FPBH: A feasibility pump based heuristic for multi-objective mixed integer linear programming

•We study multi-objective mixed integer linear programs.•We develop a generic heuristic algorithm to approximate the nondominated frontier.•The algorithm combines the underlying idea of several existing algorithms.•The algorithm supports execution on multiple processors. Feasibility pump is one of t...

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Bibliographic Details
Published in:Computers & operations research Vol. 112; p. 104760
Main Authors: Pal, Aritra, Charkhgard, Hadi
Format: Journal Article
Language:English
Published: New York Elsevier Ltd 01.12.2019
Pergamon Press Inc
Subjects:
Algorithms
Computer models
Feasibility
Feasibility pump
Integer programming
Knapsack problem
Linear programming
Local branching
Local search
Mixed integer
Multi-objective mixed integer linear programming
Multiple objective analysis
Operations research
Optimization
Parallel processing
Parallelization
Programming languages
Solvers
Local search
Multi-objective mixed integer linear programming
Local branching
Parallelization
Feasibility pump
ISSN:0305-0548, 1873-765X, 0305-0548
Online Access:Get full text
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Summary:•We study multi-objective mixed integer linear programs.•We develop a generic heuristic algorithm to approximate the nondominated frontier.•The algorithm combines the underlying idea of several existing algorithms.•The algorithm supports execution on multiple processors. Feasibility pump is one of the successful heuristics developed almost a decade ago for computing high-quality feasible solutions of single-objective integer linear programs, and it is implemented in exact commercial solvers such as CPLEX and Gurobi. In this study, we present the first Feasibility Pump Based Heuristic (FPBH) for approximately generating nondominated frontiers of multi-objective mixed integer linear programs with an arbitrary number of objectives. The proposed algorithm extends our recent study for bi-objective pure integer programs and employs a customized version of several existing algorithms in the literature of both single-objective and multi-objective optimization. The method has two desirable characteristics: (1) There is no parameter to be tuned by users other than the time limit; (2) It can naturally exploit parallelism. An extensive computational study shows the efficacy of the proposed method on some existing standard test instances in which the true frontier is known, and also some randomly generated instances. We also numerically show the importance of parallelization feature of FPBH and illustrate that FPBH outperforms MDLS developed by Tricoire (2012) on instances of multi-objective knapsack problem. We test the effect of using different commercial and non-commercial linear programming solvers for solving linear programs arising during the course of FPBH, and show that the performance of FPBH is almost the same in all cases. It is worth mentioning that FPBH is available as an open source Julia package, named as ‘FPBH.jl’, on GitHub. The package is compatible with the popular JuMP modeling language and supports input in LP and MPS file formats. The package can plot nondominated frontiers, can compute different quality measures (hypervolume, cardinality, coverage and uniformity), supports execution on multiple processors, and can use any linear programming solver supported by MathProgBase.jl (such as CPLEX, Clp, GLPK, etc).
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2019.07.018