Generating efficient faces for multiobjective linear programming problems

In this paper, we propose a new method for generating the efficient solutions in multiobjective linear programming (MOLP) problems. An exact tree‐based method is proposed to generate all the pareto set by adopting a bottom‐up approach. This method is suitable for small‐ and medium‐sized problems. For large‐scaled problems, we develop a tabu search‐based heuristic combined with a dichotomic exploration of the efficient set. This method generates potentially maximal efficient faces. The two methods are empirically compared. Experimental results show that the tree‐based method ensures finding the entire efficient set in a reasonable central processing unit (CPU) time. Furthermore, the dichotomic TS method has a significant advantage for solving large‐scaled instances of MOLP problems. It features good compromise between the central processing unit (CPU) time and the size of the generated efficient set.