Benson's algorithm
Benson's algorithm, named after Harold Benson, is a method for solving multi-objective linear programming problems and vector linear programs.  This works by finding the "efficient extreme points in the outcome set".  The primary concept in Benson's algorithm is to evaluate the upper image of the vector optimization problem by cutting planes.

Idea of algorithm 
Consider a vector linear program

for , ,  and a polyhedral convex ordering cone  having nonempty interior and containing no lines. The feasible set is . In particular, Benson's algorithm finds the extreme points of the set , which is called upper image.

In case of , one obtains the special case of a multi-objective linear program (multiobjective optimization).

Dual algorithm 
There is a dual variant of Benson's algorithm, which is based on geometric duality for multi-objective linear programs.

Implementations 
Bensolve - a free VLP solver
 www.bensolve.org
Inner
 Link to github

References 

Linear programming
Optimization algorithms and methods