Page 34 - 33-3

Optimal Allocation of Capacitated Facilities Considering Time-Dependent User Preference for User Number
Maximization

into the pool if they are feasible and the worst two plans will be removed from the pool.
Besides, for the small and medium sizes of problem, we run the genetic algorithm for 2,000
iterations; for the large size problem, the number of iterations is 10,000. After iterations,
the genetic algorithm will return the best construction plan in the pool.

5.3 Solution Performance
In this section, we use z to denote the objective value of the solution found by
GSAMFE, and z to denote that found by mathematical model.
*
In Table 10, we find that our algorithm performs well in three problem sizes and
average performance is better in the medium size. When the problem size increases, there
is more chance to select non-optimal facilities. However, the effect of selecting single
wrong facility and scale level may also impact less on the total objective value when the

problem size increases. Moreover, the number of iterations increase with the problem size.
Therefore, even if the algorithms choose a non-optimal facility in an iteration, there are
more chances for them to choose good facilities in the following iterations.
Table 11 shows that our algorithm performs well in two scenarios, and it performs

better when there is only one scale level. If a facility has multiple scale levels, the
difficulty of the problem increases. There are more chances to pick the non-optimal facility
and scale levels, so our algorithm is easily to get a better solution when the number of
scale levels is less.

Table 10 Numerical Result of Problem Size
Average Minimum
Instance size z z GA z z GA
z* z* z* z*
Small 0.9855 0.9308 0.7231 0.6702
Medium 0.9915 0.8558 0.8342 0.5917
Large 0.9857 0.7865 0.6656 0.5189

26