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Using objective values to start multiple objective linear programming algorithms

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  • Arbel, Ami
  • Korhonen, Pekka

Abstract

We introduce in this paper a new starting mechanism for multi-objective linear programming (MOLP) algorithms. This makes it possible to start an algorithm from any solution in objective space. The original problem is first augmented in such a way that a given starting point is feasible. The augmentation is explicitly or implicitly controlled by one parameter during the search process, which verifies the feasibility (efficiency) of the final solution. This starting mechanism can be applied either to traditional algorithms, which search the \f2exterior\f1 of the constraint polytope, or to the algorithms moving through the \2interior\f1 of the constraints. We provide recommendations on the suitability of an algorithm for the various locations of a starting point in objective space. Numerical considerations illustrate these ideas.
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  • Arbel, Ami & Korhonen, Pekka, 2001. "Using objective values to start multiple objective linear programming algorithms," European Journal of Operational Research, Elsevier, vol. 128(3), pages 587-596, February.
    • Handle: RePEc:eee:ejores:v:128:y:2001:i:3:p:587-596
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    References listed on IDEAS

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    1. Abel, Ami & Korhonen, Pekka, 1996. "Using aspiration levels in an interactive interior multiobjective linear programming algorithm," European Journal of Operational Research, Elsevier, vol. 89(1), pages 193-201, February.
    2. Pekka Korhonen & Jyrki Wallenius, 1988. "A pareto race," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(6), pages 615-623, December.
    3. P. Korhonen, 1998. "Multiple Objective Programming Support," Working Papers ir98010, International Institute for Applied Systems Analysis.
    4. Korhonen, Pekka J. & Laakso, Jukka, 1986. "A visual interactive method for solving the multiple criteria problem," European Journal of Operational Research, Elsevier, vol. 24(2), pages 277-287, February.
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    1. H V Junior & M P E Lins, 2009. "A WIN-WIN approach to multiple objective linear programming problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(5), pages 728-733, May.
    2. Korhonen, Pekka J. & Wallenius, Jyrki & Genc, Tolga & Xu, Peng, 2021. "On rational behavior in multi-attribute riskless choice," European Journal of Operational Research, Elsevier, vol. 288(1), pages 331-342.

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