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A Compact Formulation for the mDmSOP: Theoretical and Computational Time Analysis

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Evolution in Computational Intelligence (FICTA 2023)

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 370))

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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 \(w<0.5\), 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 \(w=0.5\).

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Authors and Affiliations

  1. Department of CSIS, Birla Institute of Technology and Science, Pilani, 333031, India

    Ravi Kant & Abhishek Mishra

Authors
  1. Ravi Kant
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  2. Abhishek Mishra
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Corresponding author

Correspondence to Ravi Kant .

Editor information

Editors and Affiliations

  1. Department of Electronics Engineering, Faculty of Engineering and Technology (UNSIET), Veer Bahadur Singh Purvanchal University, Jaunpur, Uttar Pradesh, India

    Vikrant Bhateja

  2. Middlesex University, London, UK

    Xin-She Yang

  3. Faculty of Engineering, University of Porto, Porto, Portugal

    Marta Campos Ferreira

  4. Cardiff Metropolitan University, Cardiff, Warwickshire, UK

    Sandeep Singh Sengar

  5. Institute for Technological Development and Innovation in Communications, University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain

    Carlos M. Travieso-Gonzalez

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Kant, R., Mishra, A. (2023). A Compact Formulation for the mDmSOP: Theoretical and Computational Time Analysis. In: Bhateja, V., Yang, XS., Ferreira, M.C., Sengar, S.S., Travieso-Gonzalez, C.M. (eds) Evolution in Computational Intelligence. FICTA 2023. Smart Innovation, Systems and Technologies, vol 370. Springer, Singapore. https://doi.org/10.1007/978-981-99-6702-5_9

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