A compact formulation for the mdmsop: theoretical and computational time analysis

Abstract

The multi-Depot multiple Set Orienteering Problem (mDmSOP) is one of the recently proposed variants of the Set Orienteering Problem (SOP), which has applicability in different real-life applications such as delivering products and mobile crowd-sensing. The objective of the problem is to collect maximum profit from clusters within a given budget. In this paper, we propose an improved integer linear programming (ILP) formulation of the mDmSOP and conduct a time analysis of the results. We solved it using GAMS 39.2.0 and found that we can reduce a large number of constraints while changing sub-tour elimination constraints only. In the case of small instances, the improved mathematical formulation gives better results in all of the test cases for small instances up to 76 vertices except one instance of 16eil76 when , and it gives better results in 93.33% of cases for small instances and 88.23% of cases while simulating on mid-size instances up to 198 nodes when .