Multiobjective Fitness Functions for Stable Marriage Problem using Genetic Algrithm

Abstract

In this paper we propose a genetic algorithm (GA)-based approach to find out stable matchings in the stable marriage problem depending on different criteria such as stable matching with man-optimal, woman-optimal, egalitarian and sex-fair. The stable marriage problem is an extensively-studied combinatorial problem with many practical applications. Gale-Shapley (GS) algorithm is well known by which the stable matching found is extremal among many (for the worst case, in exponential order) stable matchings. So that Gale-Shapley algorithm can only search the man-optimal (or woman-pessimal) stable matching. The proposed algorithm has been evaluated by simulation experiment compared to other existing algorithms. It has been found that the proposed algorithm is quite efficient in finding stable matchings depending on different criteria.

Two-Sided Matching with Indifferences: Using Heuristics to Improve Properties of Stable Matchings

“…Aldershof and Carducci (1999) describe a GA to compute stable solutions from random initial assignments, with stability as the sole objective. Furthermore, both Vien and Chung (2006) and Kimbrough and Kuo (2010) compare a GA with multiple objectives to the standard algorithms, yet neither of them consider indifferences in preferences. However, when indifferences are allowed finding either AMR-optimal or fairness-optimal stable solutions becomes NP-hard (Manlove et al 2002), and the corresponding scenario is referred to as Stable Matching with Ties (SMT).…”

“…Axtell and Kimbrough (2008) discuss trade-offs between stability and matched ranks; Klaus and Klijn (2006b) study (procedural) fairness and stability; and Iwama et al (2010) propose an algorithm that approximately yields the fairness-best stable matching. Other approaches that look at different or multiple objectives for certain matching problems include (Vien and Chung 2006;Klaus and Klijn 2006a); (Pais 2008;Pini et al 2011); and (Boudreau 2011) which also consider economic criteria such as matched ranks.…”

Finding optimal mentor-mentee matches: A case study in applied two-sided matching

“…For this specific case, approximation algorithms have been developed that provide lower-bound quality guarantees for the solutions [11] , [10] , [12] . In addition, other approaches that aim to increase the solution quality are heuristics such as Genetic Algorithms with multi-objective target functions [19] , [20] , [7] . While heuristics do not provide lower bound quality guarantees, they have been shown to work well on average and offer the flexibility to optimize multiple solution criteria simultaneously.…”

On heuristics for two-sided matching

“…Two-sided matching problems, and the stable marriage problem in particular, have received exploratory investigation as dual objective problems in [2], [7] and in [20]. Aldershof and Carducci [1] report optimistically on application of a genetic algorithm to two-sided matching problems, but the problems they examine are smaller than the 20×20 problems discussed here, so they do no address scaling issues.…”