Research on Zero-Wait Scheduling Problems in Multiproduct Processes with Due Dates - Intelligent Computing for Sustainable Energy and Environment - page 328

Fig. 3. Convergence characteristic of the worst programming model

α = 0.7

Fig. 2 and 3 illustrate the evolution curve of the two models. In each figure, curve
F_gbest is the optimal value of objective, which shows the best frog in each iteration;
curve Avg_fit is the mean value of the objective of all frogs in memeplexes. Along
with the increases of evolutionary generation, the curve gradually tends to a stable
value, which indicating that the convergence of the method. When α is 0.7, the
optimal objective of the optimal programming is 2280.5, and the processing sequence
is [6 8 9 2 1 7 4 10 5 3]; the optimal objective of the worst programming is 3569.5,
and the processing sequence is [7 2 1 6 8 9 4 10 5 3].
The parameter selection is critical to ISFLA performance. ISFLA has four
parameters: the number M of memeplexes, the number N of frogs in a sub-memeplex,
the number N max of local evolution in a sub-memeplex and the maximum step size
S max. In the test, the maximum step size S max is devised to be the same with the
number of products, so the other three parameters will be determined through
extensive experiments. Some benchmark instances with different sizes have been
selected to test, which have the objective of makespan. For each test problem, a total
of 10 run with different combinations of the parameters. Firstly, the frog memeplex is
fixed to 10, and each sub-memeplex has 20 frogs. The local exploration for each sub-
memeplex is set to 15, 30, 50, 75, and 100. And we defined the maximal deviation
MDP in this paper as follows,

opt _ max − opt _ min

MDP = × 100 %

(6)

opt _ min

Supposed opt_max be the maximum objective value found in the optimization
computation, opt _ min be the minimum objective. MDP can indicate the extent of
scatter of the objective set. Table 2 illustrates the comparison of different local
exploration iteration for every sub-memeplex. From the table, when N max is set to15
or 75,100, the MDP value is not better than that of 30.