Discrete Set Handling - Differential Evolution: A Topic for Global Permutation-Based Combinatorial Optimization - page 196

Table 7.23. FSS operating parameters

Parameters Values

Strategy Rand 1 Bin

F 0.4

CR 0.1

7.6.3 Flow Shop Scheduling Results

The primary experimentation was conducted on Taillard benchmark Flowshop Schedul-
ing [21]. These sets are considered primary with a core mix of complexity and scale.
Altogether 120 problem sets are involved, 10 problem instances of n job and m machine
problems of 20x5, 20x10, 20x20, 50x5, 50x10, 50x20 100x5, 100x10, 100x20, 200x10,
200x20, and 500x10 are involved. For each problem instance, two bounds are given, the
upper bound and the lower bound. Most reference is taken from the upper bound, which
is the hypothetical optimal of a particular instance.
So the objective then is not to find the optimal solution (one can if one wants), but
to gauge how effective a heuristic is over the entire range of these problems. In others
words, to observe the consistency of the heuristic. To this effect, the results are presented
in the following format by applying Equation 7.14.

Δ avg = ( H

− U ) • 100

(7.14)

U

Equation 7.14 is where H represents the obtained value and U is the bound specified
by [21]. The Δ avg , gives the average value for all the instances in that particular class,

and gives the standard deviation across all the instances. This is important in order to
gauge the consistency of the heuristic.
The operating parameters of DE using Discrete Set Handling ( DE DSH )isgivenin
Table 7.24. The values of CR and F were obtained through extensive parameter tuning
and NP (population size) and Gen (number of generations) was kept at 700.

Table 7.24. DE DSH operating parameters

Parameters CR F NP Gen

Value 0.5 0.1 500 700

The collated results are presented in Table 7.25. These results are presented with the
results compiled by [22].
Generally, two classes of heuristics are observed: those, which are canonical, and
those, which have embedded local search. To the first class of heuristics belong GA (Ge-
netic Algorithm), PSO spv (Particle Swamp Optimization with smallest position value)
and DE spv (Differential Evolution with smallest position value). The second class has
DE spv + exchange ,whichis DE spv with local search.