Edge detection is the first step and very important step in image analysis. We cast edge detec¬tion as a problem in cost maximization. This is acheived by the formulation of a cost function that evaluates the quality of edge configurations. The cost function can be used as a basis for compar¬ing the performances of different detectors. We used a Genetic Algorithm for maximizing cost func¬tion. Genetic algorithms are a class of adaptive search techniques that have been intensively stud¬ied in recent years and have been prone to converge prematurely before the best solution has been found. This paper shows that carefully chosen modifications(three factors of the crossover opera¬tor) are implemented can be effective in alleviating this problem.