Fathoming rules for biobjective mixed integer linear programs
نویسندگان
چکیده
We consider the class of biobjective mixed integer linear programs (BOMILPs). We review fathoming rules for general BOMILPs and present them in a unified manner. We then propose new fathoming rules that rely on solving specially designed LPs, hence making no assumption on the type of problem and only using polynomial-time algorithms. Although all these rules can be carried out by performing a limited number of pivot operations on an LP, we provide insight that helps to make these rules even more efficient by either focusing on a smaller number of feasible solutions or by resorting to heuristics that limit the number of LPs solved.
منابع مشابه
A Branch-and-bound Algorithm for Biobjective Mixed-integer Programs
We propose a branch-and-bound (BB) algorithm for biobjective mixed-integer linear programs (BOMILPs). Our approach makes no assumption on the type of problem and we prove that it returns all Pareto points of a BOMILP. We discuss two techniques upon which the BB is based: fathoming rules to eliminate those subproblems that are guaranteed not to contain Pareto points and a procedure to explore a ...
متن کاملBranch-and-bound for biobjective mixed-integer programming
We present a generic branch-and-bound method for finding all the Pareto solutions of a biobjective mixed integer program. Our main contribution is new algorithms for obtaining dual bounds at a node, for checking node fathoming, presolve and duality gap measurement. Our various procedures are implemented and empirically validated on instances from literature and a new set of hard instances. We a...
متن کاملEfficient storage of Pareto points in biobjective mixed integer programming
In biobjective mixed integer linear programs (BOMILPs), two linear objectives are minimized over a polyhedron while restricting some of the variables to be integer. Since many of the techniques for finding or approximating the Pareto set of a BOMILP use and update a subset of nondominated solutions, it is highly desirable to efficiently store this subset. We present a new data structure, a vari...
متن کاملFinding equidistant nondominated points for biobjective mixed integer programs
The nondominated frontier of a multiobjective optimization problem can be overwhelming to a decision maker, as it is often either exponential or infinite in size. Instead, a representation of this set in the form of a small sample of points is often preferred. In this paper we present a new biobjective criterion space search method for generating a small set of equidistant points based on the s...
متن کاملAn Improved Algorithm for Biobjective Integer Programs
A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed. The algorithm is based on the weighted Chebyshev (Tchebycheff) scalarization, and its running time is asymptotically optimal. A number of extensions are described, including: a technique for handling weakly dominated outcomes, a Pareto set approximation scheme, and an interactive version that pro...
متن کامل