Method for solving nonlinear goal programming with interval coefficients using genetic algorithm

Traditional formulations on reliability optimization problems have assumed that the coefficients of models are known as fixed quantities and reliability design problem is treated as deterministic optimization problems. Because that the optimal design of system reliability is resolved in the same stage of overall system design, model coefficients are highly uncertainty and imprecision during design phase and it is usually very difficult to determine the precise values for them. However, these coefficients can be roughly given as the intervals of confidence.

In this paper, we formulated reliability optimization problem as nonlinear goal programming with interval coefficients and develop a genetic algorithm to solve it. The key point is how to evaluate each solution with interval data. We give a new definition on deviation variables which take interval relation into account. Numerical example is given to demonstrate the efficiency of the proposed approach.