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19
Improving the Feasibility Pump
 DISCRETE OPTIMIZATION, SPECIAL ISSUE
, 2005
"... The Feasibility Pump of Fischetti, Glover, Lodi, and Bertacco [8, 7] has proved to be a very successful heuristic for finding feasible solutions of mixed integer programs. The quality of the solutions in terms of the objective value, however, tends to be poor. This paper proposes a slight modificati ..."
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Cited by 17 (3 self)
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The Feasibility Pump of Fischetti, Glover, Lodi, and Bertacco [8, 7] has proved to be a very successful heuristic for finding feasible solutions of mixed integer programs. The quality of the solutions in terms of the objective value, however, tends to be poor. This paper proposes a slight modification of the algorithm in order to find better solutions. Extensive computational results show the success of this variant: in 89 out of 121 MIP instances the modified version produces improved solutions in comparison to the original Feasibility Pump.
Feasibility pump 2.0
, 2008
"... Finding a feasible solution of a given MixedInteger Programming (MIP) model is a very important N Pcomplete problem that can be extremely hard in practice. Feasibility Pump (FP) is a heuristic scheme for finding a feasible solution to general MIPs that can be viewed as a clever way to round a sequ ..."
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Cited by 13 (1 self)
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Finding a feasible solution of a given MixedInteger Programming (MIP) model is a very important N Pcomplete problem that can be extremely hard in practice. Feasibility Pump (FP) is a heuristic scheme for finding a feasible solution to general MIPs that can be viewed as a clever way to round a sequence of fractional solutions of the LP relaxation, until a feasible one is eventually found. In this paper we study the effect of replacing the original rounding function (which is fast and simple, but somehow blind) with more clever rounding heuristics. In particular, we investigate the use of a divinglike procedure based on rounding and constraint propagation— a basic tool in Constraint Programming. Extensive computational results on binary and general integer MIPs from the literature show that the new approach produces a substantial improvement of the FP success rate, without slowingdown the method and with a significantly better quality of the feasible solutions found.
Experiments with a Feasibility Pump approach for nonconvex MINLPs
 SYMPOSIUM ON EXPERIMENTAL AND EFFICIENT ALGORITHMS
, 2010
"... We present a new Feasibility Pump algorithm tailored for nonconvex Mixed Integer Nonlinear Programming problems. Differences with the previously proposed Feasibility Pump algorithms and difficulties arising from nonconvexities in the models are extensively discussed. The main methodological innovati ..."
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Cited by 7 (3 self)
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We present a new Feasibility Pump algorithm tailored for nonconvex Mixed Integer Nonlinear Programming problems. Differences with the previously proposed Feasibility Pump algorithms and difficulties arising from nonconvexities in the models are extensively discussed. The main methodological innovations of this variant are: (a) the first subproblem is a nonconvex continuous Nonlinear Program, which is solved using global optimization techniques; (b) the solution method for the second subproblem is complemented by a tabu list. We exhibit computational results showing the good performance of the algorithm on instances taken from the MINLPLib.
Heuristics of the BranchCutandPriceFramework SCIP
, 2007
"... In this paper we give an overview of the heuristics which are integrated into the open source branchcutandpriceframework SCIP. We briefly describe the fundamental ideas of different categories of heuristics and present some computational results which demonstrate the impact of heuristics on the ..."
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Cited by 4 (3 self)
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In this paper we give an overview of the heuristics which are integrated into the open source branchcutandpriceframework SCIP. We briefly describe the fundamental ideas of different categories of heuristics and present some computational results which demonstrate the impact of heuristics on the overall solving process of SCIP. 1
Solving Hard Mixed Integer Programming Problems with XpressMP: A MIPLIB 2003 Case Study
, 2007
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New concave penalty functions for improving the Feasibility Pump
"... MixedInteger optimization represents a powerful tool for modeling manyoptimization problems arising from realworld applications. The Feasibilitypump is a heuristic for finding feasible solutions to mixed integer linear problems. In this work, we propose a new feasibilitypump approach using concave ..."
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Cited by 2 (2 self)
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MixedInteger optimization represents a powerful tool for modeling manyoptimization problems arising from realworld applications. The Feasibilitypump is a heuristic for finding feasible solutions to mixed integer linear problems. In this work, we propose a new feasibilitypump approach using concave nondifferentiable penaltyfunctions for measuring solution integrality. We present computational results on binaryMILP problems from the MIPLIB libraryshowing the effectiveness of our approach.
Using the analytic center in the feasibility pump
, 2010
"... The feasibility pump (FP) [5, 7] has proved to be a successful heuristic for finding feasible solutions of mixed integer linear problems (MILPs). FP was improved in [1] for finding better quality solutions. Briefly, FP alternates between two sequences of points: one of feasible solutions for the rel ..."
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Cited by 2 (0 self)
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The feasibility pump (FP) [5, 7] has proved to be a successful heuristic for finding feasible solutions of mixed integer linear problems (MILPs). FP was improved in [1] for finding better quality solutions. Briefly, FP alternates between two sequences of points: one of feasible solutions for the relaxed problem (but not integer), and another of integer points (but not feasible for the relaxed problem). Hopefully, the procedure may eventually converge to a feasible and integer solution. Integer points are obtained from the feasible ones by some rounding procedure. This short paper extends FP, such that the integer point is obtained by rounding a point on the (feasible) segment between the computed feasible point and the analytic center for the relaxed linear problem. Since points in the segment are closer (may be even interior) to the convex hull of integer solutions, it may be expected that the rounded point has more chances to become feasible, thus reducing the number of FP iterations. When the selected point to be rounded is the feasible solution of the relaxation (i.e., one of the two end points of the segment), this analytic center FP variant behaves as the standard FP. Computational results show that this variant may be efficient in some MILP instances.
Experiments with a feasibility pump approach for nonconvex MINLPs
 SYMPOSIUM ON EXPERIMENTAL ALGORITHMS, VOLUME 6049 OF LNCS
, 2010
"... We present a new Feasibility Pump algorithm tailored for nonconvex Mixed Integer Nonlinear Programming problems. Differences with the previously proposed Feasibility Pump algorithms and difficulties arising from nonconvexities in the models are extensively discussed. The main methodological innovati ..."
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Cited by 2 (2 self)
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We present a new Feasibility Pump algorithm tailored for nonconvex Mixed Integer Nonlinear Programming problems. Differences with the previously proposed Feasibility Pump algorithms and difficulties arising from nonconvexities in the models are extensively discussed. The main methodological innovations of this variant are: (a) the first subproblem is a nonconvex continuous Nonlinear Program, which is solved using global optimization techniques; (b) the solution method for the second subproblem is complemented by a tabu list. We exhibit computational results showing the good performance of the algorithm on instances taken from the MINLPLib.
A new class of functions for measuring solution integrality in the Feasibility Pump approach

, 2013
"... Mixed integer optimization is a powerful tool for modeling many optimization problems arising from realworld applications. Finding a first feasible solution represents the first step for several mixed integer programming (MIP) solvers. The feasibility pump is a heuristic for finding feasible solut ..."
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Cited by 1 (1 self)
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Mixed integer optimization is a powerful tool for modeling many optimization problems arising from realworld applications. Finding a first feasible solution represents the first step for several mixed integer programming (MIP) solvers. The feasibility pump is a heuristic for finding feasible solutions to mixed integer linear programming (MILP) problems which is effective even when dealing with hard MIP instances. In this work, we start by interpreting the feasibility pump as a Frank–Wolfe method applied to a nonsmooth concave merit function. Then we define a general class of functions that can be included in the feasibility pump scheme for measuring solution integrality, and we identify some merit functions belonging to this class. We further extend our approach by dynamically combining two different merit functions. Finally, we define a new version of the feasibility pump algorithm, which includes the original version of the feasibility pump as a special case, and we present computational results on binary MILP problems showing the effectiveness of our approach.