Differential Evolution for Permutation-Based Combinatorial Problems - Differential Evolution: A Topic for Global Permutation-Based Combinatorial Optimization - page 32

able to transform a combinatorial problem into a space which is amenable for search,
and that there is no such thing as an “all-cure” algorithm for combinatorial problems.
For example, particle swarm optimization (PSO) works fairly well for combinatorial
problems, but only in combination with a good tailored heuristic. If such a heuristic is
used, then PSO can locate promising regions. The same logic applies to a number of
optimization approaches.
While the anatomy described in Table 2.6 favors the adjacency matrix and permuta-
tion matrix approaches, compared to the forward/backward transformation relative po-
sition indexing approaches, it is not known in the literature where the adjacency matrix
and permutation matrix approaches have been applied to real − life permutation-based

combinatorial problems.
In this topic, it is therefore concluded that:

1. The original classical DE which Storn and Price developed was designed to solve
only problems characterized by continuous parameters. This means that only a sub-
set of real-world problems could be solved by the original canonical DE.
2. For quite some time, this deficiency made DE not to be employed to a vast number
of real-world problems which characterized by permutative-based combinatorial
parameters.
3. This topic complements that of [10] and vice versa. Taken together therefore, both
topics will be needed by practitioners and students interested in DE in order to
have the full potentials of DE at their disposal. In other words, DE as an area of
optimization is incomplete unless it can deal with real

life problems in the areas
of continuous space as well as permutative-based combinatorial domain.

−

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