Table 2 List of notations used in HFTTC-TMBF

 NoP_uv

Number of paths between two nodes u and v

 Path_{uv, l}

Indices of nodes on the lth path between two nodes u and v

 \( {\widehat{H}}_{uv,l} \)

Normalized value of the number of hops on the lth path between two nodes u and v

 \( {B}_{uv,l}^{n_x} \)

Number of usage of node n_x located on the lth path between nodes u and v on other paths

 \( {P}_{uv,l}^{sum} \)

Total power consumption of links on the lth path between two nodes u and v

 \( {P}_{uv,l}^{max} \)

Maximum power consumption of links on the lth path between two nodes u and v

 \( {\widehat{P}}_{uv,l} \)

Normalize power factor on the lth path between two nodes u and v

 \( {B}_{uv,l}^{sum} \)

Total number of the usages of the nodes on the lth path between the two nodes u and v on other paths

 \( {B}_{uv,l}^{max} \)

Maximum number of the usages of the nodes on the lth path between the two nodes u and v on other paths

 \( {\widehat{B}}_{uv,l} \)

Normalized balance factor on the lth path between the two nodes u and v

 RCF_{uv, ℓ}

Cost function of the lth path between nodes u and v

 Γ^FTL

The set of required links to achieve a K-connected graph

 |Γ^FTL|

Number of members in set Γ^FTL

 \( {X}_{ij\omega}^{g\tau} \)

Gene in GB-LCA algorithm that is 1 if channel ω is assigned to link e_ij in generation g and chromosome τ

 C^gτ

Chromosome in GB-LCA algorithm

 G^g

Generation population

 PI^gτ

Potential interference on each chromosome C^gτ belonging to generation g

 \( {\sigma}_{PI}^{2, g\tau} \)

Variance of potential interference in each chromosome

 \( {PI}_{\omega}^{g\tau} \)

Potential interference on each chromosome C^gτbelonging to generation g in frequency channel ω

 PI^gmax

Maximum potential interference among all chromosomes of generation g

 \( {\sigma}_{PI}^{2,g\max } \)

Maximum variance of interference among all chromosomes of generation g

 COST(C^gτ)

Cost function of chromosome C^gτ

 C^gfa

First parent (Father)

 C^gma

Second parent (Mother)

 \( {\mathbf{C}}_c^{g\tau} \)

Children chromosome

 \( {\overset{\frown }{X}}_{ij\omega}^{g{\tau}_1} \)

Children gene

 \( {\mathbf{C}}_m^{g\tau} \)

Mutation chromosome

 μ

Mutation rate

 n_m

Number of chromosomes resulting from mutation

 n_μ

Number of mutated genes

 n_p

Number of chromosomes in current generation

 n_c

Number of children chromosomes

 \( {\boldsymbol{\Gamma}}_{\omega}^{LCA} \)

Set of links with frequency channel  ω ∈ Ω

 \( {P}_{ij}^{g\tau} \)

Gene in GB-CSF that is the transmission power of each link e_ijbelonging to \( {\boldsymbol{\Gamma}}_{\omega}^{LCA} \)

 S^gτ

Chromosome in GB-CSF algorithm

 \( {\rho}_{ij}^{g\tau} \)

Transmission rate correspondent to gene \( {P}_{ij}^{g\tau} \)

 \( {\sigma}_{\rho}^{2, g\tau} \)

Transmission rate variance of links in the chromosome τ

 \( {\overline{\rho}}^{g\tau} \)

Transmission rate average of all links of the chromosome τ

 P^gmax

Maximum value of transmission power of the chromosome τ

 ρ^gmax

Maximum value of transmission rate of the chromosome τ

 \( {\sigma}_{\rho}^{2,g\max } \)

Maximum variance of transmission rate

 COST(S^gτ)

Cost function of chromosome S^gτ

 S^gfa

First parent (Father)

 S^gma

Second parent (Mother)

 \( {\mathbf{S}}_c^{g\tau} \)

Children chromosome

 \( {\overset{\frown }{P}}_{ij}^{g{\tau}_1} \)

Children gene

 \( {\mathbf{S}}_m^{g\tau} \)

Mutation chromosome

 \( {\tilde{P}}_{ij}^{g\tau} \)

Mutation gene

 \( {X}_{uvk}^{g\tau} \)

This gene is 1 if kth path is selected for traffic flow of (u,v)

 Ρ^gτ

Chromosome in GB-CLPS algorithm

 \( {LT}_{ij}^{\tau } \)

Traffic on link e_ij when all paths are selected based on chromosome τ

 \( {\chi}_{uv{l}^{\prime}}^{ij} \)

A binary parameter that is 1 if link e_ijis on l’th path between nodes u and v

 \( {TN}_{\omega m}^{g\tau} \)

Number of time slots when mth configuration set is active on frequency channel ωin chromosome τ

 \( {\boldsymbol{\Gamma}}_m^{\omega } \)

Set of links belong to mth configuration set on frequency channel ω

 \( {\sigma}_{SF}^{2, g\tau} \)

Variance of satisfaction factor of different traffic flows

 \( {SF}_{uv}^{\tau } \)

Satisfaction factor of each traffic flow (u,v)

 \( {TN}_s^{g\max } \)

Maximum number of total time slots of all chromosomes

 \( {C}_{uv}^{\tau } \)

Transmission rate of the link on the path from u to v which requires maximum number of time slots for transmission

 \( {path}_{uv}^{\tau } \)

Set of links on the path selected between nodes u and v in chromosome τ

 \( {\sigma}_n^{2, g\tau} \)

Variance of node utilization

 \( {\sigma}_c^{2, g\tau} \)

Variance of frequency channel utilization

 \( {V}_a^{\tau } \)

Set of active nodes in chromosome τ

 \( {n}_a^{\tau } \)

Number of active nodes in chromosome τ

 \( {U}_i^{\tau } \)

Utilization of node i in chromosome τ

 \( {\overline{U}}_n^{\tau } \)

Average of node utilization in chromosome τ

 \( {\boldsymbol{\Omega}}_a^{\tau } \)

Set of active frequency channels in chromosome τ

 \( \left|{\boldsymbol{\Omega}}_a^{\tau}\right| \)

Number of active frequency channels in chromosome τ

 \( {U}_{\omega}^{\tau } \)

Utilization of frequency channel ω in chromosome τ

 \( {\overline{U}}_c^{\tau } \)

Average of frequency channel utilization in chromosome τ

 P^gfa

First parent (Father)

 P^gma

Second parent (Mother)

 \( {\mathbf{P}}_c^{g\tau} \)

Children chromosome

 \( {\overset{\frown }{X}}_{uvk}^{g\tau} \)

Children gene

 \( {\mathbf{P}}_m^{g\tau} \)

Mutation chromosome