This article deals with the problem of finding the maximum number of maximum cliques in a weighted graph with all edges between vertices from different d-division of a graph with the minimum total weight of all these cliques, and the problem of finding the maximum number of maximum cliques in a nonweighted graph with not all edges between vertices from different d-division of the graph. This article presents new ant algorithms with new desire functions for these problems. These algorithms were tested for their purpose with different changing input parameters, the test results were tabulated and discussed, the best algorithms were indicated.