Heuristics for Synthesizing Robust Networks with a Diameter Constraint

Algorithm 1

𝑘-opt exchange.

(1)  Input: 𝐷 (positive integer)

(2)  𝒯₀← Initial feasible solution satisfying diameter constraints

(3)  𝜆₀← 𝜆₂(𝐿(𝒯₀))

(4)  𝐸_del← Subset of 𝑘-edge combinations considered for possible deletion as obtained by the edge ranking procedure in

  Section 3.1

(5)  for each edge combination in 𝐸_del  do

(6)  Delete the 𝑘 edges present in the edge combination to obtain connected components 𝐶₁,𝐶₂,𝐶₃,…,𝐶_𝑘+1

(7)  𝐸_add← Subset of 𝑘-edge combinations considered for possible addition as obtained by the edge ranking procedure

   in Section 3.2

(8)   Let 𝒯₁ be the spanning tree which is feasible and has the largest connectivity obtained from adding the edges in an

   edge combination from 𝐸_add

(9)   if  𝜆₂(𝐿(𝒯₁))>𝜆₀  then

(10)   𝒯₀←𝒯₁

(11)   𝜆₀←𝜆₂(𝐿(𝒯₁))

(12)  end if

(13)  end for

(14)  Output 𝒯₀ as the (new) current solution