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Computing the nadir point for multiobjective discrete optimization problems

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  • Gokhan Kirlik
  • Serpil Sayın

Abstract

We investigate the problem of finding the nadir point for multiobjective discrete optimization problems (MODO). The nadir point is constructed from the worst objective values over the efficient set of a multiobjective optimization problem. We present a new algorithm to compute nadir values for MODO with $$p$$ p objective functions. The proposed algorithm is based on an exhaustive search of the $$(p-2)$$ ( p - 2 ) -dimensional space for each component of the nadir point. We compare our algorithm with two earlier studies from the literature. We give numerical results for all algorithms on multiobjective knapsack, assignment and integer linear programming problems. Our algorithm is able to obtain the nadir point for relatively large problem instances with up to five-objectives. Copyright Springer Science+Business Media New York 2015

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  • Gokhan Kirlik & Serpil Sayın, 2015. "Computing the nadir point for multiobjective discrete optimization problems," Journal of Global Optimization, Springer, vol. 62(1), pages 79-99, May.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:1:p:79-99
    DOI: 10.1007/s10898-014-0227-6
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    4. Diehlmann, Florian & Hiemsch, Patrick S. & Wiens, Marcus & Lüttenberg, Markus & Schultmann, Frank, 2020. "A novel approach to include social costs in humanitarian objective functions," Working Paper Series in Production and Energy 52, Karlsruhe Institute of Technology (KIT), Institute for Industrial Production (IIP).
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