Hybrid Mesh Adaptive Direct Search and Genetic Algorithms for solving fuzzy non-linear optimization problems

In this paper, computational and simulation results are presented for the performance of the fitness function, decision variables and CPU time of the proposed hybridization method of Mesh Adaptive Direct Search (MADS) and Genetic Algorithm (GA). MADS is a class of direct search algorithms for nonlinear optimization. The MADS algorithm is a modification of the Pattern Search (PS) algorithm. The algorithms differ in how the set of points forming the mesh is computed. The PS algorithm uses fixed direction vectors, whereas the MADS algorithm uses random selection of vectors to define the mesh. A key advantage of MADS over PS is that local exploration of the space of variables is not restricted to a finite number of directions (poll directions). This is the primary drawback of PS algorithms, and therefore the main motivation in using MADS to solve the industrial production planning problem is to overcome this restriction. A thorough investigation on hybrid MADS and GA is performed for the quality of the best fitness function, decision variables and computational CPU time.