Cover Inequalities
نویسندگان
چکیده
Cover inequalities are a special kind of linear inequalities thatare satisfied by the feasible solutions to knapsack problems. Although ini-tially defined in the context of knapsack problems, cover inequalities andtheir variants can be used as cutting planes for a variety of integer program-ming and combinatorial optimisation problems. We review the theory ofthese inequalities, discuss certain algorithmic aspects of them, and surveysome of the applications.
منابع مشابه
Lifted flow cover inequalities for mixed 0-1 integer programs
We investigate strong inequalities for mixed 0-1 integer programs derived from flow cover inequalities. Flow cover inequalities are usually not facet defining and need to be lifted to obtain stronger inequalities. However, because of the sequential nature of the standard lifting techniques and the complexity of the optimization problems that have to be solved to obtain lifting coefficients, lif...
متن کاملThree-partition flow cover inequalities for constant capacity fixed-charge network flow problems
Flow cover inequalities are among the most effective valid inequalities for capacitated fixed-charge network flow problems. These valid inequalities are based on implications for the flow quantity on the cut arcs of a two-partitioning of the network, depending on whether some of the cut arcs are open or closed. As the implications are only on the cut arcs, flow cover inequalities can be obtaine...
متن کاملFacets of the Complementarity Knapsack Polytope
We present a polyhedral study of the complementarity knapsack problem. Traditionally, complementarity constraints are modeled by introducing auxiliary binary variables and additional constraints, and the model is tightened by introducing strong inequalities valid for the resulting MIP. We use an alternative approach, in which we keep in the model only the continuous variables, and we tighten th...
متن کاملA multi-item production planning model with setup times: algorithms, reformulations, and polyhedral characterizations for a special case
We study a special case of a structured mixed integer programming model that arises in production planning. For the most general case of the model, called PI, we have earlier identified three families of facet–defining valid inequalities: (l, S) inequalities (introduced for the uncapacitated lot–sizing problem by Barany, Van Roy, and Wolsey), cover inequalities, and reverse cover inequalities. ...
متن کاملSimultaneously lifting sets of binary variables into cover inequalities for knapsack polytopes
Cover inequalities are commonly used cutting planes for the 0–1 knapsack problem. This paper describes a linear-time algorithm (assuming the knapsack is sorted) to simultaneously lift a set of variables into a cover inequality. Conditions for this process to result in valid and facet-defining inequalities are presented. In many instances, the resulting simultaneously lifted cover inequality can...
متن کامل