A New Strategy to Solve Linear Integer Problems With Simplex Directions

Abstract

In this paper, we propose a new heuristic strategy to solve linear integer mathematical problems. The strategy begins by finding the optimal solution of the continuous associated problem and the simplex directions from that optimal solution. A total of n − m problems are generated and solved by the strategy, where m is the number of constraints and n is the number of variables of the problem. The best solution to those problems is the solution to the original problem. Several instance problems were randomly generated to validate the strategy, and our strategy finds good solutions in 80% of the instances. We also tested the proposed strategy with instances of the MIPLIB 2017. We compare a total of 39 instances and on average our strategy performed 47% fewer iterations than the solver, in 34 of 39 instances, the strategy found good solutions.

Solving Linear Integer Models with Variable Bounding

“…Data envelopment analysis (DEA)-related problems were solved to prove the efficiency and validity of the method; however, proving the validity of DEA-related problems only limited the study. A new strategy to solve linear integer programming problems with simplex directions was presented by [12]. To prove the validity of the method, the results were compared with CPLEX software results.…”