Revised Simplex Algorithm Applied to Problems with Restrictions

Applied Researches in Technics, Technologies and Education, 2013, vol.2, pp.143-150
The simplex method is one of the most commonly used for solving linear optimization problems. In this work the problem is modeled using a dynamic data structure, which guarantees unlimited number of parameters for optimization. Due to the applied heuristic for choosing between equal elements for inclusion in the base set, it is possible to obtain a cyclic repetition of solutions. The later results in termination of the optimization process, because of reaching either a time limit or maximal number of iterations, but not an optimal solution in the chosen sense. The paper offers a bijective indexing of the basic solutions. The stored indexes form the history of the optimization process. The history allows for return at the beginning of the cycle formation and selection of an alternative basis. The algorithm is applied in some software packages for optimizing animal feed and feed rations of animals and humans. Future applications will be associated with processing and analysis of images.