An Optimal Solution for the Stable Marriage Problem using Particle Swarm Optimization and Firefly Algorithms

Abstract

This paper proposes a hybrid approach to solving the Stable Marriage Problem (SM) by fusing ideas from the firefly optimization (FA) and particle swarm optimization (PSO) methods. It is commonly known that there is always at least one stable matching exists for each instance. The conventional Gale-Shapley formula, on the other hand, produces a partnership that either strongly favours men over women or vice versa. Our proposed approach uses a hybrid optimization technique to solve the problem of stable marriage by providing the best possible pairs. The fitness function is defined here on the basis of the type of optimal solution. To categorize the kind of optimal solution two score functions are defined in this work.The proposed research uses FA to explore the undiscovered solution space, in contrast to our suggested technique which is based on PSO. The particles are then subjected to a dynamic adaptation mechanism for certain parameters, which gradually raises their values as part of the process of determining the velocities. The generation number of the swarm is the dynamic value for these parameters. These two parameters will use their predetermined values for the remaining particles in the swarm. It's worth noting that the dynamic values will be used by different particles in each generation. The proposed method is found to be superior than the conventionaltechniques in terms of the performance scores representing the quality of matching for different types of optimal solutions.