Finding non dominated points for multiobjective integer convex programs with linear constraints

In this paper, we present a branch-and-bound based algorithm to generate all non dominated points for a multiobjective integer programming problem with convex objective functions and linear constraints (MOICP). The principle is to solve a single objective program (P) defined from the original MOICP program with relaxed integrality constraints. Whenever an integer solution is found through the branching process, a node is created in the search tree for each criterion. That is, by adding a cutting plane that locally approximates the criterion, as to exclude a subset of dominated points. The nodes are traversed according to the depth-first strategy and the same process is repeated for the obtained programs as (P). Finally, as to illustrate the efficiency of the suggested algorithm, we present an experimental study, where we assess its efficiency using randomly generated quadratic multiobjective integer problems with linear constraints.