scholarly journals The Use of an Exact Algorithm within a Tabu Search Maximum Clique Algorithm

Algorithms ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 253 ◽  
Author(s):  
Derek H. Smith ◽  
Roberto Montemanni ◽  
Stephanie Perkins
Keyword(s):  
Tabu Search ◽  
Undirected Graph ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Maximum Clique ◽  
Exact Algorithm ◽  
Maximum Clique Problem ◽  
Tabu Search Algorithm ◽  
Vertex Set ◽  
Clique Algorithm

Let G=(V,E) be an undirected graph with vertex set V and edge set E. A clique C of G is a subset of the vertices of V with every pair of vertices of C adjacent. A maximum clique is a clique with the maximum number of vertices. A tabu search algorithm for the maximum clique problem that uses an exact algorithm on subproblems is presented. The exact algorithm uses a graph coloring upper bound for pruning, and the best such algorithm to use in this context is considered. The final tabu search algorithm successfully finds the optimal or best known solution for all standard benchmarks considered. It is compared with a state-of-the-art algorithm that does not use exact search. It is slower to find the known optimal solution for most instances but is faster for five instances and finds a larger clique for two instances.

scholarly journals Tabu Search Algorithm Based on Lower Bound and Exact Algorithm Solutions for Minimizing the Makespan in Non-Identical Parallel Machines Scheduling

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mohammed A. Noman ◽  
Moath Alatefi ◽  
Abdulrahman M. Al-Ahmari ◽  
Tamer Ali
Keyword(s):  
Lower Bound ◽  
Tabu Search ◽  
Parallel Machines ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Exact Algorithm ◽  
Tabu Search Algorithm ◽  
Scheduling Problems ◽  
Parallel Machines Scheduling ◽  
Hard Problems

Recently, several heuristics have been interested in scheduling problems, especially those that are difficult to solve via traditional methods, and these are called NP-hard problems. As a result, many methods have been proposed to solve the difficult scheduling problems; among those, effective methods are the tabu search algorithm (TS), which is characterized by its high ability to adapt to problems of the large size scale and ease of implementation and gives solution closest to the optimum, but even though those difficult problems are common in many industries, there are only a few numbers of previous studies interested in the scheduling of jobs on unrelated parallel machines. In this paper, a developed TS algorithm based on lower bound (LB) and exact algorithm (EA) solutions is proposed with the objective of minimizing the total completion time (makespan) of jobs on nonidentical parallel machines. The given solution via EA was suggested to enhance and assess the solution obtained from TS. Moreover, the LB algorithm was developed to evaluate the quality of the solution that is supposed to be obtained by the developed TS algorithm and, in addition, to reduce the period for searching for the optimal solution. Two numerical examples from previous studies from the literature have been solved using the developed TS algorithm. Findings show that the developed TS algorithm proved its superiority and speed in giving it the best solution compared to those solutions previously obtained from the literature.

hClique: An exact algorithm for maximum clique problem in uniform hypergraphs

2017 ◽  
Vol 09 (06) ◽  
pp. 1750078 ◽  
Author(s):  
Jose Torres-Jimenez ◽  
Jose Carlos Perez-Torres ◽  
Gildardo Maldonado-Martinez
Keyword(s):  
Maximum Clique ◽  
Exact Algorithm ◽  
Maximum Clique Problem ◽  
Uniform Hypergraph ◽  
Uniform Hypergraphs ◽  
Vertex Set ◽  
Clique Problem

A hypergraph [Formula: see text] with vertex set [Formula: see text] and edge set [Formula: see text] differs from a graph in that an edge can connect more than two vertices. An r-uniform hypergraph [Formula: see text] is a hypergraph with hyperedges of size [Formula: see text]. For an r-uniform hypergraph [Formula: see text], an r-uniform clique is a subset [Formula: see text] of [Formula: see text] such as every subset of [Formula: see text] elements of [Formula: see text] belongs to [Formula: see text]. We present hClique, an exact algorithm to find a maximum r-uniform clique for [Formula: see text]-uniform graphs. In order to evidence the performance of hClique, 32 random [Formula: see text]-graphs were solved.

An Improved Tabu Search Algorithm for Global Optimization of Engineering Design Problems

2013 ◽  
Vol 441 ◽  
pp. 762-767
Author(s):  
Ning Wang ◽  
Shi You Yang
Keyword(s):  
Tabu Search ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Tabu Search Algorithm ◽  
Global Optimal Solution ◽  
Design Problems ◽  
Engineering Design Problems ◽  
Multimodal Function ◽  
Global Optimal ◽  
Continuous And Discrete Variables

To find the global optimal solution of a multimodal function with both continuous and discrete variables, an improved tabu search algorithm is proposed. The improvements include new generating mechanisms for initial and neighborhood solutions, the exclusive use of the tabu list, the restarting methodology for different cycle of iterations as well as the shifting away from the worst solutions. The numerical results on two numerical examples are reported to demonstrate the feasibility and merit of the proposed algorithm.

scholarly journals A Framing Link Based Tabu Search Algorithm for Large-Scale Multidepot Vehicle Routing Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Xuhao Zhang ◽  
Shiquan Zhong ◽  
Yiliu Liu ◽  
Xuelian Wang
Keyword(s):  
Tabu Search ◽  
Vehicle Routing ◽  
Large Scale ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Tabu Search Algorithm ◽  
Routing Problem ◽  
Selection Principles ◽  
Speed Up ◽  
Computation Speed

A framing link (FL) based tabu search algorithm is proposed in this paper for a large-scale multidepot vehicle routing problem (LSMDVRP). Framing links are generated during continuous great optimization of current solutions and then taken as skeletons so as to improve optimal seeking ability, speed up the process of optimization, and obtain better results. Based on the comparison between pre- and postmutation routes in the current solution, different parts are extracted. In the current optimization period, links involved in the optimal solution are regarded as candidates to the FL base. Multiple optimization periods exist in the whole algorithm, and there are several potential FLs in each period. If the update condition is satisfied, the FL base is updated, new FLs are added into the current route, and the next period starts. Through adjusting the borderline of multidepot sharing area with dynamic parameters, the authors define candidate selection principles for three kinds of customer connections, respectively. Link split and the roulette approach are employed to choose FLs. 18 LSMDVRP instances in three groups are studied and new optimal solution values for nine of them are obtained, with higher computation speed and reliability.

scholarly journals Minimizing makespan of Personal Scheduling problem in available time-windows with split-min and setup-time constraints

2018 ◽  
Vol 34 (2) ◽  
pp. 97-111
Author(s):  
SON HONG TRANG ◽  
NGUYEN TUONG HUYNH ◽  
LANG VAN TRAN
Keyword(s):  
Tabu Search ◽  
Search Algorithm ◽  
Time Windows ◽  
Optimal Solution ◽  
Setup Time ◽  
Exact Method ◽  
Time Constraints ◽  
Tabu Search Algorithm ◽  
Scheduling Problem ◽  
Maximum Completion Time

This paper deals with personal scheduling problem in available time-windows with split-min and setup-time constraints. The jobs are splitable into sub-jobs and a common lower bound on the size of each sub-job is imposed. The objective function aims to find a feasible schedule that minimizes the maximum completion time of all jobs. The proposed scheduling problem was proved to be strongly NP-hard by a reduction to 3-SAT problem in the preliminary results. We propose in this paper an exact method based on MILP model to find optimal solution, some heuristics to find feasible solution and a meta-heuristic based on tabu search algorithm to find good solution. The computational results show the performance of proposed exact method, some heuristics and tabu search algorithm.

scholarly journals Performance Improvement of Decision Tree: A Robust Classifier Using Tabu Search Algorithm

2021 ◽  
Vol 11 (15) ◽  
pp. 6728
Author(s):  
Muhammad Asfand Hafeez ◽  
Muhammad Rashid ◽  
Hassan Tariq ◽  
Zain Ul Abideen ◽  
Saud S. Alotaibi ◽  
...  
Keyword(s):  
Machine Learning ◽  
Tabu Search ◽  
Decision Tree ◽  
Decision Trees ◽  
Search Algorithm ◽  
Learning Algorithms ◽  
Performance Comparison ◽  
Machine Learning Algorithms ◽  
Supervised Machine Learning ◽  
Tabu Search Algorithm

Classification and regression are the major applications of machine learning algorithms which are widely used to solve problems in numerous domains of engineering and computer science. Different classifiers based on the optimization of the decision tree have been proposed, however, it is still evolving over time. This paper presents a novel and robust classifier based on a decision tree and tabu search algorithms, respectively. In the aim of improving performance, our proposed algorithm constructs multiple decision trees while employing a tabu search algorithm to consistently monitor the leaf and decision nodes in the corresponding decision trees. Additionally, the used tabu search algorithm is responsible to balance the entropy of the corresponding decision trees. For training the model, we used the clinical data of COVID-19 patients to predict whether a patient is suffering. The experimental results were obtained using our proposed classifier based on the built-in sci-kit learn library in Python. The extensive analysis for the performance comparison was presented using Big O and statistical analysis for conventional supervised machine learning algorithms. Moreover, the performance comparison to optimized state-of-the-art classifiers is also presented. The achieved accuracy of 98%, the required execution time of 55.6 ms and the area under receiver operating characteristic (AUROC) for proposed method of 0.95 reveals that the proposed classifier algorithm is convenient for large datasets.

An extreme‐point tabu‐search algorithm for fixed‐charge network problems

Networks ◽  
2021 ◽  
Vol 77 (2) ◽  
pp. 322-340 ◽  
Author(s):  
Richard S. Barr ◽  
Fred Glover ◽  
Toby Huskinson ◽  
Gary Kochenberger
Keyword(s):  
Tabu Search ◽  
Extreme Point ◽  
Search Algorithm ◽  
Fixed Charge ◽  
Tabu Search Algorithm ◽  
Network Problems
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