In this paper we use a compromise approach to identify a lexicographic optimal solution of a multiple objective programming (MOP) problem. With this solution concept, we first find the maximization of each objection f...In this paper we use a compromise approach to identify a lexicographic optimal solution of a multiple objective programming (MOP) problem. With this solution concept, we first find the maximization of each objection function as the ideal value. Then, we construct a lexicographic order for the compromise (differences) between the ideal values and objective functions. Based on the usually lexicographic optimality structure, we discuss some theoretical properties about our approach and derive a constructing algorithm to compute such a lexicographic optimal solution.展开更多
We show that for a submodular polyhedron and its dual supermodular polyhedron the exists a unique lexicographically optimal base with respect to a weight vector and they coincide.We also present a dual algorithm to ge...We show that for a submodular polyhedron and its dual supermodular polyhedron the exists a unique lexicographically optimal base with respect to a weight vector and they coincide.We also present a dual algorithm to get the lexicograpllically optima base of a submodular polyhedron which works on its dula superlnodular polyhedron.This dual algorithm completely agrees to the algorithm of Morton,G.and von Tandow,R.and Ringwald,K.[1985],where their underlying distributive lattice is a chaill poset greedoid.Finally we show that finding the lesicographically optimal base of a submodular system is essentially equivalent to finding the lexicographically optimal base of a simple submodular system,where its underlying distributive lattice is a poset greedoid.This fact.indicates the importance of greedoids in a further development of submodular system theory.展开更多
文摘In this paper we use a compromise approach to identify a lexicographic optimal solution of a multiple objective programming (MOP) problem. With this solution concept, we first find the maximization of each objection function as the ideal value. Then, we construct a lexicographic order for the compromise (differences) between the ideal values and objective functions. Based on the usually lexicographic optimality structure, we discuss some theoretical properties about our approach and derive a constructing algorithm to compute such a lexicographic optimal solution.
文摘We show that for a submodular polyhedron and its dual supermodular polyhedron the exists a unique lexicographically optimal base with respect to a weight vector and they coincide.We also present a dual algorithm to get the lexicograpllically optima base of a submodular polyhedron which works on its dula superlnodular polyhedron.This dual algorithm completely agrees to the algorithm of Morton,G.and von Tandow,R.and Ringwald,K.[1985],where their underlying distributive lattice is a chaill poset greedoid.Finally we show that finding the lesicographically optimal base of a submodular system is essentially equivalent to finding the lexicographically optimal base of a simple submodular system,where its underlying distributive lattice is a poset greedoid.This fact.indicates the importance of greedoids in a further development of submodular system theory.
