Algorithm For Set Covering Problem Research Articles

Theoretical Properties of a Neighborhood-based Approach for Widening

Most of the research in parallel data mining and machine learning algorithms is focused on improving the efficiency of existing algorithms. However, our focus is the improvement of the solution quality, or model accuracy. We are looking for "smart" strategies to invest parallel compute resources in order to achieve a better exploration of the search space by exploring several solutions in parallel, referred to as Widening. In this paper, we discuss the theoretical properties of a neighborhood-based Widening using a type of neighborhoods, optimality neighborhoods and contrast this communicationless approach to the straightforward beam-like Top-k Widening approach, which requires communication. We show a bound on the number of parallel workers needed for the communicationless approach to guarantee that it has a solution of the same quality as the Top-k approach. In addition to the theoretical comparison, we experimentally compare these two approaches in terms of running time and quality of final solution, using a widened version of the greedy algorithm for set cover problem.

A New Genetic Algorithm for Set Covering Problems

An indirect genetic algorithm for the non-unicost set covering problem is presented. The algorithm is a two-stage meta-heuristic, which in the past was successfully applied to similar multiple-choice optimisation problems. The two stages of the algorithm are an ‘indirect’ genetic algorithm and a decoder routine. First, the solutions to the problem are encoded as permutations of the rows to be covered, which are subsequently ordered by the genetic algorithm. Fitness assignment is handled by the decoder, which transforms the permutations into actual solutions to the set covering problem. This is done by exploiting both problem structure and problem specific information. However, flexibility is retained by a self-adjusting element within the decoder, which allows adjustments to both the data and to stages within the search process. Computational results are presented.

An Improved Greedy Algorithm for Set Cover Problem

An Improved Greedy Algorithm for Set Cover Problem

An Adaptive Scheduling Algorithm for Set Cover Problem in Wireless Sensor Networks: A Cellular Learning Automata Approach

Redundant node deployment is a common strategy in wireless sensor networks. This redundancy can be due to various reasons such as high probability of failures, long lifetime expectation, etc. One major problem in wireless sensor networks is to use this redundancy in order to extend the network lifetime while keeping the entire area under the coverage of the network. In this problem, which is known as set cover problem, the main objective is to select a subset of sensor nodes as active nodes so that the set of active nodes covers the entire area of the network. In this paper, an scheduling algorithm is presented for solving the set cover problem using cellular learning automata. In this algorithm, each node is equipped with a learning automaton which locally decides for the node to be active or not based on the situations of its neighbors. Simulation results in J-sim simulator environment specify the efficiency of the proposed scheduling algorithm over existing algorithms such as PEAS and PECAS. In this paper, a distributed, adaptive scheduling algorithm based on cellular learning automata for wireless sensor networks is proposed. The main purpose of this algorithm is to maintain coverage in the network with minimum number of active nodes, so that the total consumed energy of nodes is minimized. In the proposed algorithm, each node is equipped with a learning automaton which decides for the node to be active or not based on the states (either active or not) of its neighboring sensor nodes. We used J-sim simulator to evaluate the performance of the proposed algorithm. Simulation results specify the efficiency of the proposed algorithm over existing algorithms such as PEAS (2) and PECAS (3) -especially against high ratio of unexpected failures. The rest of this paper is organized as follows. In Section II, a literature overview is presented. In Section III, learning automata and cellular learning automata are briefly reviewed. The problem statement is given in Section IV. The proposed scheduling algorithm is described in Section V. Simulation results are given in Section VI. Section VII is the conclusion.

데드라인을 고려하는 효율적인 지능형 로봇 커버리지 알고리즘

이 논문은 지능형 로봇을 위한 새로운 커버리지 알고리즘을 제안한다. 커버리지 알고리즘의 성능을 향상하기 위한 많은 연구들은 전체 커버리지 완료 시간을 최소화하는데 초점을 맞추어왔다. 그러나, 만일 전체 커버리지를 완료하기에 충분한 시간이 없다면, 최적의 경로는 달라질 수 있다. 이러한 문제를 해결하기 위하여 본 논문에서는 MaxCoverage라고 하는 데드라인이 있을 경우에 가능한 많은 면적을 커버하기 위한 새로운 커버리지 알고리즘을 제안한다. MaxCoverage 알고리즘은 이동 경로를 셋 커버 문제를 위한 그리디 알고리즘을 이용하여 결정한다. 실험 결과에 의하면 MaxCoverage 알고리즘은 임의의 데드라인에 대하여 다른 알고리즘들에 비해 향상된 성능을 보여준다. This paper proposes a new coverage algorithm for intelligent robot. Many algorithms for improving the performance of coverage have been focused on minimizing the total coverage completion time. However, if one does not have enough time to finish the whole coverage, the optimal path could be different. To tackle this problem, we propose a new coverage algorithm, which we call MaxCoverage algorithm, for covering maximal area within the deadline. The MaxCoverage algorithm decides the navigation flow by greedy algorithm for Set Covering Problem. The experimental results show that the MaxCoverage algorithm performs better than other algorithms for random deadlines.

An Application of Wedelin's Method to Railway Crew Scheduling Problem

So many scheduling problems arise in railway industries. One of the typical scheduling problems is Crew Scheduling Problem. Much attention has been paid to this problem by a lot of researchers, but many studies have not been done to the problems in railway industries in Japan. In this paper, we consider a railway crew scheduling problem in Japan. The problem can be formulated into Set Covering Problem (SCP). In SCP, a row corresponds to a trip representing a minimal task and a column corresponds to a pairing representing a sequence of trips performed by a certain crew. Many algorithms have been developed and proposed for it. On the other hand, in practical use, it is important to investigate how these algorithms behave and work on a certain problem. Therefore, we focus on Wedelin's algorithm, which is based on Lagrange relaxation and is known as one of the high performance algorithms for SCP, and mainly examine the basic idea of this algorithm. Furthermore, we show effectiveness of this procedure through computational experiments on instances from Japanese railway.

A 3-flip neighborhood local search for the set covering problem

The set covering problem (SCP) calls for a minimum cost family of subsets from n given subsets, which together covers the entire ground set. In this paper, we propose a local search algorithm for SCP, which has the following three characteristics. (1) The use of 3-flip neighborhood, which is the set of solutions obtainable from the current solution by exchanging at most three subsets. As the size of 3-flip neighborhood is O( n 3), the neighborhood search becomes expensive if implemented naively. To overcome this, we propose an efficient implementation that reduces the number of candidates in the neighborhood without sacrificing the solution quality. (2) We allow the search to visit the infeasible region, and incorporate the strategic oscillation technique realized by adaptive control of penalty weights. (3) The size reduction of the problem by using the information from the Lagrangian relaxation is incorporated, which is indispensable for solving very large instances. According to computational comparisons on benchmark instances with other existing heuristic algorithms for SCP, our algorithm performs quite effectively for various types of problems, especially for very large-scale instances.

Algorithms for the Set Covering Problem

The Set Covering Problem (SCP) is a main model for several important applications, including crew scheduling in railway and mass-transit companies. In this survey, we focus our attention on the most recent and effective algorithms for SCP, considering both heuristic and exact approaches, outlining their main characteristics and presenting an experimental comparison on the test-bed instances of Beasley's OR Library.