FEATURES OF METAHEURISTIC METHODS

Abstract

The essence of tasks and classification, as well as the necessity of fulfillment of conditions and relations on the set are analyzed. The properties of the equivalence relation are specified. As elementary fragments are analyzed all edges of the graph. The conditions of attachment of an edge are the next: this edge is a ray of an existing star or has no common vertices with already constructed stars of coverage. Emphasis is placed on the lack of optimality of such a solution. The aim of this work is to construct metaheuristics for finding a suboptimal classification defined by a tolerance relation on a finite set. This approach allows one to construct partitions close to optimal sets in accordance with the relation of “proximity” of elements. Moreover, this relationship of proximity is not transitive. The proposed algorithms can find wide application in applied problems related to the problem of object classification by a number of attributes. Such problems often arise in the economic, social and technical sciences. The urgency of the fragmentary structure of the problem was emphasized. Specifies the ability to build classes by looking at the entire list of objects that are classified in a specific order. On the basis of fragmentary structure it is proposed to use evolutionary algorithm. The prospect of using a genetic algorithm to find the best classifications was evaluated. The step-by-step sequence of operations of the genetic algorithm with examples is shown: selection, crossing, mutation, selection. Examples of key operators are given, named crossovers and mutations. A detailed algorithm of the evolutionary model is clearly illustrated. The principle of action of the evolutionary fragmentary algorithm is described in detail. As a set of feasible solutions, a subset of maximal fragments on a given fragmentary structure is considered. The mechanism of checking the quality of the genetic algorithm on a fragmentary structure, which reduces to a lot of variants, is defined. The problem of finding optimal classifications on a finite set is investigated. It is shown that the problem of finding the optimal classification generated by the tolerance relation on a finite set is reduced to the problem of optimization on the set of permutations. A modification of the method of mixed jumping frogs for finding suboptimal solutions of the classification problem is proposed.