Set covering algorithms using cutting planes, heuristics, and subgradient optimization : a computational study
نویسندگان
چکیده
We report on the implementation and computational testing of several versions of a set covering algorithm, based on the family of cutting planes from conditional bounds discussed in the companion paper [2]. The algorithm uses a set of heuristics to find prime covers, another set of heuristics to find feasible solutions to the dual linear program which are needed to generate cuts, and subgradient optimization to find lower bounds. It also uses implicit enumeration with some new branching rules. Each of the ingredients was implemented and tested in several versions. The variant of the algorithm that emerged as best was run on 55 randomly generated test problems (20 of them from the literature), with up to 200 constraints and 2000 variables. The results show the algorithm to be more reliable and efficient than earlier procedures on large, sparse set covering problems. University Libraries Carnegie Mellon University Pittsburgh, Pennsylvania 1521:3 SET COVERING ALGORITHMS USING CUTTING PLANES, HEURISTICS, AND SUBGRADIENT OPTIMIZATION: A COMPUTATIONAL STUDY
منابع مشابه
On Disjunctive Cuts for Combinatorial Optimization
In the successful branch-and-cut approach to combinatorial optimization, linear inequalities are used as cutting planes within a branch-and-bound framework. Although researchers often prefer to use facet-inducing inequalities as cutting planes, good computational results have recently been obtained using disjunctive cuts, which are not guaranteed to be facet-inducing in general. A partial expla...
متن کاملA hybrid Lagrangean heuristic with GRASP and path-relinking for set k-covering
The set multicovering or set k-covering problem is an extension of the classical set covering problem, in which each object is required to be covered at least k times. The problem finds applications in the design of communication networks and in computational biology. We describe a GRASP with pathrelinking heuristic for the set k-covering problem, as well as the template of a family of Lagrange...
متن کاملBranch-and-Cut for the Maximum Feasible Subsystem Problem
This paper presents a branch-and-cut algorithm for the NPhard maximum feasible subsystem problem: For a given infeasible linear inequality system, determine a feasible subsystem containing as many inequalities as possible. The complementary problem, where one has to remove as few inequalities as possible in order to make the system feasible, can be formulated as a set covering problem. The rows...
متن کاملSome Results on facets for linear inequality in 0-1 variables
The facet of Knapsack ploytope, i.e. convex hull of 0-1 points satisfying a given linear inequality has been presented in this current paper. Such type of facets plays an important role in set covering set partitioning, matroidal-intersection vertex- packing, generalized assignment and other combinatorial problems. Strong covers for facets of Knapsack ploytope has been developed in the first pa...
متن کاملThree Meta-heuristic Algorithms for the Single-item Capacitated Lot-sizing Problem (RESEARCH NOTE)
This paper proposes a mixed integer programming model for single-item capacitated lot-sizing problem with setup times, safety stock, demand shortages, outsourcing and inventory capacity. Due to the complexity of problem, three meta-heuristics algorithms named simulated annealing (SA), vibration damping optimization (VDO) and harmony search (HS) have been used to solve this model. Additionally, ...
متن کامل