A recombination‐based matheuristic for mixed integer programming problems with binary variables

This work introduces a heuristic for mixed integer programming (MIP) problems with binary variables, based on information obtained from differences between feasible solutions as well as solutions from the linear relaxation. This information is used to build a neighborhood that is explored as a sub‐M...

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Published in:International transactions in operational research Vol. 27; no. 1; pp. 418 - 434
Main Authors: Maravilha, André L., Carrano, Eduardo G., Campelo, Felipe
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.01.2020
Subjects:
branch and bound
combinatorial optimization
Heuristic
Integer programming
Linear programming
local search
Mathematical programming
metaheuristics
Mixed integer
Operations research
Polishing
ISSN:0969-6016, 1475-3995
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Abstract This work introduces a heuristic for mixed integer programming (MIP) problems with binary variables, based on information obtained from differences between feasible solutions as well as solutions from the linear relaxation. This information is used to build a neighborhood that is explored as a sub‐MIP problem. The proposed heuristic is evaluated using 45 problems from the MIPLIB repository. Its performance, in terms of solution improvement over the results obtained after exploring 50,000 nodes of the branch‐and‐bound tree, is compared against that of Solution Polishing, which is another recombination‐based heuristic for MIP problems used within the CPLEX solver; as well as against the solution obtained by running the default CPLEX branch‐and‐cut (B&C) method under a same time limit. The computational results indicate that the proposed method is able to yield results that are significantly better than those obtained by the default CPLEX B&C approach and comparable to those of Solution Polishing in terms of the mean solution quality. This equivalence of expected solution quality, coupled with a simpler implementation, suggests the use of the proposed approach as a possible alternative for improving the quality of solutions in MIP problems.
AbstractList This work introduces a heuristic for mixed integer programming (MIP) problems with binary variables, based on information obtained from differences between feasible solutions as well as solutions from the linear relaxation. This information is used to build a neighborhood that is explored as a sub‐MIP problem. The proposed heuristic is evaluated using 45 problems from the MIPLIB repository. Its performance, in terms of solution improvement over the results obtained after exploring 50,000 nodes of the branch‐and‐bound tree, is compared against that of Solution Polishing, which is another recombination‐based heuristic for MIP problems used within the CPLEX solver; as well as against the solution obtained by running the default CPLEX branch‐and‐cut (B&C) method under a same time limit. The computational results indicate that the proposed method is able to yield results that are significantly better than those obtained by the default CPLEX B&C approach and comparable to those of Solution Polishing in terms of the mean solution quality. This equivalence of expected solution quality, coupled with a simpler implementation, suggests the use of the proposed approach as a possible alternative for improving the quality of solutions in MIP problems.
Author Carrano, Eduardo G.
Maravilha, André L.
Campelo, Felipe
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  organization: Operations Research and Complex Systems Laboratory (ORCS Lab)
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SubjectTerms branch and bound
combinatorial optimization
Heuristic
Integer programming
Linear programming
local search
Mathematical programming
metaheuristics
Mixed integer
Operations research
Polishing
Title A recombination‐based matheuristic for mixed integer programming problems with binary variables
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