@misc{Chu1992, author = {Chu, Nguyen Ngoc}, title = {An Algorithm for Optimizing a Linear Function over the Integer Efficient Set.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-930}, number = {SC-92-23}, year = {1992}, abstract = {Whereas optimization of a linear function over an efficient set is a favourite topic for theoretical studies, the problem (\$P^I\$) of finding a maximal value of a linear function \$dx\$ over an integer efficient set is still open. The problem (\$P^I\$) is NP-hard and it is very unlikely that the maximal objective value of the integer problem (\$P^I\$) in many cases is greater than the maximal objective value of it's corresponding continuous problem (\$P\$). In this paper we pay atention to the study of the problem (\$P^I\$) and some related properties of the problem (\$P\$). In particular, we establish conditions determining whether or not an optimal solution to the problem (\$P\$) is an optimal solution to the it's corresponding linear program. For the problem (\$P^I\$) we find an upper bound for it's optimal objective value and present an algorithm which gives a global optimal solution after a finite number of steps. We also study two particular classes of problems (\$P^I\$) : the bicriteria case and the case when \$d\$ is a nonnegative linear combination of the vectors-criteria defining the efficient set. Key words: Multiple objective linear programming, integer efficient set, efficient cone, cutting plane.}, language = {en} }