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A direction based classical method to obtain complete Pareto set of multi-criteria optimization problems

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Abstract

This paper provides a direction based parameter dependent classical method to find entire Pareto set of multi-criteria optimization problems. Proposed method is non-gradient based and parameter of the technique essentially lies on the unit sphere in the criterion space. Sequentially solving a set of problems, corresponding to each particular parameter vector on the unit sphere, entire Pareto set of the problem is captured. It is obtained that the method bears a necessary and sufficient condition for Pareto optimality. It is also shown that a simple modification on the constraint set of the formulated problem can ensure general D-Pareto optimality of the outcome solutions, where D is any pointed convex cone. In specific, proposed method can extract 𝜖-Pareto optimal points. As at any 𝜖-Pareto point, trade-off between any two objectives are bounded, outcome solution set of the studied method can facilitate decision maker for final selection of solution. Proposed technique and its illustrations are supported by several numerical and pictorial representations.

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Acknowledgments

We are really thankful to the anonymous reviewers for their constructive comments which substantially improve quality of the paper. Special thanks to Prof. Nicolas Hadjisavvas, Professor, Department of Product and Systems Design Engineering, University of the Aegean, Greece, for his fruitful comments on an initial version of this paper. First author gratefully acknowledges a research scholarship awarded by the Council of Scientific and Industrial Research, Government of India (award no. 09/081(1054)/2010-EMR-I). Second author acknowledges financial support given by the Department of Science and Technology, Government of India (SR/S4/M: 497/07).

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  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721 302, West Bengal, India

    Debdas Ghosh & Debjani Chakraborty

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  1. Debdas Ghosh
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  2. Debjani Chakraborty
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Correspondence to Debjani Chakraborty.

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Ghosh, D., Chakraborty, D. A direction based classical method to obtain complete Pareto set of multi-criteria optimization problems. OPSEARCH 52, 340–366 (2015). https://doi.org/10.1007/s12597-014-0178-1

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