Mathematical Interpretation between Genotype and Phenotype Spaces and Induced Geometric Crossovers

In this paper, we present that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. Quotient space can be considered as mathematically-defined phenotype space in the evolutionary computation theory. The quotient geometric crossover has the effect of reducing the search space actually searched by geometric crossover, and it introduces problem knowledge in the search by using a distance better tailored to the specific solution interpretation. Quotient geometric crossovers are directly applied to the genotype space but they have the effect of the crossovers performed on phenotype space. We give many example applications of the quotient geometric crossover

A Mathematical Unification of Geometric Crossovers Defined on Phenotype Space

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. This paper is motivated by the fact that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. In this paper, we study a metric transformation, the quotient metric space, that gives rise to the notion of quotient geometric crossover. This turns out to be a very versatile notion. We give many example applications of the quotient geometric crossover

CSM-467: Quotient Geometric Crossovers

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. In previous work we have started studying how metric transformations of the distance associated with geometric crossover affect the original geometric crossover. In particular, we focused on the product of metric spaces. This metric transformation gives rise to the notion of product geometric crossover that allows to build new geometric crossovers combining pre-existing geometric crossovers in a simple way. In this paper, we study another metric transformation, the quotient metric space, that gives rise to the notion of quotient geometric crossover. This turns out to be a very versatile notion. We give many examples of application of the quotient geometric crossover

Accounting for Recent Changes of Gain in Dealing with Ties in Iterative Methods for Circuit Partitioning

In iterative methods for partitioning circuits, there is often a choice among several modules which will all produce the largest available reduction in cut size if they are moved between subsets in the partition. This choice, which is usually made by popping modules off a stack, has been shown to have a considerable impact on performance. By considering the most recent change in the potential reduction in cut size associated with moving each module between subsets, the performance of this LIFO (last-in first-out) approach can be significantly improved

Graph Partitioning-Based Coordination Methods for Large-Scale Multidisciplinary Design Optimization Problems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97127/1/AIAA2012-5522.pd