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Nonlinear goal programming using multi-objective genetic algorithms

Author

Listed:
  • K Deb

    (Indian Institute of Technology Kanpur)

Abstract

Goal programming is a technique often used in engineering design activities primarily to find a compromised solution which will simultaneously satisfy a number of design goals. In solving goal programming problems, classical methods reduce the multiple goal-attainment problem into a single objective of minimizing a weighted sum of deviations from goals. This procedure has a number of known difficulties. First, the obtained solution to the goal programming problem is sensitive to the chosen weight vector. Second, the conversion to a single-objective optimization problem involves additional constraints. Third, since most real-world goal programming problems involve nonlinear criterion functions, the resulting single-objective optimization problem becomes a nonlinear programming problem, which is difficult to solve using classical optimization methods. In tackling nonlinear goal programming problems, although successive linearization techniques have been suggested, they are found to be sensitive to the chosen starting solution. In this paper, we pose the goal programming problem as a multi-objective optimization problem of minimizing deviations from individual goals and then suggest an evolutionary optimization algorithm to find multiple Pareto-optimal solutions of the resulting multi-objective optimization problem. The proposed approach alleviates all the above difficulties. It does not need any weight vector. It eliminates the need of having extra constraints needed with the classical formulations. The proposed approach is also suitable for solving goal programming problems having nonlinear criterion functions and having a non-convex trade-off region. The efficacy of the proposed approach is demonstrated by solving a number of nonlinear goal programming test problems and an engineering design problem. In all problems, multiple solutions (each corresponding to a different weight vector) to the goal programming problem are found in one single simulation run. The results suggest that the proposed approach is an effective and practical tool for solving real-world goal programming problems.

Suggested Citation

  • K Deb, 2001. "Nonlinear goal programming using multi-objective genetic algorithms," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(3), pages 291-302, March.
    • Handle: RePEc:pal:jorsoc:v:52:y:2001:i:3:d:10.1057_palgrave.jors.2601089
    DOI: 10.1057/palgrave.jors.2601089
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    Citations

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    Cited by:

    1. Audet, Charles & Savard, Gilles & Zghal, Walid, 2010. "A mesh adaptive direct search algorithm for multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 204(3), pages 545-556, August.
    2. Pokharel, Shaligram, 2008. "A two objective model for decision making in a supply chain," International Journal of Production Economics, Elsevier, vol. 111(2), pages 378-388, February.
    3. Miglierina, E. & Molho, E. & Recchioni, M.C., 2008. "Box-constrained multi-objective optimization: A gradient-like method without "a priori" scalarization," European Journal of Operational Research, Elsevier, vol. 188(3), pages 662-682, August.
    4. Julio B. Clempner, 2018. "Computing multiobjective Markov chains handled by the extraproximal method," Annals of Operations Research, Springer, vol. 271(2), pages 469-486, December.
    5. S Dhouib & A Kharrat & H Chabchoub, 2011. "Goal programming using multiple objective hybrid metaheuristic algorithm," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 677-689, April.
    6. T. Reshma & K. Reddy & Deva Pratap & Mehdi Ahmedi & V. Agilan, 2015. "Optimization of Calibration Parameters for an Event Based Watershed Model Using Genetic Algorithm," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(13), pages 4589-4606, October.
    7. Gezen, Mesliha & Karaaslan, Abdulkerim, 2022. "Energy planning based on Vision-2023 of Turkey with a goal programming under fuzzy multi-objectives," Energy, Elsevier, vol. 261(PA).
    8. Bagdon, Benjamin A. & Huang, Ching-Hsun & Dewhurst, Stephen, 2016. "Managing for ecosystem services in northern Arizona ponderosa pine forests using a novel simulation-to-optimization methodology," Ecological Modelling, Elsevier, vol. 324(C), pages 11-27.
    9. Prashant M. Ambad & Makarand S. Kulkarni, 2017. "A goal programming approach for multi-objective warranty optimization," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(4), pages 842-861, December.
    10. S. Dutta & B.C. Sahoo & Rajashree Mishra & S. Acharya, 2016. "Fuzzy Stochastic Genetic Algorithm for Obtaining Optimum Crops Pattern and Water Balance in a Farm," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(12), pages 4097-4123, September.
    11. Molina, Julin & Santana, Luis V. & Hernandez-Daz, Alfredo G. & Coello Coello, Carlos A. & Caballero, Rafael, 2009. "g-dominance: Reference point based dominance for multiobjective metaheuristics," European Journal of Operational Research, Elsevier, vol. 197(2), pages 685-692, September.
    12. Yanling Chang & Alan Erera & Chelsea White, 2015. "A leader–follower partially observed, multiobjective Markov game," Annals of Operations Research, Springer, vol. 235(1), pages 103-128, December.

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