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Motivation for Differential Evolution for
Permutative
Based Combinatorial Problems
Godfrey Onwubolu 1 and Donald Davendra 2
1
Knowledge Management & Mining, Inc., Richmond Hill, Ontario, Canada
onwubolu g@dsgm.ca
2
Tomas Bata Univerzity in Zlin, Faculty of Applied Informatics, Nad Stranemi 4511,
Zlin 76001, Czech Republic
davendra@fai.utb.cz
Abstract. It is generally accepted that Differential Evolution (DE) was originally designed to
solve problems which are defined in continuous form. Some researchers have however, felt that
this is a limiting factor on DE, hence there have been vigorous research work to extend the
functionalities of DE to include permutative-based combinatorial problems. This chapter sets the
scene for the topic by discussing the motivation for presenting the foundational theories for a
number of variants of DE for permutative-based combinatorial problems. These DE variants are
presented by their initiators or proposers, to the best of our knowledge.
1.1
Introduction
Whether in industry or in research, users generally demand that a practical optimization
technique should fulfil three requirements:
1. the method should find the true global minimum, regardless of the initial system
parameter values;
2. convergence should be fast; and
3. the program should have a minimum of control parameters so that it will be easy to
use.
[2] invented the differential evolution (DE) algorithm in a search for a technique that
would meet the above criteria. DE is a method, which is not only astonishingly simple,
but also performs extremely well on a wide variety of test problems. It is inherently
parallel because it is a population based approach and hence lends itself to computation
via a network of computers or processors. The basic strategy employs the difference of
two randomly selected parameter vectors as the source of random variations for a third
parameter vector.
There are broadly speaking two types of real
world problems that may be solved:
1. those that are characterized by continuous parameters; and
2. those that are characterized by permutative-based combinatorial parameters..
This classification is important in the context of the motivation for this topic. The
original canonical DE which Storn and Price developed was designed to solve only
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