Using Hyperstars to Create Facial-Defining Inequalities of General Binary Integer Programs
نویسندگان
چکیده
AbstractTheoretical results relating to the facial structure of the general binary integer-programming polytope conv({x ∈ {0, 1} : Ax ≤ b}) where A ∈ r n × R , and b ∈R are presented. A conflict hypergraph is constructed and some induced hyperstars create valid inequalities of . BIP P These inequalities are further shown to produce large dimensional faces. Some computational results show the benefit of using hyperstar inequalities for the project allocation problem. KeywordsHypergraphs, Hyperstars, Polyhedral theory, Integer programming, Project allocation problem
منابع مشابه
Generation of a reduced first - level mixed integer programmimg problem
We introduce a new way of generating cutting planes of a mixed integer programme by way of taking binary variables. Four binary variables are introduced to form quartic inequalities, which results in a reduced first-level mixed integer programme. A new way of weakening the inequalities is presented. An algorithm to carryout the separation of the inequalities, which are exponential in number, is...
متن کاملA packing integer program arising in two-layer network design
In this paper we study a certain cardinality constrained packing integer program which is motivated by the problem of dimensioning a cut in a two-layer network. We prove NP-hardness and consider the facial structure of the corresponding polytope. We provide a complete description for the smallest nontrivial case and develop two general classes of facet-defining inequalities. This approach exten...
متن کاملSolving Mixed Integer Bilinear Problems Using MILP Formulations
In this paper, we examine a mixed integer linear programming (MILP) reformulation for mixed integer bilinear problems where each bilinear term involves the product of a nonnegative integer variable and a nonnegative continuous variable. This reformulation is obtained by first replacing a general integer variable with its binary expansion and then using McCormick envelopes to linearize the resul...
متن کاملBinary clutter inequalities for integer programs
We introduce a new class of valid inequalities for general integer linear programs, called binary clutter (BC) inequalities. They include the {0, 1 2 }-cuts of Caprara and Fischetti as a special case and have some interesting connections to binary matroids, binary clutters and Gomory corner polyhedra. We show that the separation problem for BC-cuts is strongly NPhard in general, but polynomiall...
متن کاملInequalities and Target Objectives for Metaheuristic Search - Part I: Mixed Binary Optimization
Recent adaptive memory and evolutionary metaheuristics for mixed integer programming have included proposals for introducing inequalities and target objectives to guide the search. These guidance approaches are useful in intensification and diversification strategies related to fixing subsets of variables at particular values, and in strategies that use linear programming to generate trial solu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006