In this work we present a beam-search approach applied to the Set Covering Problem. The goal of this problem is to choose a subset of columns of minimal cost covering every row. Beam Search constructs a search tree by using a breadthfirst search strategy, however only a fixed number of nodes are kept and the rest are discarded. Even though original beam search has a deterministic nature, our pr...

This paper investigates the development of an effective heuristic to solve the set covering problem (SCP) by applying the meta-heuristic Meta-RaPS (Meta-heuristic for Randomized Priority Search). In Meta-RaPS, a feasible solution is generated by introducing random factors into a construction method. Then the feasible solutions can be improved by an improvement heuristic. In addition to applying...

The set covering problem is a well-known NP-hard combinatorial optimization problem with wide practical applications. This paper introduces a novel heuristic for the uni-cost set covering problem. An iterated approximation algorithm (ITEG) based on this heuristic is developed: in the rst iteration a cover is constructed, and in the next iterations a new cover is built by starting with part of t...

In this paper, we address the following probabilistic version (PSC) of the set covering problem:min{cx |P(Ax ≥ ξ) ≥ p, x ∈ {0, 1}N }where A is a 0-1matrix, ξ is a random 0-1 vector and p ∈ (0, 1] is the threshold probability level. We introduce the concepts of p-inefficiency and polarity cuts. While the former is aimed at deriving an equivalentMIP reformulation of (PSC), the latter is used as a...

The Set Covering Problem is a formal model for many practical optimization problems. It consists in finding a subset of columns in a zero/one matrix such that they cover all the rows of the matrix at a minimum cost. To solve the Set Covering Problem we will use a metaheuristic called Fireworks Algorithm (FWA) inspired by the fireworks explosion. Through the observation of the way that fireworks...

In this paper an enumeration technique for solving linear fractional fuzzy set covering problem is defined. Set covering problems belong to the class of 0-1 integer programming problems that are NP-complete. Many applications arises having the set covering problems, switching theory, testing of VLSI circuits and line balancing often take on a set covering structure. Linear fractional set coveri...

The set covering problem (SCP) is central in a wide variety of practical applications for which finding good feasible solutions quickly (often in real-time) is crucial. Surrogate constraints normalization is a classical technique used to derive appropriate weights for surrogate constraint relaxations in mathematical programming. This framework remains the core of the most effective one-pass con...

A mean field feedback artificial neural network algorithm is developed and explored for the set covering problem. A convenient encoding of the inequality constraints is achieved by means of a multilinear penalty function. An approximate energy minimum is obtained by iterating a set of mean field equations, in combination with annealing. The approach is numerically tested against a set of public...

A mean eld feedback artiicial neural network algorithm is developed and explored for the set covering problem. A convenient encoding of the inequality constraints is achieved by means of a multilinear penalty function. An approximate energy minimum is obtained by iterating a set of mean eld equations, in combination with annealing. The approach is numerically tested against a set of publicly av...

We present instance-specific custom computing machines for the set covering problem. Four accelerator architectures are developed that implement branch & bound in 3-valued logic and many of the deduction techniques found in software solvers. We use set covering benchmarks from two-level logic minimization and Steiner triple systems to derive and discuss experimental results. The resulting raw s...