Non-linear Goal Programming Using Multi-Objective Genetic Algorithms

Goal programming is a technique often used in engineering de sign activities primarily to find a compromised solution which will simultaneously satisfy a numb er of design goals. In solving goal programming problems, classical methods reduce the multiple goalatt inment problem into a single objective of minimizing a weighted sum of deviations from goals. Moreove r, 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 programmi ng problem as a multi-objective optimization problem of minimizing deviations from individual goals. Th is procedure eliminates the need of having extra constraints needed with classical formulations and als o eliminates the need of any user-defined weight factor for each goal. The proposed technique can also solve g oal programming problems having nonconvex trade-off region, which are difficult to solve using c lassical methods. The efficacy of the proposed method is demonstrated by solving a number of non-linear tes t problems and by solving an engineering design problem. The results suggest that the proposed appro ch is an unique, effective, and most practical tool for solving goal programming problems.