CS 495: Evolutionary Computation, Fall 2002 Instructor: Jeffrey Horn
(2) PROBLEM ENCODINGS
SIZE-K SUBSET SELECTION:
Consider subselection problems such as the groundwater monitoring problem, where the task is to fplace K monitors in the optimal subset of K monitoring wells. In general, given a set S of M distinct items (e.g. monitoring wells), choose some subset s of fixed size K, where 0 <= K <= M, such that some function, f(s) is optimized.
The most common binary encoding used for this subset selection is a "binary selection vector" (BSV)in which the M bits stand for elements of S from 0 to M-1, and the ith bit represents the membership of the ith element. Thus for a small set of 4 elements, where M=4 and K =2, the binary string 0101 means that elements 1 and 3 are included in the subset, while elements 0 and 2 are excluded.
But the BSV encoding has never really worked well, especially for the fixed size K subset selection we are discussing. One major problem is that a single bit-wise mutation will result in an invalid chromosome (one too many or one too few elements in the subset). Most crossovers will also generate invalid chromosomes. Now, these can be repaired using chromosome repair mechanisms, but these add complexity.
Can you come up with an alternative encoding? Keep it to a binary string, but try to improve on the "common" encoding above. Describe your idea!