In the article the modified paradigm of bee colonies for hiking trails through the solution of combinatorial problems on graphs: the selection in the column independent subset of vertices of maximum pairing in column coloring graph, click in the selection box are studied. Based on the analysis of behavioral models of self colony of bees, methods and mechanisms of formation of the ideas are developed, the formation of combinatorial problems on graphs is discussed. Methods of forming search space are studied. Position in the search space is represented as an ordered list. The key operation of bee algorithm is promising research positions and their surroundings in the search space. In this paper, a method of forming neighborhood solutions with adjustable degree of similarity and closeness between them is suggested. We offer three approaches to determining the number of foragers agents who are sent around each base position.