Cone Decomposition for the Solution of Efficient Extreme Points in Parallel

Abstract

The solution of a multiple objective linear program (MOLP) is often characterized by the enumeration of all efficient extreme points. Unfortunately, the larger the problem, the larger the number of efficient extreme points and the longer the computation time required. Using vector maximum algorithms, the set of efficient extreme points is effectively enumerated by maximizing LPs whose objective function gradients point into the relative interior of the criterion cone (cone generated by strictly positive linear combinations of the gradients of the MOLP objective functions). In this way, each efficient extreme point can be associated with a conal subset of the criterion cone. In this paper, we present a divide and conquer routine for computing efficient extreme points by decomposing the criterion cone into subsets and then solving the sub-problems associated with these subset criterion cones in parallel. Computational results are also reported.