersection between groups.

<sup>X</sup> � <sup>1</sup>:<sup>96</sup> <sup>σ</sup>

the similarity matrix; μ, average similarity.

6.3 Food source representation

18

ffiffiffiffi N d xi; yi

where d, distance between centroid of cluster yi and a service xi; yi, centroid of cluster i; xi: one of the services included in cluster i. No group of services should be

The first stage of the hybrid algorithm consists of filtering of the eight matrices that contain the information of similarities between Web services. The filtering consists of discarding values that exceed the limits allowed and established by the similarity measures, as a result of this filtering, new matrices are generated with a degree of 95% certainty in the measurements. Eq. (5) shows the filtering calculation:

<sup>p</sup> <sup>≤</sup>μ≤<sup>X</sup> <sup>þ</sup> <sup>1</sup>:<sup>96</sup> <sup>σ</sup>

where X, average matrix; 1.96, table value; σ, standard deviation; N, element of

After the filtering process, all obtained data is stored in an average matrix (food sources) discarding the positions that contain null or zero information; that is,

ffiffiffiffi N

p (5)

� � (4)

information (memory) to choose and adjust the food source value. This value depends on the proximity to the nest, the richness or concentration of honey energy [18]. The exchange of information occurs during the waggle dance at the hive. Onlooker foragers watch numerous dances at the dancing area and decide to employ themselves at the most profitable food source. When an onlooker forager recruit starts searching and locates the food source, then it utilizes its own capability to memorize the location and starts exploiting it. The onlooker forager becomes an employed forager. In the ABC algorithm the set of possible solutions represent the food sources, and the food source value represents the quality of the solution. A general representation of the ABC workflow algorithm is presented in Figure 5.

Advanced Analytics and Artificial Intelligence Applications

6. Hybrid algorithm description

6.1 Objective function

6.2 Filtering similarities

Using the average matrix a set of arrays is generated representing the bees and other important information as the number of groups and centroids. Table 3 shows the structure of the solution generated.


$$\mathbf{X}'\_{\text{new}} = \text{round } \left( \mathbf{X}'\_{\text{i}} - \phi(\mathbf{X}'\_{\text{i}} - \mathbf{X}'\_{\text{s}}) \right) \tag{6}$$

where X<sup>0</sup> new, new vector; X<sup>0</sup> i , first vector generated by the algorithm; ϕ, aleatory number between 0 and 1



Table 3.

Composition of the vector with information of generated groups.
