Dispatching rules are extensively addressed in the dynamic job shop scheduling literature and are commonly adopted in many industrial practices. The manual design of dispatching rules is a tedious process that requires a great deal of time and experience. Due to the growth in computational power, the design process is automated using various machine learning and optimization techniques to evolve superior dispatching rules compared to human-made ones. Genetic Programming (GP) is one of the most promising approaches in the field of automated design of scheduling rules, especially under dynamic conditions. Considering a large set of terminals that reflects various job and machine attributes helps GP to obtain efficient rules, but in return extends the search space. Also, the impact of terminals can vary greatly among various scenarios, objective functions, and evolutionary stages. Therefore, an efficient feature selection mechanism can support the GP searching ability by eliminating irrelevant terminals and facilitating the process of high-quality rule search by focusing more on the promising regions in the search space. In this paper, we propose a new representation for the GP individuals that reflects the importance of each terminal in this rule. Also, an adaptive feature selection mechanism is developed that uses the information gained from the previous evolutionary step in restricting the search space at the current generation. Experimental results show that the proposed approaches assist the GP to obtain compact rules in a shorter computational time without sacrificing the performance compared with the standard GP algorithm and another representation from the literature.