Limits...
An algorithm for efficient constrained mate selection.

Kinghorn BP - Genet. Sel. Evol. (2011)

Bottom Line: Mate selection can be used as a framework to balance key technical, cost and logistical issues while implementing a breeding program at a tactical level.The resulting mating lists accommodate optimal contributions of parents to future generations, in conjunction with other factors such as progeny inbreeding, connection between herds, use of reproductive technologies, management of the genetic distribution of nominated traits, and management of allele/genotype frequencies for nominated QTL/markers.The much higher speed of the method presented here extends the use of mate selection and enables implementation in relatively large programs across breeding units.

View Article: PubMed Central - HTML - PubMed

Affiliation: School of Environmental and Rural Science, Universiy of New England, Armidale, NSW 2350, Australia. bkinghor@une.edu.au

ABSTRACT

Background: Mate selection can be used as a framework to balance key technical, cost and logistical issues while implementing a breeding program at a tactical level. The resulting mating lists accommodate optimal contributions of parents to future generations, in conjunction with other factors such as progeny inbreeding, connection between herds, use of reproductive technologies, management of the genetic distribution of nominated traits, and management of allele/genotype frequencies for nominated QTL/markers.

Methods: This paper describes a mate selection algorithm that is widely used and presents an extension that makes it possible to apply constraints on certain matings, as dictated through a group mating permission matrix.

Results: This full algorithm leads to simpler applications, and to computing speed for the scenario tested, which is several hundred times faster than the previous strategy of penalising solutions that break constraints.

Conclusions: The much higher speed of the method presented here extends the use of mate selection and enables implementation in relatively large programs across breeding units.

Show MeSH
Fitness of the best solution by generation of the DE algorithm for different strategies. This figure censors results for those strategies and generations in which the best solution breaks a constraint, and this is seen as gaps in the plot for each strategy; the right-hand graph gives generation on a logarithmic scale to help differentiate the strategies; the strategies are GroupFix and the four penalising strategies denoted by their penalty weighting, Pen, as labelled on the right-hand graph. Strategies Pen = 0.01 and Pen = 0.005 cross over at about generation 150,000.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3037843&req=5

Figure 3: Fitness of the best solution by generation of the DE algorithm for different strategies. This figure censors results for those strategies and generations in which the best solution breaks a constraint, and this is seen as gaps in the plot for each strategy; the right-hand graph gives generation on a logarithmic scale to help differentiate the strategies; the strategies are GroupFix and the four penalising strategies denoted by their penalty weighting, Pen, as labelled on the right-hand graph. Strategies Pen = 0.01 and Pen = 0.005 cross over at about generation 150,000.

Mentions: Figure 3 shows fitness of the best solution by generation of the DE algorithm for each strategy, with a weighting of -1 for progeny inbreeding. The best solution in the first generation of the evolutionary algorithm for the Groupfix method gave values of 7.30, 0.0054 and 0.0076 for the mean progeny index, mean progeny inbreeding and mean parental coancestry, with the latter figure being low due to essential panmixia. In generation one million of the Groupfix algorithm, these figures were 10.53, 0.0021 and 0.0485. The GroupFix strategy converged essentially after about 100,000 generations, when it had reached 99.5% of the fitness from generation one million compared to the fitness from generation one (itself the best of 50 randomly generated legal solutions). This stage was reached in 3559 seconds on a 2.4 GHz laptop computer. At this stage, the best penalising strategy was 78.5% converged, which was reached by the GroupFix strategy by generation 216. None of the penalising strategies converged even close to the optimal solution after one million generations of the DE algorithm, with regular small improvements still being made up to that stage. Of course the optimal solution and maximal fitness are the same for all strategies, illustrating that the penalising strategies performed very badly indeed. In fact, the best of these strategies at one million generations (23,327 CPU seconds) had a lower fitness than the GroupFix strategy had reached by generation 1057 (29 CPU seconds).


An algorithm for efficient constrained mate selection.

Kinghorn BP - Genet. Sel. Evol. (2011)

Fitness of the best solution by generation of the DE algorithm for different strategies. This figure censors results for those strategies and generations in which the best solution breaks a constraint, and this is seen as gaps in the plot for each strategy; the right-hand graph gives generation on a logarithmic scale to help differentiate the strategies; the strategies are GroupFix and the four penalising strategies denoted by their penalty weighting, Pen, as labelled on the right-hand graph. Strategies Pen = 0.01 and Pen = 0.005 cross over at about generation 150,000.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3037843&req=5

Figure 3: Fitness of the best solution by generation of the DE algorithm for different strategies. This figure censors results for those strategies and generations in which the best solution breaks a constraint, and this is seen as gaps in the plot for each strategy; the right-hand graph gives generation on a logarithmic scale to help differentiate the strategies; the strategies are GroupFix and the four penalising strategies denoted by their penalty weighting, Pen, as labelled on the right-hand graph. Strategies Pen = 0.01 and Pen = 0.005 cross over at about generation 150,000.
Mentions: Figure 3 shows fitness of the best solution by generation of the DE algorithm for each strategy, with a weighting of -1 for progeny inbreeding. The best solution in the first generation of the evolutionary algorithm for the Groupfix method gave values of 7.30, 0.0054 and 0.0076 for the mean progeny index, mean progeny inbreeding and mean parental coancestry, with the latter figure being low due to essential panmixia. In generation one million of the Groupfix algorithm, these figures were 10.53, 0.0021 and 0.0485. The GroupFix strategy converged essentially after about 100,000 generations, when it had reached 99.5% of the fitness from generation one million compared to the fitness from generation one (itself the best of 50 randomly generated legal solutions). This stage was reached in 3559 seconds on a 2.4 GHz laptop computer. At this stage, the best penalising strategy was 78.5% converged, which was reached by the GroupFix strategy by generation 216. None of the penalising strategies converged even close to the optimal solution after one million generations of the DE algorithm, with regular small improvements still being made up to that stage. Of course the optimal solution and maximal fitness are the same for all strategies, illustrating that the penalising strategies performed very badly indeed. In fact, the best of these strategies at one million generations (23,327 CPU seconds) had a lower fitness than the GroupFix strategy had reached by generation 1057 (29 CPU seconds).

Bottom Line: Mate selection can be used as a framework to balance key technical, cost and logistical issues while implementing a breeding program at a tactical level.The resulting mating lists accommodate optimal contributions of parents to future generations, in conjunction with other factors such as progeny inbreeding, connection between herds, use of reproductive technologies, management of the genetic distribution of nominated traits, and management of allele/genotype frequencies for nominated QTL/markers.The much higher speed of the method presented here extends the use of mate selection and enables implementation in relatively large programs across breeding units.

View Article: PubMed Central - HTML - PubMed

Affiliation: School of Environmental and Rural Science, Universiy of New England, Armidale, NSW 2350, Australia. bkinghor@une.edu.au

ABSTRACT

Background: Mate selection can be used as a framework to balance key technical, cost and logistical issues while implementing a breeding program at a tactical level. The resulting mating lists accommodate optimal contributions of parents to future generations, in conjunction with other factors such as progeny inbreeding, connection between herds, use of reproductive technologies, management of the genetic distribution of nominated traits, and management of allele/genotype frequencies for nominated QTL/markers.

Methods: This paper describes a mate selection algorithm that is widely used and presents an extension that makes it possible to apply constraints on certain matings, as dictated through a group mating permission matrix.

Results: This full algorithm leads to simpler applications, and to computing speed for the scenario tested, which is several hundred times faster than the previous strategy of penalising solutions that break constraints.

Conclusions: The much higher speed of the method presented here extends the use of mate selection and enables implementation in relatively large programs across breeding units.

Show MeSH