Efficient algorithms for optimization of objects and systems

Efficient algorithms are needed for optimization of objects and systems, because the user would like to be sure that the optimum is global. The paper shows a very well scalable discrete firefly algorithm, developed for solving a supplier selection problem. The built in general reduced gradient and evolutionary algorithms of the Excel solver are also compared solving this problem. The results show that the firefly algorithm solves the problem in the fragment of the running time of the evolutionary algorithm. In the second part of the article, a mathematical model was formulated to solve the fixed destination multidepot multiple tour multiple traveling salesmen problem (mdmMTSP)