BIOINSPIRED ALGORITHM FOR SOLVING INVARIANT GRAPH PROBLEMS

Abstract

A bioinspired method for solving a set of invariant combinatorial-logical problems on
graphs is proposed: the formation of a graph matching, the selection of an internally stable set of
vertices, and the selection of a graph clique. A modified paradigm of the ant colony is described,
which uses, in contrast to the canonical method, the mechanisms for generating solutions on the
search space model in the form of a star graph. The problem of forming an internally stable set of
vertices in a graph can be formulated as a partitioning problem. At the initial stage, the same
(small) amount of pheromone ξ/m, where m=|E|, is deposited on all edges of the star graph H.
The process of finding solutions is iterative. Each iteration l includes three stages. Agents have
memory. At each step t, the memory of the agent ak contains the amount of pheromone фj(t) deposited
on each edge of the graph H. At the first stage, each agent ak of the population uses a constructive
algorithm to find the solution Ur 0k, calculates the estimate of the solution ξk(Ur
0k) and the value of the degree of suitability of the solution obtained by the agent φk (the amount of pheromone corresponding to the estimate). At the second stage, after the complete formation of solutions
by all agents at the current iteration, the pheromone ωj accumulated in the j-th cell in the
CEPб buffer array is added to each j-th cell of the main array Q2={qj|j=1,2,…,m} of the CEP0
collective evolutionary memory. At the third stage, the general evaporation of the pheromone occurs
on the set of edges E of the star graph H. The time complexity of the algorithm, obtained experimentally,
coincides with theoretical studies and for the considered test problems is O(n2).