By Georgiev P., Pardalos P., Theis F.
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Therefore x1 ≻ x2 ⇔ cmpF (x1 , x2 ) < 0. Modeling and Simulating While there are a lot of problems where the objective functions are mathematical expressions that can directly be computed, there exist problem classes far away from such simple function optimization that require complex models and simulations. 45 (Model). A model41 is an abstraction or approximation of a system that allows us to reason and to deduce properties of the system. Models are often simpliﬁcations or idealization of real-world issues.
26) The Connection between Search and Problem Space If the search space diﬀers from the problem space, a translation between them is furthermore required. In our car example we would need to transform the binary strings processed by the genetic algorithm to objects which represent the corresponding car conﬁgurations and can be processed by the objective functions. 30 (Genotype-Phenotype Mapping). 7 on page 413) which maps the elements of search space G to elements in the problem space X. 27) 26 1 Introduction 0 0 0 0 0 0 0 1 0 0 1 0 ...
The solution candidates that are not able to fulﬁll any of the goals succumb to those which fulﬁll at least some goals. • Only the solutions that are in the same group are compared on basis on the Pareto domination relation. By doing so, the optimization process will be driven into the direction of the interesting part of the Pareto frontier. Less eﬀort will be spent in creating and evaluating individuals in parts of the problem space that most probably do not contain any valid solution. 10, we apply the Method of Inequalities to our ﬁrst graphical example.