Optimal selection for multiple quantitative trait loci and contributions of individuals using genetic algorithm

Two methods (Scheme A and Scheme B) were developed to optimize the relative weights on quantitative trait loci (QTL) and contributions of selected individuals simultaneously to maximize selection response while constraining the rate of inbreeding to the rate observed in gene assisted selection (GAS). In Scheme A, both the relative weights give to QTL and contributions of the selected individuals were optimized using a genetic algorithm. The possible solutions for relative weights of QTL and contributions of the selected individuals were encoded simultaneously. A physical selection population was used to evaluate the fitness of each encoded solution using stochastic simulation with 50 replicates. The fitness of each solution was the mean of all replicates for accumulative discounted sum of genetic means of all generations in physical selection population. In Scheme B, the optimization for relative weights on QTL was similar to Scheme A, and also was implemented based on a genetic algorithm. However, unlike Scheme A, an optimal contribution algorithm (OC) was used to optimize contributions of selection candidates. When compared with GAS, Schemes A and B resulted in up to 15.88 and 22.26% extra discounted sum of genetic value of all generations in a long planning horizon, respectively. Compared GAS+OC and Scheme B, most of the increase (about 78%) in genetic gain was produced by only optimizing contributions of selected individuals. The optimization for relative weight given to QTL just avoided the long-term loss (about 22%) observed in GAS scheme.