KPotential Best Paths Selection (KPBP)

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 Kconnected graph

Γ^{FTL}

Number of members in set Γ^{FTL}

Genetic Based Links Channel Assignment (GBLCA)

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

Gene in GBLCA algorithm that is 1 if channel ω is assigned to link e_{ij} in generation g and chromosome τ

C^{gτ}

Chromosome in GBLCA 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^{gτ}belonging 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

Genetic Based Compatible Sets Formation (GBCSF)

\( {P}_{ij}^{g\tau} \)

Gene in GBCSF that is the transmission power of each link e_{ij}belonging to \( {\boldsymbol{\Gamma}}_{\omega}^{LCA} \)

S^{gτ}

Chromosome in GBCSF 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

Genetic Based Cross Layer Path Selection (GBCLPS)

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

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

Ρ^{gτ}

Chromosome in GBCLPS 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_{ij}is 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
