Simulated binary crossover (SBX) is a real-parameter recombination operator which is commonly used in the evolutionary algorithm (EA) literature. The operator involves a parameter which dictates the spread of offspring solutions vis-a-vis that of the parent solutions. In all applications of SBX so far, researchers have kept a fixed value throughout a simulation run. In this paper, we suggest a self-adaptive procedure of updating the parameter so as to allow a smooth navigation over the function landscape with iteration. Some basic principles of classical optimization literature are utilized for this purpose. The resulting EAs are found to produce remarkable and much better results compared to the original operator having a fixed value of the parameter. Studies on both single and multiple objective optimization problems are made with success. Categories and Subject Descriptors I.2.8 [Computing Methodologies]: Problem Solving, Control Methods, and Search General Terms Algorithms Keyw...