Evolutionary Algorithms for Solving Multi-Objective Problems by Carlos A. Coello Coello, David A. Van Veldhuizen, Gary B.

By Carlos A. Coello Coello, David A. Van Veldhuizen, Gary B. Lamont (auth.)

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This genotype defines an individual organism when 5 Although GP and learning classifier systems may be classified as EA techniques. , 1997). 6There is no shortage of introductory EA texts. The general reader is referred to Goldberg (1989), Michalewicz (1996) or Mitchell (1996). A more technical presentatio,n is given by Back (1996). 22 EAS FOR SOLVING MULTI-OBJECTIVE PROBLEMS Locus (Position) Population 12345678910 1 o 1 1 1 1 o 0 1 0 -- Chromosome (String) 1 010 o 0 1 1 1 0 -- Chromosome (String) 1 0 o 1 1 1 1 1 0 o0 o 1 o0 1 0 1 1 1 1 .

A more technical presentatio,n is given by Back (1996). 22 EAS FOR SOLVING MULTI-OBJECTIVE PROBLEMS Locus (Position) Population 12345678910 1 o 1 1 1 1 o 0 1 0 -- Chromosome (String) 1 010 o 0 1 1 1 0 -- Chromosome (String) 1 0 o 1 1 1 1 1 0 o0 o 1 o0 1 0 1 1 1 1 . 12. 3964 Allele (Value) =1 Generalized EA Data Structure and Terminology it is expressed (decoded) into a phenotype. A genotype is composed of one or more chromosomes, where each chromosome is composed of separate genes which take on certain values (alleles) from some genetic alphabet.

32 EAS FOR SOLVING MULTI-OBJECTIVE PROBLEMS The displaced ideal technique (Zeleny, 1977) which proceeds to define an ideal point, a solution point, another ideal point, etc. is an extension of compromise programming. Another variation of this technique is the method suggested by Wierzbicki (1978;1980) in which the global function has a form such that it penalizes the deviations from the so-called reference objective. Any reasonable or desirable point in the space of objectives chosen by the decision maker can be considered as the reference objective.

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