We introduce two competitive strategies into conventional differential evolution (DE) to speed up its convergence by increasing competitive pressures among individuals and evaluate the proposals. The first strategy gives individuals with better fitness a higher opportunity for generating more offspring individuals, while conventional DE allows each parent individual to generate only one offspring individual fairly. This strategy compares each of poor individuals with a randomly selected individual from the current population. If the latter becomes a winner, the latter can generate one more offspring individual, but the former loses an opportunity for generating its offspring. If the former becomes a winner, no one loses this opportunity, and each of them generates one offspring individual. The second strategy does not compare a generated offspring individual with its parent but the worst individual in the current population, which can accelerate the elimination of poor individuals and keep better individuals. We design a set of controlled experiments to evaluate these two strategies using CEC2013 benchmark functions with three different dimensions. The experimental results indicate that properly enhancing competition among individuals in DE can speed up its convergence and improve optimization performance.