A review of interactive methods for multiobjective integer and mixed-integer programming

A review of interactive methods for multiobjective integer and mixed-integer programming

This paper makes a review of interactive methods devoted to multiobjective integer and mixed-integer programming (MOIP/MOMIP) problems. The basic concepts concerning the characterization of the non-dominated solution set are first introduced, followed by a remark about non-interactive methods vs. interactive methods. Then, we focus on interactive MOIP/MOMIP methods, including their characteriza...

Deterministic Methods for Mixed Integer Nonlinear Programming

ALTERNATIVE MIXED INTEGER PROGRAMMING FOR FINDING EFFICIENT BCC UNIT

Data Envelopment Analysis (DEA) cannot provide adequate discrimination among efficient decision making units (DMUs). To discriminate these efficient DMUs is an interesting research subject. The purpose of this paper is to develop the mix integer linear model which was proposed by Foroughi (Foroughi A.A. A new mixed integer linear model for selecting the best decision making units in data envelo...

Second order symmetric duality for nonlinear multiobjective mixed integer programming

9 Abstract 10 We formulate two pairs of second order symmetric duality for nonlinear multiobjective mixed integer programs for 11 arbitrary cones. By using the concept of efficiency and second order invexity, we establish the weak, strong, converse 12 and self-duality theorems for our dual models. Several known results are obtained as special cases. 17 Following the earlier works of Dorn [5], D...

An interactive reference point approach for multiobjective mixed-integer programming using branch-and-bound

We propose an interactive reference point approach for multiple objective (mixed) integer linear programming problems that exploits the use of branch-and-bound techniques for solving the scalarizing programs. At each dialogue phase, the decision maker must specify a criterion reference point or just choose an objective function he/she wants to improve in respect to the previous ecient (nondomi...