This paper compares four selection schemes used in genetic algorithms: proportionate reproduction, ranking selection, tournament selection, and Genitor (or "steady state") selection. The analysis is based on deterministic difference or differential equations, verified through computer simulations. The study provides approximate or exact solutions, convergence time estimates, and growth ratio calculations. It recommends practical applications of these analyses and suggests further research into selection techniques. The paper begins by discussing the importance of understanding the expected performance of selection schemes in genetic algorithms (GAs). It then introduces the concept of birth, life, and death equations, which describe the dynamics of population changes. These equations are used to model the expected performance of each selection scheme. Proportionate reproduction is analyzed by considering the expected number of copies of a class of individuals in the next generation. The analysis shows that proportionate reproduction can be modeled using deterministic difference equations, and the solutions agree well with computer simulations. The paper also discusses the time complexity of proportionate reproduction, showing that it can be implemented in O(n log n) time. Ranking selection is analyzed by considering the assignment of individuals based on their function values. The paper introduces the concept of assignment functions and uses them to derive difference equations for various ranking schemes. The analysis shows that linear ranking and binary tournament selection have similar expected performance. The paper also discusses the time complexity of ranking selection, showing that it can be implemented in O(n log n) time. Tournament selection is analyzed by considering the selection of individuals based on their function values. The paper shows that tournament selection can be modeled using deterministic difference equations, and the solutions agree well with computer simulations. The analysis also discusses the time complexity of tournament selection, showing that it can be implemented in O(n) time. Genitor selection is analyzed by considering the selection of individuals based on their function values. The paper shows that Genitor selection can be modeled using deterministic difference equations, and the solutions agree well with computer simulations. The analysis also discusses the time complexity of Genitor selection, showing that it can be implemented in O(n log n) time. The paper concludes by comparing the growth ratios, takeover times, and time complexity of the four selection schemes. It suggests that proportionate reproduction, ranking selection, and tournament selection have similar expected performance, while Genitor selection has a higher growth ratio but may require additional fixes such as large population sizes or multiple populations to avoid premature convergence. The paper also discusses the importance of balancing exploration and exploitation in GAs, and suggests that further research is needed to understand the optimal selection schemes for different problems.This paper compares four selection schemes used in genetic algorithms: proportionate reproduction, ranking selection, tournament selection, and Genitor (or "steady state") selection. The analysis is based on deterministic difference or differential equations, verified through computer simulations. The study provides approximate or exact solutions, convergence time estimates, and growth ratio calculations. It recommends practical applications of these analyses and suggests further research into selection techniques. The paper begins by discussing the importance of understanding the expected performance of selection schemes in genetic algorithms (GAs). It then introduces the concept of birth, life, and death equations, which describe the dynamics of population changes. These equations are used to model the expected performance of each selection scheme. Proportionate reproduction is analyzed by considering the expected number of copies of a class of individuals in the next generation. The analysis shows that proportionate reproduction can be modeled using deterministic difference equations, and the solutions agree well with computer simulations. The paper also discusses the time complexity of proportionate reproduction, showing that it can be implemented in O(n log n) time. Ranking selection is analyzed by considering the assignment of individuals based on their function values. The paper introduces the concept of assignment functions and uses them to derive difference equations for various ranking schemes. The analysis shows that linear ranking and binary tournament selection have similar expected performance. The paper also discusses the time complexity of ranking selection, showing that it can be implemented in O(n log n) time. Tournament selection is analyzed by considering the selection of individuals based on their function values. The paper shows that tournament selection can be modeled using deterministic difference equations, and the solutions agree well with computer simulations. The analysis also discusses the time complexity of tournament selection, showing that it can be implemented in O(n) time. Genitor selection is analyzed by considering the selection of individuals based on their function values. The paper shows that Genitor selection can be modeled using deterministic difference equations, and the solutions agree well with computer simulations. The analysis also discusses the time complexity of Genitor selection, showing that it can be implemented in O(n log n) time. The paper concludes by comparing the growth ratios, takeover times, and time complexity of the four selection schemes. It suggests that proportionate reproduction, ranking selection, and tournament selection have similar expected performance, while Genitor selection has a higher growth ratio but may require additional fixes such as large population sizes or multiple populations to avoid premature convergence. The paper also discusses the importance of balancing exploration and exploitation in GAs, and suggests that further research is needed to understand the optimal selection schemes for different problems.