MOSGA: A Multi Objective Version of Snow Geese Algorithm for Unconstrained and Constrained Optimization Problems

Snow Geese Algorithm is a newly developed nature-inspired metaheuristic algorithm that showed its superiority over other commonly used algorithms in solving various real-life optimization problems. However, the major drawback of this algorithm is its incapability to solve problems with multiple objectives. To get over this limitation, the work developed a crowding distance-based snow geese algorithm (MOSGA) for solving multiple objective problems. The algorithm assigns each individual to one of three groups-best, mediocre, or weak-mainly based on its dominance relative to other individuals. However, it utilizes crowding distance for grouping when individuals are non-dominant to each other. The proposed algorithm adopts a new strategy that uses the positions of individuals in the objective search space to update their locations during exploration. The algorithm has also employed two different mutation operators for updating positions of individuals during exploitation in addition to the traditional strategy. The algorithm is then applied to solve five unconstrained benchmark problems with two objectives, six unconstrained benchmark problems with three objectives, and four constrained benchmark problems with two objectives. During the investigation, four parameters, namely spacing, maximum spread, inverted generational distance, and generational distance, are used to evaluate the performance of the algorithm. Later, its performance is compared with the performance of two of the most popular algorithms, namely NSGA-II and MOPSO, and four of the latest metaheuristics, such as MOCrySA, MMRO, MBO, and MSMA. The comparison results revealed that MOSGA performs 13.68%, 35.42%, 32.72%, 42.46%, 22.02%, and 48.87% better overall than NSGA-II, MOPSO, MOCrySA, MMRO, MBO, and MSMA, respectively, in terms of generational distance. An overall improvement of 68.552%, 49.732%, 73.192%, 59.186%, 58.768% and 62.046% in inverted generational distance is observed using MOSGA in place of NSGA-II, MOPSO, MOCrySA, MMRO, MBO, and MSMA, respectively. The spacing results indicate the superiority of MOSGA, with an overall improvement of 22.87%, 35.7%, 57.38%, 64.05%, 32.29%, and 51.65% compared to NSGA-II, MOPSO, MOCrySA, MMRO, MBO, and MSMA, respectively. Additionally, it is observed that MOSGA achieves a maximum spread value of one in most cases. Moreover, the stochasticity of MOSGA is found to be less than all the compared algorithms. Lastly, the paired t-tests between MOSGA and other existing algorithms for all considered performance metrics reveal that MOSGA is a significantly better performer overall as compared to others.