NDLI: A New Class of Functions for Measuring Solution Integrality in the Feasibility Pump Approach

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	De Santis, M. Lucidi, S. Rinaldi, F.
Copyright Year	2013
Abstract	Mixed integer optimization is a powerful tool for modeling many optimization problems arising from real-world 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.
Starting Page	1575
Ending Page	1606
Page Count	32
File Format	PDF
ISSN	10526234
DOI	10.1137/110855351
e-ISSN	10957189
Journal	SIAM Journal on Optimization (SJOPE8)
Issue Number	3
Volume Number	23
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2013-08-01
Access Restriction	Subscribed
Subject Keyword	Integer programming Frank--Wolfe algorithm Approximation methods and heuristics mixed integer programming feasibility problem Mixed integer programming Nonlinear programming concave penalty functions Large-scale problems
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Software

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