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A decision support approach for two-stage multi-objective index tracking using improved lagrangian decomposition

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  • Wu, Dexiang
  • Wu, Desheng Dash

Abstract

We present a decision support approach for a network structured stochastic multi-objective index tracking problem in this paper. Due to the non-convexity of this problem, the developed network is modeled as a Stochastic Mixed Integer Linear Program (SMILP). We also propose an optimization-based approach to scenario generation to protect against the risk of parameter estimation for the SMILP. Progressive Hedging (PH), an improved Lagrangian scheme, is designed to decompose the general model into scenario-based sub-problems. Furthermore, we innovatively combine tabu search and the sub-gradient method into PH to enhance the tracking capabilities of the model. We show the robustness of the algorithm through effectively solving a large number of numerical instances.

Suggested Citation

  • Wu, Dexiang & Wu, Desheng Dash, 2020. "A decision support approach for two-stage multi-objective index tracking using improved lagrangian decomposition," Omega, Elsevier, vol. 91(C).
    • Handle: RePEc:eee:jomega:v:91:y:2020:i:c:s0305048316310179
    DOI: 10.1016/j.omega.2018.12.006
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    2. Li, Yuchen & Zhang, Jianghua & Yu, Guodong, 2020. "A scenario-based hybrid robust and stochastic approach for joint planning of relief logistics and casualty distribution considering secondary disasters," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    3. F. Hooshmand & Z. Rasouli, 2023. "Enhanced index tracking problem: a new optimization model and a sum-of-ratio based algorithm," OPSEARCH, Springer;Operational Research Society of India, vol. 60(3), pages 1286-1311, September.

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