2019/07/20 by İrfan Caner Kaya, Kaya, Irfan Caner, Fırdevs Ulus +1
Decision Sciences · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1907.08813
openalex publication_date 2019/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An application area of vertex enumeration problem (VEP) is the usage within\nobjective space based linear/convex vector optimization algorithms whose aim\nis to generate (an approximation of) the Pareto frontier. In such algorithms,\nVEP, which is defined in the objective space, is solved in each iteration and\nit has a special structure. Namely, the recession cone of the polyhedron to be\ngenerated is the ordering cone. We consider and give a detailed description\nof a vertex enumeration procedure, which iterates by calling a modified\n`double description (DD) method' that works for such unbounded polyhedrons. We\nemploy this procedure as a function of an existing objective space based\nvector optimization algorithm (Algorithm 1); and test the performance of it\nfor randomly generated linear multiobjective optimization problems. We compare\nthe efficiency of this procedure with another existing DD method as well as\nwith the current vertex enumeration subroutine of Algorithm 1. We observe that\nthe modified procedure excels the others especially as the dimension of the\nvertex enumeration problem (the number of objectives of the corresponding\nmultiobjective problem) increases.\n