Abstract. The paper considers a combinatorial object (a fragmentary structure) and investigates the properties of this object. It is shown that a number of discrete optimization problems can be considered as optimization problems on a fragmentary structure. Optimization problem reduces to an unconditional combinatorial optimization problem on a set of permutations. Variants of algorithms to find approximate solutions for optimization problems of fragmentary structure are proposed.

Keywords: discrete optimization, fragmentary structure, local algorithm, evolutionary algorithm, ant algorithm.