Unicost Set Research Articles

A Local Search Algorithm Proposal Based on Adaptive Row Weighting for Unicost Set Covering Problem

Gerçek hayatta işletmelerin karşılaştığı birçok problemin modellenebildiği eş maliyetli küme kapsama problemi, temel bir matematiksel problemdir. Problemde, veri setinde yer alan gözlemlerin tamamını barındıracak şekilde en az sayıda küme seçilmesi amaçlanmaktadır. Tam sayılı programlama şeklinde ifade edilen problemin çözümünde, klasik ve kesin sonuç veren yöntemlerin yetersiz kalması nedeniyle çeşitli iteratif yaklaşımlar kullanılmaktadır. Bu yaklaşımlardan biri ise yerel arama algoritmalarıdır. Çalışma kapsamında problemin kendi yapısına uygun ve gözlemleri adaptif ağırlıklandırmaya dayalı bir yerel arama algoritması önerilmiştir. Adaptif yapı kullanılarak oluşturulan değişkenler için, optimizasyon sürecinde elde edilen çıktılar girdi parametreleri olarak ele alınmıştır. Bu sayede yerel arama yaklaşımının daha akıllı hale getirilmesi amaçlanmıştır. Önerilen adaptif metot, örnek eş maliyetli küme kapsama problemlerinin çözümünde kullanılmış ve performansı literatürde yer alan diğer adaptif yöntemlerle kıyaslanmıştır. Sonuçlar incelenerek, geliştirilen metodun etkinliği ortaya konmuştur.

Weighting-based Variable Neighborhood Search for Optimal Camera Placement

The optimal camera placement problem (OCP) aims to accomplish surveillance tasks with the minimum number of cameras, which is one of the topics in the GECCO 2020 Competition and can be modeled as the unicost set covering problem (USCP). This paper presents a weighting-based variable neighborhood search (WVNS) algorithm for solving OCP. First, it simplifies the problem instances with four reduction rules based on dominance and independence. Then, WVNS converts the simplified OCP into a series of decision unicost set covering subproblems and tackles them with a fast local search procedure featured by a swap-based neighborhood structure. WVNS employs an efficient incremental evaluation technique and further boosts the neighborhood evaluation by exploiting the dominance and independence features among neighborhood moves. Computational experiments on the 69 benchmark instances introduced in the GECCO 2020 Competition on OCP and USCP show that WVNS is extremely competitive comparing to the state-of-the-art methods. It outperforms or matches several best performing competitors on all instances in both the OCP and USCP tracks of the competition, and its advantage on 15 large-scale instances are over 10%. In addition, WVNS improves the previous best known results for 12 classical benchmark instances in the literature.

An improved configuration checking-based algorithm for the unicost set covering problem

• We study the unicost set covering problem. • The element-state configuration checking is designed to cut down search spaces. • The novel multi-level scoring function is proposed. • The novel heuristic algorithm outperforms the recent algorithms. Configuration Checking (CC) is a simple tool that can be added to local search algorithms to prevent cycling. The generic forms of CC and local search may not be suitable to solve large-scale unicost set covering problem (USCP) instances. Thus, in this study, we introduce an improved CC-based algorithm to solve USCPs. Unlike previous CC implementations that only consider subset states to prevent cycling, the proposed algorithm also checks the element states to minimize the number of subsets, in order to cut down unnecessary search spaces. Therefore, we refer to this technique as the element-state configuration checking (ES-CC) algorithm. Moreover, in our proposed algorithm, the score value (a numerical measure to differentiate between subsets) considers multiple levels of element covering. This multi-level scoring (MLS) value is a new powerful contribution compared to the single-level scoring used in previous CC algorithms. Using these two novel ideas, MLS and ES-CC, we implement the new MLSES-CC algorithm to solve the USCP. The MLSES-CC algorithm also implements a more aggressive local search routine that simultaneously changes the status of the three subsets. We use the MLSES-CC algorithm to solve 176 USCP instances that belong to standard and novel benchmarking sets and compare our results to the best-known USCP algorithms, in terms of solution quality and computation time. Computational experiments indicate that the MLSES-CC algorithm can be considered as a new state-of-the-art algorithm to solve USCPs.

The Relationship between the Unicost Set Covering Problem and the Attribute Reduction Problem in Rough Set Theory

The unicost set covering problem and the attribute reduction problem are NP-complete problems. In this paper, the relationship between these two problems are discussed. Based on the transformability between attribute reductions and minimal solutions in unicost set covering models, two methods are provided. One is to induce an information table from a given unicost set covering model. With no doubt, it shows that the unicost set covering problem can be investigated by rough set theory. The other is to induce a unicost set covering model from a given information table. Similarly, it shows that the attribute reduction problem can be studied by set covering theory. As an application of the proposed theoretical results, a rough set heuristic algorithm is presented for the unicost set covering problem.

Hybrid differential evolution algorithms for the optimal camera placement problem

PurposeThis paper aims to investigate to what extent hybrid differential evolution (DE) algorithms can be successful in solving the optimal camera placement problem.Design/methodology/approachThis problem is stated as a unicost set covering problem (USCP) and 18 problem instances are defined according to practical operational needs. Three methods are selected from the literature to solve these instances: a CPLEX solver, greedy algorithm and row weighting local search (RWLS). Then, it is proposed to hybridize these algorithms with two hybrid DE approaches designed for combinatorial optimization problems. The first one is a set-based approach (DEset) from the literature. The second one is a new similarity-based approach (DEsim) that takes advantage of the geometric characteristics of a camera to find better solutions.FindingsThe experimental study highlights that RWLS and DEsim-CPLEX are the best proposed algorithms. Both easily outperform CPLEX, and it turns out that RWLS performs better on one class of problem instances, whereas DEsim-CPLEX performs better on another class, depending on the minimal resolution needed in practice.Originality/valueUp to now, the efficiency of RWLS and the DEset approach has been investigated only for a few problems. Thus, the first contribution is to apply these methods for the first time in the context of camera placement. Moreover, new hybrid DE algorithms are proposed to solve the optimal camera placement problem when stated as a USCP. The second main contribution is the design of the DEsim approach that uses the distance between camera locations to fully benefit from the DE mutation scheme.

A novel local search for unicost set covering problem using hyperedge configuration checking and weight diversity

The unicost version of well-known set covering problem (SCP) is central to a wide variety of practical applications for which finding an optimal solution quickly is crucial. In this paper, we propose a new local searchbased algorithm for the unicost SCP which follows the general framework of the popular stochastic local search with a particular focus on the hyperedge selection strategy and weight diversity strategy. Specifically, a strategy as called hyperedge configuration checking strategy is proposed here to avoid the search trajectory which leads to local optima. Additionally, a new weight diversity strategy is proposed for the diversification of search results, by changing the weight of both covered and uncovered vertices in the current solution. The experimental results show that our algorithm significantly outperforms the state-of-the-art heuristic algorithm by one to two orders of magnitudes on the 85 classical instances. Also, our algorithm improves the current optimal solutions of 11 instances.

An efficient local search heuristic with row weighting for the unicost set covering problem

Abstract The Set Covering Problem (SCP) is NP -hard. We propose a new Row Weighting Local Search (RWLS) algorithm for solving the unicost variant of the SCP, i.e., USCPs where the costs of all sets are identical. RWLS is a heuristic algorithm that has three major components united in its local search framework: (1) a weighting scheme, which updates the weights of uncovered elements to prevent convergence to local optima, (2) tabu strategies to avoid possible cycles during the search, and (3) a timestamp method to break ties when prioritizing sets. RWLS has been evaluated on a large number of problem instances from the OR-Library and compared with other approaches. It is able to find all the best known solutions (BKS) and improve 14 of them, although requiring a higher computational effort on several instances. RWLS is especially effective on the combinatorial OR-Library instances and can improve the best known solution to the hardest instance CYC11 considerably. RWLS is conceptually simple and has no instance-dependent parameters, which makes it a practical and easy-to-use USCP solver.

A rough set method for the unicost set covering problem

In this paper, we aim to provide a rough set method to deal with a class of set covering problem called the unicost set covering problem, which is a well-known problem in binary optimization. Firstly, by constructing a Multi-Relation Granular Computing (GrC) model of a given unicost set covering problem, the problem can be equivalently converted to the knowledge reduction problem in rough set theory. Thus, various kinds of efficient knowledge reduction methods in rough set theory can be used to solve the unicost set covering problem. Secondly, a commonly used reduction algorithm based on information entropy is proposed to compute a local minimum of the unicost set covering problem. Finally, the feasibility and efficiency of the proposed algorithm is examined by an example.

Scheduling multi-colour print jobs with sequence-dependent setup times

In this paper, a scheduling problem is considered which arises in the packaging industry. Plastic and foil wrappers used for packaging candy bars, crisps and other snacks typically require overlay printing with multiple colours. Printing machines used for this purpose usually accommodate a small number of colours which are loaded into a magazine simultaneously. If two consecutively scheduled print jobs require significantly different colour overlays, then substantial down times are incurred during the transition from the former magazine colour configuration to the latter, because ink cartridges corresponding to colours not required for the latter job have to be cleaned after completion of the former job. The durations of these down times are therefore sequence dependent (the washing and refilling time is a function of the number of colours in which two consecutive printing jobs differ). It is consequently desirable to schedule print jobs so that the accumulated down times associated with all magazine colour transitions are as short as possible for each printing machine. We show that an instance of this scheduling problem can be modelled as the well-known tool switching problem, which is tractable for small instances only. The problem can, however, be solved rather effectively in heuristic fashion by decomposing it into two subproblems: a job grouping problem (which can be modelled as a unicost set covering problem) and a group sequencing problem (which is a generalisation of the celebrated travelling salesman problem). We solve the colour print scheduling problem both exactly and heuristically for small, randomly generated test problem instances, studying the trade-off between the time efficiency and solution quality of the two approaches. Finally, we apply both solution approaches to real problem data obtained from a printing company in the South African Western Cape as a special case study.

An electromagnetism metaheuristic for the unicost set covering problem

In this paper we propose a new heuristic algorithm to solve the unicost version of the well-known set covering problem. The method is based on the electromagnetism metaheuristic approach which, after generating a pool of solutions to create the initial population, applies a fixed number of local search and movement iterations based on the “electromagnetism” theory. In addition to some random aspects, used in the construction and local search phases, we also apply mutation in order to further escape from local optima. The proposed algorithm has been tested over 80 instances of the literature. On the classical benchmark instances, where the number of columns is larger than the number of rows, the algorithm, by using a fixed set of parameters, always found the best known solution, and for 12 instances it was able to improve the current best solution. By using different parameter settings the algorithm improved 4 additional best known solutions. Moreover, we proved the effectiveness of the electromagnetism metaheuristic approach for the unicost set covering problem by embedding the procedures of the proposed algorithm in a genetic algorithm scheme. The worse results obtained by the genetic algorithm show the impact of the electromagnetism metaheuristic approach in conducting the search of the solution space by applying the movements based on the electromagnetism theory. Finally, we report the results obtained by modifying the proposed electromagnetism metaheuristic algorithm for solving the non-unicost set covering problem.

A Reactive Tabu Search algorithm with variable clustering for the Unicost Set Covering Problem

We develop a Reactive Tabu Search (RTS) algorithm for solving the Unicost Set Covering Problem (SCP) – USCP-TS. We solve a Linear Programming (LP) relaxation of the problem and use the LP optimum to construct a quality solution profile. We cluster the problem variables based on this profile and partition the solution space into orbits. We tested our algorithm on 65 benchmark problems and compared the results against the previous best-known solutions and those obtained by CPLEX 9.0 under varied settings. USCP-TS outperforms CPLEX in solution quality for 32 of the problems and achieves the same solution as CPLEX faster on 21 of the remaining problems.

Solution techniques for the Large Set Covering Problem

Given a finite set E and a family F = { E 1 , … , E m } of subsets of E such that F covers E , the famous unicost set covering problem (USCP) is to determine the smallest possible subset of F that also covers E . We study in this paper a variant, called the Large Set Covering Problem (LSCP), which differs from the USCP in that E and the subsets E i are not given in extension because they are very large sets that are possibly infinite. We propose three exact algorithms for solving the LSCP. Two of them determine minimal covers, while the third one produces minimum covers. Heuristic versions of these algorithms are also proposed and analysed. We then give several procedures for the computation of a lower bound on the minimum size of a cover. We finally present algorithms for finding the largest possible subset of F that does not cover E . We also show that a particular case of the LSCP is to determine irreducible infeasible sets in inconsistent constraint satisfaction problems. All concepts presented in the paper are illustrated on the k -colouring problem which is formulated as a constraint satisfaction problem.

A GRASP algorithm to solve the unicost set covering problem

The set covering problem (SCP) is a well-known combinatorial optimization problem. This paper presents a GRASP algorithm to solve a special SCP case known in the literature as the unicost set covering problem. The algorithm incorporates a local improvement procedure based on the heuristics to solve binary constraint satisfiability problems (SAT). The quality of the proposed algorithm is tested on a set of reference instances, comparing the obtained results with those found in the literature. Our algorithm improves the best-known solutions for many of these instances.

Heuristics for railway infrastructure saturation

This research concerns the problem of the evaluation of the railway infrastructure capacity. It is an important question when railway authorities have to choose between different infrastructure investment projects. We developped independently two heuristic approaches to solve the infrastructure saturation problem. The first is based on a constraint programming model which is solved using a greedy heuristic. The second approach identifies the saturation problem as a unicost set packing problem and its resolution is ensured by an adaption of GRASP metaheuristic. Currently, both resolution techniques are not in competition. The goal is to grasp the resolution ability of the heuristics and to analyse the kind of solutions produced. The Pierrefitte-Gonesse junction has been used as experimental support. A software environment allows to simulate several timetables involving TGV, Inter City and Freight trains.

A comparison of algorithm RS with algorithm OPTSOL70

In a very recent paper (Alminana and Pastor (1997)) we proposed a new lagrangian surrogate heuristic, called RS, for solving the location (or unicost) set covering problem. In that paper we show that RS is more accurate than the pair of greedy type heuristics FMC/CMA and that RS outperforms the surrogate heuristic SH. Here we are going to compare algorithms RS with the best designed hybrid algorithm for the location set covering problem, known as OPTSOL70.