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A method for generating the facet of underlying polytopes in positive 0.1 integer programs

Gyana R. Parija, W. Wilhelm

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Abstract

We present a new cutting plane method for solving positive 0/1 integer programs. The method is based on strong separation of convex sets and assumes no a priori knowledge about the underlying polyhedral structure. A new characterization for positive 0/1 polytopes is obtained that assures the generation of these cutting planes in a polynomial number of steps. Also, the cutting planes are provably stronger than a particular class of Fenchel cutting planes. Potential applications are discussed and promising computational experience is described.

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What this paper is about

We present a new cutting plane method for solving positive 0/1 integer programs. The method is based on strong separation of convex sets and assumes no a priori knowledge about the underlying polyhedral structure. A new characterization for positive 0/1 polytopes is obtained that assures the generation of these cutting planes in a polynomial number of steps. Also, the cutting planes are provably stronger than a particular class of Fenchel cutting planes. Potential applications are discussed and promising computational experience is described.

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Available abstract

We present a new cutting plane method for solving positive 0/1 integer programs. The method is based on strong separation of convex sets and assumes no a priori knowledge about the underlying polyhedral structure. A new characterization for positive 0/1 polytopes is obtained that assures the generation of these cutting planes in a polynomial number of steps. Also, the cutting planes are provably stronger than a particular class of Fenchel cutting planes. Potential applications are discussed and promising computational experience is described.

Key concepts: Cutting-plane method, Polytope, Facet (psychology), Polyhedral combinatorics, Integer programming, Integer (computer science), Combinatorics, Regular polygon

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