An Iterative Vertex Enumeration Method for Objective Space Based Vector Optimization Algorithms.

An application area of vertex enumeration problem (VEP) is the usage withinobjective space based linear/convex vector optimization algorithms whose aimis to generate (an approximation of) the Pareto frontier. In such algorithms,VEP, which is defined in the objective space, is solved in each iteration andit has a special structure. Namely, the recession cone of the polyhedron to begenerated is the ordering cone. We consider and give a detailed descriptionof a vertex enumeration procedure, which iterates by calling a modified`double description (DD) method' that works for such unbounded polyhedrons. Weemploy this procedure as a function of an existing objective space basedvector optimization algorithm (Algorithm 1); and test the performance of itfor randomly generated linear multiobjective optimization problems. We comparethe efficiency of this procedure with another existing DD method as well aswith the current vertex enumeration subroutine of Algorithm 1. We observe thatthe modified procedure excels the others especially as the dimension of thevertex enumeration problem (the number of objectives of the correspondingmultiobjective problem) increases.