Finding all equitably non-dominated points of multiobjective integer programming problems

Abstract

Equitable multiobjective programming (E-MOP) problems are multiobjective programming problems of a special type. In E-MOP, the decision-maker has equity concerns and hence has an equitable rational preference model. In line with this, our aim is to find all equitably non-dominated points (EN) of the multi-objective integer problems. There are different approaches to solving E-MOP problems. We use equitable aggregation functions and develop two different algorithms; one for equitable biobjective integer programming (E-BOIP) problems and one for equitable multiobjective integer programming (E-MOIP) problems with more than two objectives. In the first algorithm, we solve Pascoletti Serafini (PS) scalarization models iteratively while ensuring getting a weakly equitably non-dominated point in each iteration. In the second algorithm, we use cumulative ordered weighted average in the ExA algorithm of Özpeynirci and Köksalan [1] to find all extreme supported equitably non-dominated points (ESN) first. After finding all ESNs, we use them to define the regions that could contain EN. Then we use split algorithm and find all the remaining ENs. We also provide a split only version of the algorithm since the process of finding all ESNs could be time consuming. We compare two versions in multiobjective assignment and knapsack problem instances. Although the split only version is quicker, the original version of the algorithm is useful since it gives information about the weight space decomposition of ESNs. The weight space decomposition discussion is also provided.