A Novel Alternative Algorithm to Find All Multiple Solutions of General Integer Linear Programs

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Şimşek Alan K.

6th International HYBRID Conference on Mathematical Advances and Applications , İstanbul, Turkey, 11 - 13 May 2023, pp.119

  • Publication Type: Conference Paper / Summary Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.119
  • Yıldız Technical University Affiliated: Yes


Integer linear programming (ILP) is often used to model and solve real-life problems. In practice, alternative solutions are very useful as they significantly increase flexibility for the decision maker. In this study, an alternative method based on parameterization obtained from the Diophantine equation is developed to find all alternative solutions of ILP problems and an easy to implement, efficient and reliable algorithm is presented. The proposed method was used without being affected by the number of variables and constraints in the problem.Numerical examples are presented to demonstrate the usefulness of the proposed method. In addition, these examples are coded in the MAPLE programming language according to the proposed algorithm.