Hybrid Multi-Gradient Pathfinder (HMGP) algorithm is a new multi-objective optimization algorithm which combines elements of MGP (Multi-Gradient Pathfinder) algorithm with elements of genetic algorithms (GA).

The main idea of the HMGP algorithm is the following: HMGP steps along a Pareto frontier in a similar way as MGP does, but periodically performs a GA-based iteration with random mutation based on archived Pareto optimal points. If a random mutation brings a dominating point then the point is declared as current point, and HMGP makes next gradient-based step from the point. Essentially, HMGP jumps on the dominating Pareto frontier as soon as it found first dominating point belonging to the frontier, and continues stepping along the dominating Pareto frontier. If the task has multiple Pareto frontiers (or multiple disjoint areas on the Pareto frontier) then HMGP sequentially steps from one Pareto frontier to another one until it finds global Pareto frontier. HMGP stops when it finds the best point on the global Pareto front with respect to preferable objective(s), or when maximum number of model evaluations is exceeded.