Some solution methods in the area of multi-objective integer and mixed integer programming problems

In this thesis, we have considered integer, bi-objective integer, bi-objective mixed integer, and multi-objective integer programming models. We have developed methods and algorithms to deal with many potential practical real-life applications. We considered a bi-objective generalized assignment model (BOGAP) and obtained the non-dominated point set for this situation. The field of mixed-integer linear programming is still an active area of research for a single objective model and it becomes more demanding for the bi-objective and multi-objective cases, determined non-dominated point set of the mixed-integer bi-objective model. Determination of ranked best solution in optimization is a complex issue, which is computationally more demanding and there are no known practical approaches to find the ranked-optimal solutions, i.e., second and third best solution etc. To address this situation two methods were developed and ranked optimal solutions for an assignment problem were obtained. A random search method for kth best solution was also developed and performance of this probabilistic approach was compared with the exact method.  Since the rank-based optimal solutions are difficult to find, a need was felt to review several methods to find these ranked based solutions were investigated. Based on these ranked solutions, a rank-based solution method (RBSM) was developed to identify non-dominated points set of a multi-objective integer programming model.