A Heuristic Algorithm for Nonlinear Lexicography Goal Programming with an Efficient Initial Solution

In this paper,  a heuristic algorithm is proposed in order to solve a nonlinear lexicography goal programming (NLGP) by using an efficient initial point. Some numerical experiments showed that the search quality by the proposed heuristic in a multiple objectives problem depends on the initial point features, so in the proposed approach the initial point is retrieved by Data Envelopment Analysis to be selected as an efficient solution. There are some weaknesses in classic NLGP algorithm that lead to trapping into the local optimum, so a simulated annealing concept is implemented during the searching stage to increase the diversity of search in the solution space. Some numerical examples with different sizes were generated and comparison of results confirms that the proposed solution heuristic is more efficient than the classic approach. Moreover the proposed approach was extended for cases with ordinal weights of inputs or outputs. The computational experiments for 5 numerical instances and the statistical analysis indicate that the proposed heuristic algorithm is a robust procedure to find better preferred solution comparing to the classic NLGP.