The stable marriage problem with ties (SMT) is a variant of the stable marriage problem in which people are permitted to express ties in their preference lists. The problem have been received many attentions of researchers due to useful applications in practice. Many methods proposed for solving the problem are to only find a stable matching of a given instance. In this paper, we present a local search based algorithm which attempts to find egalitarian and sex-equal stable matchings. The algorithm is based on the dominance of stable matchings with respect to men. Particularly, starting at the man-optimal stable matching the algorithm processes through a sequence of stable matchings to seek the egalitarian and sex-equal stable matchings. For each a stable matching of the sequence, a neighbor set of is constructed using a breaking marriage operation. The best neighbor stable matching by means of a cost function is selected to continue the search. Experimental results show that our algorithm is significant.