Well-dispersed subsets of non-dominated solutions for MOMILP ‎problem

Abstract

This paper uses the weighted L$_1-$norm to propose an algorithm for finding a well-dispersed subset of non-dominated solutions of multiple objective mixed integer linear programming problem. When all variables are integer it finds the whole set of efficient solutions. In each iteration of the proposed method only a mixed integer linear programming problem is solved and its optimal solutions generates the elements of the well-dispersed subset non-dominated solutions (WDSNDSs) of MOMILP. According to the distance of non-dominated solutions from the ideal point theelements of the WDSNDSs are ranked, hence it does not need the filtering procedures. Using suitable values for the parameter of the proposed model an appropriate WDSNDSs by less computational efforts can be generated. Two numerical examples present to illustrate the applicability of the proposed method and compare it with earlier ‎work.‎