A novel alternative algorithm to find all multiple solutions of general integer linear program

Abstract

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 to 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.