"정수계획모형과 완화 기법을 활용한 사관학교 생활관 배정 알고리즘"

Abstract

Purpose The problem addressed in this paper is to find the optimal roommate assignment which maximizes the total expected compatibility between cadets. Methods Two integer linear programming models are proposed. Since the branch-and-bound method of a typical solver cannot scale in terms of the number of cadets, we develop heuristics that recover a feasible solution using a fractional solution of the semidefinite relaxation models. Results When the number of cadets is less than 36 and rooms are homogeneous, branch-and-bound methods successfully solve the problem. The proposed heuristics also outperform the existing heuristics in terms of the relaxation gap. Conclusion Mathematical models are developed for the roommate assignment problem with various preferences of traits within roommates. Computational results also show that our proposed heuristics can find a decent quality of feasible solutions in a relatively short time.