In this paper we consider a sex-fair matching in the stable marriage problem. The sex-fair stable matching defined in this paper has a property that the sum of the partner's rank of each man in his preference list is as close as possible to the sum of the partner's rank of each woman in her preference list. We transform the sex-fair marriage problem into a graph problem which is suitable for a genetic algorithm. We propose a genetic algorithm for the sex-fair stable matching. The transformation into the graph problem makes application of the GA easier and effective. Computer experiments show the effectiveness of the proposed genetic algorithm.

This paper studies the problem of scheduling a set of n independent tasks on m identical processors so as to minimize mean weighted flow-time. The problem is known to be NP-complete for $m \geqq 2$ and to be NP-complete in the strong sense for m arbitrary. The worst case behavior of a heuristic algorithm which requires time $O(n\log n)$ is investigated, and it is shown that the mean weighted flow-time obtained by the algorithm does not exceed ${{(\sqrt 2 + 1)} / 2} \cong 1.0207$ times that of an optimal schedule. Moreover the bound ${{(\sqrt 2 + 1)} / 2}$ is best possible.