What is Non-Linear Programming

In this chapter, three meta-heuristic optimization techniques have been utilized to solve the fuzzy programming problems in industrial production systems. This chapter outlines an introduction to real-world industrial problem for product-mix selection involving eight variables and 21 constraints with fuzzy technological coefficients and thereafter, a formulation for an optimization approach to solve the problem. This problem occurs in production planning in which a decision maker plays a pivotal role in making decision under fuzzy environment. Decision-maker should be aware of his/her level of satisfaction as well as degree of fuzziness while making the product-mix decision. Genetic algorithms, pattern search, and mesh adaptive direct search methods have been employed to solve the large scale problems in real world industrial sector. The results for these techniques have been investigated thoroughly in the form of 2D, 3D plots, and tables. The industrial production planning problem which was illustrated in this chapter was solved successfully by these three meta-heuristic methods. The results are analyzed along with the optimal profit function (objective or fitness function) with level of satisfaction, decision variables, vagueness factor, and computational time (CPU).