Solving the University course timetabling problem using bat inspired algorithm

2021 ◽  
Vol 47 (2) ◽  
pp. 674-685
Author(s):  
Ushindi Limota ◽  
Egbert Mujuni ◽  
Allen Mushi
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Real Life ◽  
Bat Algorithm ◽  
Discrete Version ◽  
Timetabling Problem ◽  
Combinatorial Optimization Problems ◽  
University Course Timetabling ◽  
Metaheuristic Methods

Many mathematical optimization problems from real-life applications are NP-hard, and hence no algorithm that solves them to optimality within a reasonable time is known. For this reason, metaheuristic methods are mostly preferred when their size is big. Many meta-heuristic methods have been proposed to solve various combinatorial optimization problems. One of the newly introduced metaheuristic methods is a bat-inspired algorithm, which is based on the echolocation behaviour of microbats. Bat algorithm (BA) and its variants have been used successfully to solve several optimization problems. However, from the No-free Lunch Theorem, it is known that there is no universal metaheuristic method that can solve efficiently all optimization problems. Thus, this study work focused on investigating the usefulness of BA in solving an optimization problem called Course Teaching Problem (CTP). Since BA was originally designed to solve continuous problems, and CTP is a combinatorial optimization problem, a discrete version of BA for CPT has been proposed and tested using real-life data from the Dar es Salaam University College of Education (DUCE). The algorithm has produced promising results, as in each execution test, it generated a timetable in which all hard constraints were met and soft constraints were significantly satisfied within a few iterations. Keywords: Combinatorial optimization, Timetabling problem, Metaheuristic algorithms, Bat algorithm.

Space Contraction and Partition Algorithm for Combinatorial Optimization

2011 ◽  
Vol 421 ◽  
pp. 559-563
Author(s):  
Yong Chao Gao ◽  
Li Mei Liu ◽  
Heng Qian ◽  
Ding Wang
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Solution Space ◽  
Search Space ◽  
Small Scale ◽  
Optimal Solutions ◽  
Solution Quality ◽  
Intelligent Algorithms ◽  
Combinatorial Optimization Problems

The scale and complexity of search space are important factors deciding the solving difficulty of an optimization problem. The information of solution space may lead searching to optimal solutions. Based on this, an algorithm for combinatorial optimization is proposed. This algorithm makes use of the good solutions found by intelligent algorithms, contracts the search space and partitions it into one or several optimal regions by backbones of combinatorial optimization solutions. And optimization of small-scale problems is carried out in optimal regions. Statistical analysis is not necessary before or through the solving process in this algorithm, and solution information is used to estimate the landscape of search space, which enhances the speed of solving and solution quality. The algorithm breaks a new path for solving combinatorial optimization problems, and the results of experiments also testify its efficiency.

Matched Field Processing Based on the Simulated Annealing

2013 ◽  
Vol 651 ◽  
pp. 879-884
Author(s):  
Qi Wang ◽  
Ying Min Wang ◽  
Yan Ni Gou
Keyword(s):  
Global Optimization ◽  
Simulated Annealing ◽  
Combinatorial Optimization ◽  
Mediterranean Sea ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Combinatorial Optimization Problem ◽  
Matched Field Processing ◽  
Combinatorial Optimization Problems ◽  
Passive Localization

The matched field processing (MFP) for localization usually needs to match all the replica fields in the observation sea with the received fields, and then find the maximum peaks in the matched results, so how to find the maximum in the results effectively and quickly is a problem. As known the classical simulated annealing (CSA) which has the global optimization capability is used widely for combinatorial optimization problems. For passive localization the position of the source can be recognized as a combinatorial optimization problem about range and depth, so a new matched field processing based on CSA is proposed. In order to evaluate the performance of this method, the normal mode was used to calculate the replica field. Finally the algorithm was evaluated by the dataset in the Mediterranean Sea in 1994. Comparing to the conventional matched field passive localization (CMFP), it can be conclude that the new one can localize optimum peak successfully where the output power of CMFP is maximum, meanwhile it is faster than CMFP.

Study on Free Search for Combinatorial Optimization Problem

2013 ◽  
Vol 411-414 ◽  
pp. 1904-1910
Author(s):  
Kai Zhong Jiang ◽  
Tian Bo Wang ◽  
Zhong Tuan Zheng ◽  
Yu Zhou
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Search Process ◽  
Standard Data ◽  
Combinatorial Optimization Problems ◽  
Free Search

An algorithm based on free search is proposed for the combinatorial optimization problems. In this algorithm, a feasible solution is converted into a full permutation of all the elements and a transformation of one solution into another solution can be interpreted the transformation of one permutation into another permutation. Then, the algorithm is combined with intersection elimination. The discrete free search algorithm greatly improves the convergence rate of the search process and enhances the quality of the results. The experiment results on TSP standard data show that the performance of the proposed algorithm is increased by about 2.7% than that of the genetic algorithm.

scholarly journals A Methodology to Find the Elementary Landscape Decomposition of Combinatorial Optimization Problems

2011 ◽  
Vol 19 (4) ◽  
pp. 597-637 ◽  
Author(s):  
Francisco Chicano ◽  
L. Darrell Whitley ◽  
Enrique Alba
Keyword(s):  
Combinatorial Optimization ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Combinatorial Optimization Problem ◽  
Quadratic Assignment ◽  
Neighborhood Structure ◽  
Combinatorial Optimization Problems ◽  
Elementary Landscape

A small number of combinatorial optimization problems have search spaces that correspond to elementary landscapes, where the objective function f is an eigenfunction of the Laplacian that describes the neighborhood structure of the search space. Many problems are not elementary; however, the objective function of a combinatorial optimization problem can always be expressed as a superposition of multiple elementary landscapes if the underlying neighborhood used is symmetric. This paper presents theoretical results that provide the foundation for algebraic methods that can be used to decompose the objective function of an arbitrary combinatorial optimization problem into a sum of subfunctions, where each subfunction is an elementary landscape. Many steps of this process can be automated, and indeed a software tool could be developed that assists the researcher in finding a landscape decomposition. This methodology is then used to show that the subset sum problem is a superposition of two elementary landscapes, and to show that the quadratic assignment problem is a superposition of three elementary landscapes.

An Evaluation of Methods for Estimating the Number of Local Optima in Combinatorial Optimization Problems

2013 ◽  
Vol 21 (4) ◽  
pp. 625-658 ◽  
Author(s):  
Leticia Hernando ◽  
Alexander Mendiburu ◽  
Jose A. Lozano
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Search Space ◽  
Combinatorial Optimization Problem ◽  
Local Search Algorithms ◽  
Neighborhood Structure ◽  
Local Optima ◽  
Combinatorial Optimization Problems ◽  
Evaluation Of Methods

The solution of many combinatorial optimization problems is carried out by metaheuristics, which generally make use of local search algorithms. These algorithms use some kind of neighborhood structure over the search space. The performance of the algorithms strongly depends on the properties that the neighborhood imposes on the search space. One of these properties is the number of local optima. Given an instance of a combinatorial optimization problem and a neighborhood, the estimation of the number of local optima can help not only to measure the complexity of the instance, but also to choose the most convenient neighborhood to solve it. In this paper we review and evaluate several methods to estimate the number of local optima in combinatorial optimization problems. The methods reviewed not only come from the combinatorial optimization literature, but also from the statistical literature. A thorough evaluation in synthetic as well as real problems is given. We conclude by providing recommendations of methods for several scenarios.

scholarly journals Stability concepts in bargaining games

2021 ◽  
Author(s):  
Somnath Kundu
Keyword(s):  
Combinatorial Optimization ◽  
Cost Sharing ◽  
Optimization Problems ◽  
Real Life ◽  
Profit Sharing ◽  
Bargaining Games ◽  
Bargaining Process ◽  
Combinatorial Optimization Problems ◽  
Definition Of ◽  
Stability Concepts

In this thesis we discuss some novel concepts of stability in bargaining games, over a network setting. So far, the studies on bargaining games were done as profit sharing problems, whose underlying combinatorial optimization problems are of packing type. In our work, we study bargaining games from a cost sharing perspective, where the underlying combinatorial optimization problems are covering type problems. Unlike previous studies, where bargaining processes are restricted to only two players, we study bargaining games over a more generic hypergraph setting, which allows any bargaining process to be formed among any number of players. In previous studies of bargaining games, the objects that are being negotiated are assumed to be uniform and only the outcomes of the negotiations are allowed to be different. However, in our study, we accommodate possibilities of non-uniform weights of the objects that are being negotiated, which is closer to any real life scenario. Finally we extend our study to incorporate socially aware players by introducing a relaxed and innovative definition of stability.

scholarly journals Selected Soft Computing Algorithms for Job Shop Problem (JSP)

2021 ◽  
Vol 10 (9) ◽  
pp. 125-131
Author(s):  
Adedeji Oluyinka Titilayo ◽  
Alade Oluwaseun Modupe ◽  
Makinde Bukola Oyeladun ◽  
OYELEYE Taye E
Keyword(s):  
Combinatorial Optimization ◽  
Computer Science ◽  
Soft Computing ◽  
Operations Research ◽  
Optimization Problem ◽  
Job Shop ◽  
Optimization Problems ◽  
Combinatorial Optimization Problems ◽  
Flower Pollination

Job Shop Problem (JSP) is an optimization problem in computer science and operations research in which jobs are assigned to resources at particular times. Each operation has a specific machine that it needs to be processed on and only one operation in a job can be processed at a given time. This problem is one of the best known combinatorial optimization problems. The aim of this project is to adapt Bat, Bee, Firefly, and Flower pollination algorithms, implement and evaluate the developed algorithms for solving Job Shop Problem.

scholarly journals Enhanced Hyper-Cube Framework Ant Colony Optimization for Combinatorial Optimization Problems

Algorithms ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 286
Author(s):  
Ali Ahmid ◽  
Thien-My Dao ◽  
Ngan Van Le
Keyword(s):  
Combinatorial Optimization ◽  
Ant Colony Optimization ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Real Life ◽  
Ant Colony ◽  
Combinatorial Optimization Problems ◽  
The Right ◽  
Design Cost ◽  
Laminated Structures

Solving of combinatorial optimization problems is a common practice in real-life engineering applications. Trusses, cranes, and composite laminated structures are some good examples that fall under this category of optimization problems. Those examples have a common feature of discrete design domain that turn them into a set of NP-hard optimization problems. Determining the right optimization algorithm for such problems is a precious point that tends to impact the overall cost of the design process. Furthermore, reinforcing the performance of a prospective optimization algorithm reduces the design cost. In the current study, a comprehensive assessment criterion has been developed to assess the performance of meta-heuristic (MH) solutions in the domain of structural design. Thereafter, the proposed criterion was employed to compare five different variants of Ant Colony Optimization (ACO). It was done by using a well-known structural optimization problem of laminate Stacking Sequence Design (SSD). The initial results of the comparison study reveal that the Hyper-Cube Framework (HCF) ACO variant outperforms the others. Consequently, an investigation of further improvement led to introducing an enhanced version of HCFACO (or EHCFACO). Eventually, the performance assessment of the EHCFACO variant showed that the average practical reliability became more than twice that of the standard ACO, and the normalized price decreased more to hold at 28.92 instead of 51.17.

scholarly journals Fuzzy covering location problems with different aggregation operators

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 513-522 ◽  
Author(s):  
Darko Drakulic ◽  
Aleksandar Takaci ◽  
Miroslav Maric
Keyword(s):  
Combinatorial Optimization ◽  
Fuzzy Sets ◽  
Optimization Problems ◽  
Real Life ◽  
Aggregation Operators ◽  
Location Problems ◽  
Important Class ◽  
Combinatorial Optimization Problems ◽  
Life Problems ◽  
Standard Models

Covering location problems is well-known and very important class of combinatorial optimization problems. Standard models for covering location problems cannot encompass real-life problems, because real-life problems contain some degree of uncertainty. The use of fuzzy sets in modeling covering location problems allows the implementation of these conditions. Depending on the type of problems, it is necessary to use different aggregation operators in calculating solution?s quality. The aim of this study is introducing of fuzzy sets with different corresponding conorms in modeling most known types of covering location problems.

Website link Structure Optimization

2016 ◽  
pp. 222-251 ◽  
Author(s):  
Harpreet Singh ◽  
Parminder Kaur
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Structure Optimization ◽  
Optimization Models ◽  
Graph Structure ◽  
Link Structure ◽  
Combinatorial Optimization Problems ◽  
Web Graph ◽  
The Web

The structure of a website can be represented in the form of a graph where nodes represent pages and edges represent hyperlinks among those pages. The behaviour of website users changes continuously and hence the link structure of a website should be modified frequently. The problem of optimally rearranging the link structure of a website is known as Website Structure Optimization problem. It falls in the category of combinatorial optimization problems. Many methods have been proposed and developed by the researchers to optimize the web graph structure of a website. In this chapter taxonomy of the website link structure optimization models is presented. The formulation and explanation of the working of the models have also been provided so that the readers could easily understand the methodology used by the models.

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