Substitution Tasks Method for Discrete Optimization

The aim of the paper is to present a novel heuristic optimization method for discrete dynamic optimization problems. The method has been named substitution tasks method (ST method). According to the method, a solution is generated by means of sequence of dynamically created local optimization tasks so-called substitution tasks. The method is based on formal algebraic-logical meta model of multistage decision process (ALMM of MDP), that is given in the paper. The paper presents a formal approach for designing constructive algorithms that are based on the method. A general idea of creating substitution tasks for different optimization problems is given. Then creation of substitution tasks, based on automatic analisys of set of non-admissible states is proposed. To illustrate the presented ideas, a scheduling algorithm for a particular NP-hard problem is given and results of computer experiments are presented.