DARPA ULTRALOG Final Report - Industrial and Manufacturing ...

ω
∑
k
Max CLI j ( k )
k∈K
a
. (15)
ωk
j∈
Consequently, the minimal completion time T * can be formulated as in (16) by incorporating
topology variables and constraints in (1).
S J [
k ]
Topology problem formulation
T
*
s.t.
ω
= Min Max
k∈K
ω
∑
k∈N
∑
k∉N
x
jk
j
j
x
x
jk
jk
= 1
= 0
∈{0,1}
k
a
k
∑
j∈J
CLI
j
( k )x
jk
for all j ∈ J
for all j ∈ J
for all j ∈ J and
k ∈ K
(16)
The formulation has a simplistic form because it is completely separated from resource
allocation variables. As a result, the formulation can be mapped into the easiest multiprocessor
scheduling problem, i.e., an assignment of independent clusters to machines. As discussed, this
problem is NP-complete and there are diverse heuristic algorithms available in the literature.
Eleven heuristics were selected and examined with various problem configurations in [21]. They
are Opportunistic Load Balancing, Minimum Execution Time, Minimum Completion Time,
Min-min, Max-min, Duplex, Genetic Algorithm, Simulated Annealing, Genetic Simulated
Annealing, Tabu, and A * . Though Genetic Algorithm always gave the best performance, if
algorithm execution time is also considered, it was shown that the simple Min-min heuristic
performs well in comparison to others. So, we recommend the Min-min heuristic as an algorithm
for solving the problem formulation. By adapting to our context the Min-min heuristic is as
follows.
11