Momentum search algorithm: a new meta-heuristic optimization algorithm inspired by momentum conservation law

Abstract

A novel optimization methodology, Momentum Search Algorithm (MSA) is presented based on Newton’s laws: the law of conservation of momentum. It includes a set of masses in a closed system considering the conservation of momentum and kinetic energy of bodies. The possible solutions are presented by system bodies’ positions in an n-dimensional space. The mass of bodies is proportional to their fitness function. Larger masses represent the better solutions. At each iteration, an external body collides separately with all solution bodies and moves them toward the optimum solution. The direction of the collision depends on the position of solution bodies and the position of the body with the best fitness function. As the better solutions have heavier bodies, the external body has less effect on their positions. On the other hand, the worse solutions are lighter and moved easily by the external body toward the better positions. The best position is achieved by allowing the external body to move the solution bodies toward better positions. The numerical results obtained from several standard benchmark test functions indicate the superiority of the proposed method over many other optimization techniques such as Genetic Algorithm, Particle Swarm Optimization, Gravitational Search Algorithm, Teaching–Learning-Based Optimization, Grey Wolf Optimizer, Grasshopper Optimization Algorithm, Spotted Hyena Optimizer, and Emperor Penguin Optimizer.