Novel Web Service Selection Model Based on Discrete Group Search

Algorithm 1

Procedure for the D-GSO algorithm.

Algorithm. D-GSO

Step  1. 𝑁 classes of generic services are present in the composition component, where each class has 𝑁_𝑖(1≤𝑖≤𝑛)

candidate services. The maximum pursuit distance 𝑙_max is calculated from the following equation:

𝑙_max=∑^𝑛_𝑖=1𝑁²_𝑖,                                  (i)

Each candidate service has 𝑘 QoS attributes, which are rearranged into [𝑞¹_des,…,𝑞^𝑘_des] according to the weights in

descending sequence. The candidate services of generic service 𝐼_𝑖(1≤𝑖≤𝑛) are reordered into a set 𝐼^order_𝑖=[𝑥⁰_𝑖,…,𝑥^𝑁𝑖_𝑖]

with reference to 𝑞¹_des,…,𝑞^𝑘_des in turn.

Step  2. Set ℎ∶=0;

Randomly initialize 𝑟 instantiations 𝑋_𝑖[𝑥¹_𝑖,𝑥²_𝑖,…,𝑥^𝑛_𝑖] (1≤𝑖≤𝑟) with 𝑈(𝑞^𝑖_𝑡,𝑄^𝑖_𝑡)≤1(1≤𝑡≤𝑘) of services composition

component and head angle 𝜙_𝑖 of all initial instantiations;

Calculate the values of initial instantiations according to the cost function;

WHILE (the best instantiation is not found)

 FOR (each instantiation 𝑋^𝑖 where 𝑈(𝑞^𝑖_𝑡,𝑄^𝑖_𝑡)≤1(1≤𝑡≤𝑘) in the group)

Choose the producer:

   Find the producer 𝑋^𝑝 with the lowest cost in the group;

Perform producing:

 (a) The producer will scan at zero degree and then scan laterally by randomly sampling three instantiations in the scanning

    field: one instantiation at zero degree, one instantiation in the right-hand side of the hypercube, and one instantiation in the

   left-hand side of the hypercube. 𝑟₁∈𝑅¹ is a normally distributed random number with mean 0 and standard deviation 1,

   where as 𝑟₂∈𝑅^𝑛−1 is a uni-formly distributed random sequence in the range (0, 1);

   sub𝑋_𝑧=sub𝑋^𝑝_ℎ+round(𝑟₁𝑙_max𝐷^𝑝_ℎ(𝜙_ℎ)),                   (ii)

   sub𝑋_𝑟=sub𝑋^𝑝_ℎ+round𝑟₁𝑙_max𝐷^𝑝_ℎ𝜙_ℎ+𝑟₂𝜃_max2,           (iii)

   sub𝑋_𝑙=sub𝑋^𝑝_ℎ+round𝑟₁𝑙_max𝐷^𝑝_ℎ𝜙_ℎ−𝑟₂𝜃_max2,            (iv)

 (b) The producer will find the best instantiation 𝑋^𝑖 where 𝑈(𝑞^𝑖_𝑡,𝑄^𝑖_𝑡)≤1(1≤𝑡≤𝑘) with the lowest cost.

    If the best instantiation has a lower cost compared with the current instantiation, then the best instantiation

    will be chosen; otherwise, the current instantiation will remain and turn its head to a new randomly generated angle.

    𝛼_max∈𝑅¹ is the maximum turning angle;

    𝜙^ℎ+1=𝜙^ℎ+𝑟₂𝛼_max,                            (v)

 (c) If the producer cannot find a better instantiation after 𝑎 iterations, then the producer will turn its head back to zero degree;

    𝜙^ℎ+𝑎=𝜙^ℎ,                                          (vi)

Perform scrounging:

     Randomly select 80% members from the rest of the instantiations to perform scrounging.

   The area copying behavior of the 𝑖th scrounger can be modeled as a random walk toward the producer.

    In (vii), 𝑟₃∈𝑅^𝑛 is a uniform random sequence in the range (0, 1);

  sub𝑋_𝑖^ℎ+1=sub𝑋^ℎ_𝑖+round𝑟₃^∘sub𝑋^ℎ_𝑝−sub𝑋^ℎ_𝑖,             (vii)

Perform dispersion:

     The rest of the instantiations will be dispersed to perform ranging: (1) generate a random head angle by using (v); (2) choose

    a random distance 𝑙_𝑖 from the Gauss distribution by using (viii); transform into the new instantiation by using (ix);

    𝑙_𝑖=𝑎⋅𝑟₁𝑙_max,                      (viii)

    sub𝑋_𝑖^ℎ+1=sub𝑋^ℎ_𝑖+round𝑙_𝑖𝐷^ℎ_𝑖𝜙^ℎ+1.               (ix)

Calculate fitness:

    Calculate the values of the current instantiations according to the cost function;

 END FOR

 Set ℎ∶=ℎ+1;

END WHILE