Journal Article10.1287/OPRE.27.6.1069
Interior Path Methods for Heuristic Integer Programming Procedures
TL;DR: This paper considers heuristic procedures for general mixed integer linear programming with inequality constraints by constructing an “interior path” from which to search for good feasible solutions by constructing piecewise linear paths.
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Abstract: This paper considers heuristic procedures for general mixed integer linear programming with inequality constraints. It focuses on the question of how to most effectively initialize such procedures by constructing an “interior path” from which to search for good feasible solutions. These paths lead from an optimal solution for the corresponding linear programming problem (i.e., deleting integrality restrictions) into the interior of the feasible region for this problem. Previous methods for constructing linear paths of this kind are analyzed from a statistical viewpoint, which motivates a promising new method. These methods are then extended to piecewise linear paths in order to improve the direction of search in certain cases where constraints that are not binding on the optimal linear programming solution become particularly relevant. Computational experience is reported.
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Citations
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Matteo Fischetti,Andrea Lodi +1 more
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TL;DR: In this article, the authors present the main ideas underlying some of the heuristics proposed in the literature and focus on those algorithms developed with the aim of being tightly integrated within MILP solvers.
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Octane: A New Heuristic for Pure 0-1 Programs
TL;DR: A new heuristic for pure 0--1 programs is proposed, which finds feasible integer points by enumerating extended facets of the octahedron, the outer polar of the unit hypercube.
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Pivot, Cut, and Dive: a heuristic for 0-1 mixed integer programming
Jonathan Eckstein,Mikhail Nediak +1 more
TL;DR: A heuristic for 0-1 mixed-integer linear programming problems, focusing on “stand-alone” implementation built around concave “merit functions” measuring solution integrality, and consists of four layers: gradient-based pivoting, probing pivot, convexity/intersection cutting, and diving on blocks of variables.
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