Non-linear Goal Programming Using Multi-Objective Genetic Algorithms

Goal programming is a technique often used in engineering design activities primarily to find a compromised solution which will simultaneously satisfy a number of design goals. In solving goal programming problems, classical methods reduce the multiple goal-attainment problem into a single objective of minimizing a weighted sum of deviations from goals. Moreover, in tackling non-linear goal programming problems, classical methods use successive linearization techniques, which are sensitive to the chosen starting solution. In this paper, we pose the goal programming problem as a multi-objective optimization problem of minimizing deviations from individual goals. This procedure eliminates the need of having extra constraints needed with classical formulations and also eliminates the need of any user-defined weight factor for each goal. The proposed technique can also solve goal programming problems having nonconvex trade-off region, which are difficult to solve using classical methods. The efficacy of the proposed method is demonstrated by solving a number of non-linear test problems and by solving an engineering design problem. The results suggest that the proposed approach is an unique, effective, and most practical tool for solving goal programming problems.