Motivation for Differential Evolution for Permutative-Based Combinatorial Problems - Differential Evolution: A Topic for Global Permutation-Based Combinatorial Optimization - page 3

Fig. 1.2. The generalized Rosenbrock function problem

Ta b l e 1 . 1 . Example of job times

jobs j 1 j 2 j 3 j 4 j 5

P 1 , j k 6 4 4 5 1

P 2 , j k 4 6 2 4 3

P 3 , j k 3 3 4 1 3

P 4 , j k 4 4 5 3 1

such that:

C i , j = max C i − 1 , j , C i , j − 1 + P i , j

(1.3)

{

2 , 1 , 4 , 3 , 5

}

gives a fitness (makespan) of 31. The
solution includes a permutative schedule as well as the fitness. It is not feasible to solve
this kind of problem using the canonical DE that solves only continuous problems as
already discussed.

For this problem the schedule of

1.1.3 Suitability of Differential Evolution as a Combinatorial Optimizer
An extract from the summary of Section 4.4 of [2] reads:

” Although DE has performed well on wide-sense combinatorial problems, its
suitability as a combinatorial optimizer is still a topic of considerable debate
andadefinitive judgment cannot be given at this time ”.