Bi-objective integer programming analysis based on the characteristic equation

Masar Al-Rabeeah (), Santosh Kumar (), Ali Al-Hasani (), Elias Munapo () and Andrew Eberhard ()
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Masar Al-Rabeeah: RMIT University
Santosh Kumar: RMIT University
Ali Al-Hasani: RMIT University
Elias Munapo: North West University
Andrew Eberhard: RMIT University

International Journal of System Assurance Engineering and Management, 2019, vol. 10, issue 5, No 6, 937-944

Abstract: Abstract In this paper, a bi-objective integer programming problem is analysed using the characteristic equation that was developed to solve a single-objective pure integer program. This equation can also provides other ranked solutions i.e. 2nd, 3rd,... best solutions. These solutions are potential non-dominated points for a bi-objective integer program, which is being investigated in this paper. A “C” code is developed to solve the characteristic equation, a tool which is not available in the IBM ILOG CPLEX library. Two versions of this algorithm are developed to identify the non-dominated points for the bi-objective integer programming problem. The second version improves on the first by reducing the number of search steps. Computational experiments are carried out with respect to the two algorithms developed in this paper and comparisons have also been carried out with one of the recently developed method, the balanced box method. These computational experiments indicate that the second version of the algorithm developed in this paper performed significantly better than the first version and out performed the balanced box method with respect to both CPU time and the number of iterations.

Keywords: Bi-objective integer program; Characteristic equation; Non-dominated points; Pure integer program (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13198-019-00824-7

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