The major difficulty in applicability of genetic algorithms to various optimization problems is the lack of general methodology for handling constraints. This paper discusses a new such methodology and presents results from the experimental system GENOCOP (for GEnetic algorithm for Numerical Optimization for COnstrainted Problems). The system not only handles any objective function with any set of linear constraints, but also effectively reduces the search space. The results indicate that this approach is superior to traditional methods when applied to the nonlinear transportation problem.