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2003•Unpublished venueRequires access

Combining Cutting-and-bound Principle of Objective Equivalent Plane with the Cutting Plane Method for Solving Integer Linear Programming

Gao Pei

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Abstract

This paper combines a cutting_and_bound principle of objective equivalent plane with the Gomory cutting plane method for solving integer linear programming problems.In the algorithm presented,the insignificant parts of the feasible domain of (LP) associated with (ILP) would be cut off by decreasing the optimal objective value of the (LP),and simultaneously,the corresponding objective value is taken as an upper bound to the solution of (ILP).Finally,the solutions to(ILP) would be obtained on an objective equivalent plane through the cutting of the Gomory's cutting planes.

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What this paper is about

This paper combines a cutting_and_bound principle of objective equivalent plane with the Gomory cutting plane method for solving integer linear programming problems.In the algorithm presented,the insignificant parts of the feasible domain of (LP) associated with (ILP) would be cut off by decreasing the optimal objective value of the (LP),and simultaneously,the corresponding objective value is taken as an upper bound to the solution of (ILP).Finally,the solutions to(ILP) would be obtained on an objective equivalent plane through the cutting of the Gomory's cutting planes.

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Available abstract

This paper combines a cutting_and_bound principle of objective equivalent plane with the Gomory cutting plane method for solving integer linear programming problems.In the algorithm presented,the insignificant parts of the feasible domain of (LP) associated with (ILP) would be cut off by decreasing the optimal objective value of the (LP),and simultaneously,the corresponding objective value is taken as an upper bound to the solution of (ILP).Finally,the solutions to(ILP) would be obtained on an objective equivalent plane through the cutting of the Gomory's cutting planes.

Key concepts: Cutting-plane method, Integer programming, Mathematics, Plane (geometry), Linear programming, Branch and cut, Integer (computer science), Upper and lower bounds

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