Parameters 
$G=(V,E)$
 undirected physical supply network with the set of nodes
$V$
and the set of admissible physical links
$E$

$P$
 set of admissible physical routing paths in
$G$
for all node pairs
$(i,j)\in V\times V$
,
$i<j$

${P}_{i}$
 subset of all admissible physical routing paths in
$G$
ending at node
$i\in V$
, (
${P}_{i}\subset P$
) 
${P}_{(i,j)}$
 subset of all admissible routing paths in
$G$
between nodes
$i$
and
$j$
for every node pair
$(i,j)\in V\times V$
,
$i<j$
, (
${P}_{(i,j)}\subset P$
) 
${P}_{e}$
 subset of all admissible physical routing paths traversing
admissible physical link
$e\in E$
, (
${P}_{e}\subset P$
) 
$N$
 set of IP routers that can be installed in the network 
${R}^{n}$
 maximum switching capacity of router
$n\in N$

${\alpha}^{n}$
 power consumption of router
$n\in N$

${\beta}^{e}$
 power consumption of a fiber (OLAs and WDM terminals) installed on
link
$e\in E$

$B$
 capacity of a fiber in terms of number of wavelength channels 
${L}_{e}$
 length (in kilometers) of the physical link
$e\in E$

${N}_{a}^{e}$
 number of OLAs needed to amplify the signal at edge
$e\in E$

${\beta}^{a}$
 power consumption of a single OLA 
${\beta}^{t}$
 power consumption of a single WDM terminal 
$\gamma $
 power consumption of two line cards 
$C$
 module of bandwidth that can be installed on each path
$p\in P$

$\delta $
 maximum admissible utilization of bandwidth installed on each path
$p\in P$

${d}_{ij}$
 undirected traffic demand value between node
$i$
and node
$j$
,
$i<j$

${d}_{i}$
 the total traffic demand of a network node
$i$

$K$
 set of commodities corresponding to those nodes in
$V$
that are the source of at least one demand 
${d}_{i}^{k}$
 net demand value for commodity
$k\in K$
and node
$k\in K$

$\mathrm{\Delta}$
 maximum number of generations without improvements (GAGD) 
$\mathrm{\Theta}$
 size of the population (GAGD) 
$\mathrm{\Gamma}$
 size of
the offspring (GAGD) 
Variables 
${f}_{ij}^{ab}$
,
${f}_{ij}^{ab}$
 whether or not the traffic demand between nodes
$a\in V$
and
$b\in V$
uses the logical link between nodes
$i\in V$
and
$j\in V$
(both directions),
${f}_{ij}^{ab}$
,
${f}_{ji}^{ab}\in \{0,1\}$
, SPR formulation 
${y}_{p}$
 number of lightpaths realized on
$p\in P$
,
${y}_{p}\in {\mathbb{Z}}_{+}$

${z}_{e}$
 number of fibers installed on physical link
$e\in E$
,
${z}_{e}\in {\mathbb{Z}}_{+}$

${x}_{i}^{n}$
 whether or not router
$n\in N$
is installed at node
$i\in V$
,
${x}_{i}^{n}\in \{0,1\}$

${f}_{ij}^{k}$
,
${f}_{ij}^{k}$
 the
amount of traffic originated at node
$a\in V$
and targeted to node
$b\in V$
traversing the logical link between nodes and
$i\in V$
and
$j\in V$
(both directions),
${f}_{ij}^{k}$
,
${f}_{ji}^{k}\in {\mathbb{R}}_{+}$
, MCF formulation 
Metrics 
${L}^{\mathrm{MCF}}$
 number of lightpaths in the MCF solution 
${L}^{\mathrm{SPR}}$
 number of lightpaths in the SPR solution 
${P}^{\mathrm{MCF}}$
 total power consumption of the MCF solution 
${P}^{\mathrm{SPR}}$
 total power consumption of the SPR solution 
${P}^{2S}$
 total power consumption of a network designed with the twostep
procedure 
${P}^{J}$
 total power consumption of a network designed with the joint
procedure 
${\mathrm{\Delta}}_{L}^{\mathrm{SPR}\mathrm{MCF}}$
 relative increase of the number of lightpaths in the SPR solution
with respect to the MCF solution 
${\mathrm{\Delta}}_{P}^{\mathrm{SPR}\mathrm{MCF}}$
 relative increase of the power consumption in the SPR solution with
respect to the MCF solution 
${\mathrm{\Delta}}_{P}^{2SJ}$
 relative increase of the power consumption due to the twostep
procedure with respect to the joint procedure 