Adjacency based method for generating maximal efficient faces in multiobjective linear programming

Multiobjective linear optimization problems (MOLPs) arise when several linear objective functions have to be optimized over a convex polyhedron. In this paper, we propose a new method for generating the entire efficient set for MOLPs in the outcome space. This method is based on the concept of adjacencies between efficient extreme points. It uses a local exploration approach to generate simultaneously efficient extreme points and maximal efficient faces. We therefore define an efficient face as the combination of adjacent efficient extreme points that define its border. We propose to use an iterative simplex pivoting algorithm to find adjacent efficient extreme points. Concurrently, maximal efficient faces are generated by testing relative interior points. The proposed method is constructive such that each extreme point, while searching for incident faces, can transmit some local informations to its adjacent efficient extreme points in order to complete the faces’ construction. The performance of our method is reported and the computational results based on randomly generated MOLPs are discussed.