Inequalities for Mixed Integer Linear Programs
نویسنده
چکیده
This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these families. The tutorial also discusses computational aspects of generating the cuts and their strength.
منابع مشابه
Valid inequalities for mixed integer linear programs
This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these...
متن کامل9839 AGGREGATION and MIXED INTEGER ROUNDING toSOLVE
A separation heuristic for mixed integer programs is presented that theoretically allows one to derive several families of \strong" valid inequalities for speciic models and computationally gives results as good as or better than those obtained from several existing separation routines including ow cover and integer cover inequalities. The heuristic is based on aggregation of constraints of the...
متن کاملGap inequalities for non-convex mixed-integer quadratic programs
Laurent and Poljak introduced a very general class of valid linear inequalities, called gap inequalities, for the max-cut problem. We show that an analogous class of inequalities can be defined for general nonconvex mixed-integer quadratic programs. These inequalities dominate some inequalities arising from a natural semidefinite relaxation.
متن کاملSequential Pairing of Mixed Integer Inequalities
We present a scheme for generating new valid inequalities for mixed integer programs by taking pairwise combinations of existing valid inequalities. Our scheme is related to mixed integer rounding and mixing. The scheme is in general sequence-dependent and therefore leads to an exponential number of inequalities. For some important cases, we identify combination sequences that lead to a managea...
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 کامل