Computational Intelligence - November 2017 - 44

D. Parameter Self-Adaption

The simulation results and analysis show the
superiority and efficiency of the proposed algorithm,
which is capable of producing optimal packing
programming schemes for hundreds of extravehicular
missions with a success rate of over 90%.
k

x ij ( gen + 1)

= f k $ x kij ( gen) + 1 - f k $ T tbest
ij $ W

W=)

- F (s tbest ) if (F = F1)
,
1/F (s tbest ) if (F = F2)

(13)

= 1+W
x max = 1 - W
x min

g max
gen
g max
gen

,

(15)

Algorithm 2 Pseudocode of the ACO algorithm for EMPP

1: Set the population size NP and maximum generations
G max of the algorithm, initialize the parameter nb 0 and
nf 0, initialize the pheromone matrix and copy it to

each ant
2: for g = 1 to G max do
3:
for k = 1 to NP do
4:
Calculate b k and f k of ant k
5:
Build solution k according to the solution construction procedure in Algorithm 1
end for
6:
for k = 1 to NP do
7:
Randomly select an ant from the top 5%
8:
Update the pheromone matrix for ant k using
information of the selected ant
end for
9:
Collect successful parameters in the current
generation
10:
Update the parameter nb g and nf g
11: end for

IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2017

k

+ N (nb g, 0.5 2 ),

(16)

where b k is a random number taken from Gaussian distribution with a mean of nb g and a standard deviation of 0.5. The
nb g is updated in every generation by
nb g + 1

where g max denotes the maximum number of iterative cycles.

44

b

(14)

where gen denotes the current generation. Ant tbest is randomly
selected from the top 5% individuals in the current ant colony.
F (s tbest) is the objective function value of the solution s tbest . Equation (14) allows W to vary from a small value (mostly 0.6-0.8
according to the simulation results) to 1 irrespective of whether
F1 or F2 is used. The matrix T, which differs from the pheromone matrix, is used to store information of the relationship
between any two missions after a solution is built. For ant tbest, if
missions i and j are placed in the same package, T ijtbest = 1; otherwise it will be set to 0, which means that all of the values in
matrix T are Boolean numbers. f k is an evaporation parameter of
ant k in the range of (0, 1). Unlike classical MMAS, the range of
the pheromone values are adaptive and given by

)

The heuristic parameter b and the evaporation parameter f are self-adaptive in the
proposed ACO for EMPP. For ant k, the
heuristic parameter b k is given by [28]

= ~ b $ nb g + (1 - ~ b) $ mean (S b),

(17)

where ~ b is a random number uniformly distributed between
0.8 and 1.0, and S b is the assemblage of all the successful
heuristic parameters in the current generation. Here, the successful heuristic parameter refers to the b used by the ant that
finds a more optimal solution in the current generation. The
mean (S b) refers to the power mean of all the successful heuristic parameters and is calculated as
mean (S b) =

/

x2 / Sb ,

(18)

x ! Sb

where S b is the number of all the successful heuristic parameters. Note that the self-adaption strategy of f k is the same as
that of b k, except that the standard deviation of Gaussian distribution is changed to 0.1.
E. Pseudocode of the Algorithm

Algorithm 2 shows the pseudocode of the proposed ACO for
EMPP. Here, nb 0 and nf 0 are the initial values used to calculate b and f in the first generation.
IV. Simulations
A. Case Study

A long-term operation mission of the space station with a
five-year planning cycle from 2021 to 2025 is considered as a
case study here. The supplementary document lists a total of
171 extravehicular missions to be programmed and their
properties in these five years, such as the demand in terms of
extravehicular man-hours, and the earliest occurrence time
and deadline.
Considering the practical operation of the space station, the
number of astronauts for each spacewalk is set to 2 and the
extravehicular working time is set to be no longer than 6
hours, i.e., the maximum man-hours that can be provided for
one spacewalk is 12 mh.
B. Objective Function and Parameters

Based on the case study, the simulation results and analysis are
presented in the supplementary document, which suggest that
the objective function and parameters as listed in Table 1 are
suitable choices for solving the EMPP.



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