Abstract

In this paper, a new nature-inspired human-based optimization algorithm is proposed which is called coronavirus herd immunity optimizer (CHIO). The inspiration of CHIO is originated from the herd immunity concept as a way to tackle coronavirus pandemic (COVID-19). The speed of spreading coronavirus infection depends on how the infected individuals directly contact with other society members. In order to protect other members of society from the disease, social distancing is suggested by health experts. Herd immunity is a state the population reaches when most of the population is immune which results in the prevention of disease transmission. These concepts are modeled in terms of optimization concepts. CHIO mimics the herd immunity strategy as well as the social distancing concepts. Three types of individual cases are utilized for herd immunity: susceptible, infected, and immuned. This is to determine how the newly generated solution updates its genes with social distancing strategies. CHIO is evaluated using 23 well-known benchmark functions. Initially, the sensitivity of CHIO to its parameters is studied. Thereafter, the comparative evaluation against seven state-of-the-art methods is conducted. The comparative analysis verifies that CHIO is able to yield very competitive results compared to those obtained by other well-established methods. For more validations, three real-world engineering optimization problems extracted from IEEE-CEC 2011 are used. Again, CHIO is proved to be efficient. In conclusion, CHIO is a very powerful optimization algorithm that can be used to tackle many optimization problems across a wide variety of optimization domains.

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Abstract

In this paper, a new metaheuristic algorithm called JAYA algorithm has been adapted for feature selection. Feature selection is a typical problem in machine learning and data mining domain concerned with determining the subset of high discriminative features from the irrelevant, noisy, redundant, and high-dimensional features. JAYA algorithm is initially proposed for continuous optimization. Due to the binary nature of the feature selection problem, the JAYA algorithm is adjusted using sinusoidal (i.e., S-shape) transfer function. Furthermore, the mutation operator controlled by adaptive mutation rate (RmRm) parameter is also utilized to control the diversity during the search. The proposed binary JAYA algorithm with adaptive mutation is called BJAM algorithm. The performance of BJAM algorithm is tested using 22 real-world benchmark datasets, which vary in terms of the number of features and the number of instances. Four measures are used for performance analysis: classification accuracy, number of features, fitness values, and computational times. Initially, a comparison between binary JAYA (BJA) algorithm and the proposed BJAM algorithm is conducted to show the effect of the mutation operator in the convergence behavior. After that, the results produced by the BJAM algorithm are compared against those yielded by ten state-of-the-art methods. Surprisingly, the proposed BJAM algorithm is able to excel other comparative methods in 7 out of 22 datasets in terms of classification accuracy. This can lead to the conclusion that the proposed BJAM algorithm is an efficient algorithm for the problems belonging to the feature selection domain and is pregnant with fruitful results.

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Abstract

Feature selection is an essential stage in many data mining and machine learning and applications that find the proper subset of features from a set of irrelevant, redundant, noisy and high dimensional data. This dimensional reduction is a vital task to increase classification accuracy and thus reduce the processing time. An optimization algorithm can be applied to tackle the feature selection problem. In this paper, a β-hill climbing optimizer is applied to solve the feature selection problem. β-hill climbing is recently introduced as a local-search based algorithm that can obtain pleasing solutions for different optimization problems. In order to tailor β-hill climbing for feature selection, it has to be adapted to work in a binary context. The S-shaped transfer function is used to transform the data into the binary representation. A set of 22 de facto benchmark real-world datasets are used to evaluate the proposed algorithm. The effect of the β-hill climbing parameters on the convergence rate is studied in terms of accuracy, the number of features, fitness values, and computational time. Furthermore, the proposed method is compared against three local search methods and ten metaheuristics methods. The obtained results show that the proposed binary β-hill climbing optimizer outperforms other comparative local search methods in terms of classification accuracy on 16 out of 22 datasets. Furthermore, it overcomes other comparative metaheuristics approaches in terms of classification accuracy in 7 out of 22 datasets. The obtained results prove the efficiency of the proposed binary β-hill climbing optimizer.

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Abstract

In this paper, a new nature-inspired human-based optimization algorithm is proposed which is called coronavirus herd immunity optimizer (CHIO). The inspiration of CHIO is originated from the herd immunity concept as a way to tackle coronavirus pandemic (COVID-19). The speed of spreading coronavirus infection depends on how the infected individuals directly contact with other society members. In order to protect other members of society from the disease, social distancing is suggested by health experts. Herd immunity is a state the population reaches when most of the population is immune which results in the prevention of disease transmission. These concepts are modeled in terms of optimization concepts. CHIO mimics the herd immunity strategy as well as the social distancing concepts. Three types of individual cases are utilized for herd immunity: susceptible, infected, and immuned. This is to determine how the newly generated solution updates its genes with social distancing strategies. CHIO is evaluated using 23 well-known benchmark functions. Initially, the sensitivity of CHIO to its parameters is studied. Thereafter, the comparative evaluation against seven state-of-the-art methods is conducted. The comparative analysis verifies that CHIO is able to yield very competitive results compared to those obtained by other well-established methods. For more validations, three real-world engineering optimization problems extracted from IEEE-CEC 2011 are used. Again, CHIO is proved to be efficient. In conclusion, CHIO is a very powerful optimization algorithm that can be used to tackle many optimization problems across a wide variety of optimization domains.

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Abstract

In this study, a multi-verse optimizer (MVO) is utilised for the text document clustering (TDC) problem. TDC is treated as a discrete optimization problem, and an objective function based on the Euclidean distance is applied as similarity measure. TDC is tackled by the division of the documents into clusters; documents belonging to the same cluster are similar, whereas those belonging to different clusters are dissimilar. MVO, which is a recent metaheuristic optimization algorithm established for continuous optimization problems, can intelligently navigate different areas in the search space and search deeply in each area using a particular learning mechanism. The proposed algorithm is called MVOTDC, and it adopts the convergence behaviour of MVO operators to deal with discrete, rather than continuous, optimization problems. For evaluating MVOTDC, a comprehensive comparative study is conducted on six text document datasets with various numbers of documents and clusters. The quality of the final results is assessed using precision, recall, F-measure, entropy accuracy, and purity measures. Experimental results reveal that the proposed method performs competitively in comparison with state-of-the-art algorithms. Statistical analysis is also conducted and shows that MVOTDC can produce significant results in comparison with three well-established methods.

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Text Document Clustering; Multi-Verse Optimizer; Optimization; Swarm Intelligence.

Abstract

Economic load dispatch (ELD) is a crucial problem in the power system which is tackled by distributing the required generation power through a set of units to minimize the fuel cost required. This distribution is subject to two main constraints: (1) equality and inequality related to power balance and power output, respectively. In the optimization context, ELD is formulated as a non-convex, nonlinear, constrained optimization problem which cannot be easily solved using calculus-based techniques. Several optimization algorithms have been adapted. Due to the complexity nature of ELD search space, the theoretical concepts of these optimization algorithms have been modified or hybridized. In this paper, the grey wolf optimizer (GWO) which is a swarm intelligence is hybridized with β-hill climbing optimizer (βHC) which is a local search algorithm, to improve convergence properties. GWO is very powerful in a wide search, while βHC is very powerful in deep search. By combining the wide and deep search ability in a single optimization framework, the balance between the exploration and exploitation is correctly managed. The proposed hybrid algorithm is named β-GWO which is evaluated using five different test cases of ELD problems: 3 generating units with 850 MW; 13 generating units with 1800 MW; 13 generating units with 2520 MW; 40 generating units with 10,500 MW; and 80 generating units with 21,000 MW. β-GWO is comparatively measured using 49 comparative methods. The results obtained by β-GWO outperform others in most test cases. In conclusion, the proposed β-GWO is proved to be a powerful method for ELD problem or for any other similar problems in the power system domain.

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Economic load dispatch; Grey wolf optimizer; β-Hill climbing optimizer; Power system; Optimization.

Abstract

Dragonfly Algorithm (DA) is a recent swarm-based optimization method that imitates the hunting and migration mechanisms of idealized dragonflies. Recently, a binary DA (BDA) has been proposed. During the algorithm iterative process, the BDA updates its five main coefficients using random values. This updating mechanism can be improved to utilize the survival-of-the-fittest principle by adopting different functions such as linear, quadratic, and sinusoidal. In this paper, a novel BDA is proposed. The algorithm uses different strategies to update the values of its five main coefficients to tackle Feature Selection (FS) problems. Three versions of BDA have been proposed and compared against the original DA. The proposed algorithms are Linear-BDA, Quadratic-BDA, and Sinusoidal-BDA. The algorithms are evaluated using 18 well-known datasets. Thereafter, they are compared in terms of classification accuracy, the number of selected features, and fitness value. The results show that Sinusoidal-BDA outperforms other proposed methods in almost all datasets. Furthermore, Sinusoidal-BDA exceeds three swarm-based methods in all the datasets in terms of classification accuracy and it excels in most datasets when compared in terms of the fitness function value. In a nutshell, the proposed Sinusoidal-BDA outperforms the comparable feature selection algorithms and the proposed updating mechanism has a high impact on the algorithm performance when tackling FS problems.

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Abstract

This paper proposes an efficient version of artificial bee colony (ABC) algorithm based on the island model concepts. The new version is called the island artificial bee colony (iABC) algorithm. It uses the structured population concept by applying the island model to improve the diversification capabilities of ABC. In the island model, the population is divided into a set of sub-populations called islands, each of which is manipulated separately by an independent variant of the ABC. After a predefined number of iterations, the islands exchange their solutions by migration. This process can help ABC in controlling the diversity of the population during the search process and thus improve the performance. The proposed iABC is evaluated using global optimization functions established by the IEEE-CEC 2015 which include 15 test functions with various dimensions and complexities (i.e., 10, 30, and 50). In order to evaluate the performance of iABC, various parameter settings are utilized to test the effectiveness of their convergence properties. Furthermore, the performance of iABC is compared against 19 comparative methods that used the same IEEE-CEC 2015 test functions. The results show that iABC produced better results when compared with ABC in all IEEE-CEC 2015 test functions, while the results of iABC better than those of the other island-based algorithm on almost all test functions. Furthermore, iABC is able to obtain three new results for three test functions better than all the comparative methods. Using Friedman test and Holm’s procedure, iABC is ranked third, seventh, and ninth out of 19 comparative methods for the test functions with 10, 30, 50 dimensionality, respectively.

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Abstract

Community detection is the problem of identifying communities in which we aim to discover groups of nodes with high connectivity within the same group and with low connectivity outside the group. Community detection is considered to be a non-deterministic polynomial-time hard problem. Heuristic algorithms can be used to solve such a complex optimisation problem. Bat algorithm (BA) is a meta-heuristic optimisation algorithm. The BA can be used to model a multi-objective optimisation problem. In this paper, the multi-objective bat algorithm (MOBA) is adapted to model and solve the community detection problem. In order to evaluate the algorithm, four real-world datasets are used. The performance of the algorithm is compared with seven other methods from the literature. The comparison was in terms of two metrics to check the quality of the obtained community namely modularity (Q) and normalised mutual information (NMI). The results show that the proposed algorithm outperforms all algorithms in one dataset and that it is competitive in other cases

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Abstract

This paper presents an efficient method for aircraft landing problem (ALP) based on a mechanism that hybridizes the iterated local search (ILS) and simulated annealing (SA) algorithms. ALP is handled by scheduling each incoming aircraft to land on a runway in accordance with a predefined landing time frame. The main objective to address is to find a feasible aircraft scheduling solution within the range of target time. The proposed hybridization method complements the advantages of both ILS and SA in a single optimization framework, referred to as iterated simulated annealing (ISA). The optimization framework of ISA has two main loops: an inner loop and an outer loop. In the inner loop, SA is utilized through a cooling schedule and a relaxing acceptance strategy to allow ISA to escape the local optima. In the outer loop, the restart mechanism and perturbation operation of the standard ILS are used to empower ISA to broadly navigate different search space regions. Extensive evaluation experiments were conducted on thirteen small- and large-sized ALP instances to assess the effectiveness and solution quality of ISA. The obtained results confirm that the proposed ISA method considerably performs better than other state-of-the-art methods in which ISA is capable of reaching new best results in 4 out of 24 large-sized problem instances as well as obtaining the best results in all small-sized instances. Evaluation on large-sized instances confirms a high degree of performance. As a new line of research, ISA is an effective method for ALP which can be further investigated for other combinatorial optimization problems.

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Abstract

The flow shop scheduling with blocking is considered an important scheduling problem which has many real-world applications. This paper proposes a new algorithm which applies heuristic techniques in harmony search algorithm (HSA) to minimize the total flow time. The proposed method is called modified harmony search algorithm with neighboring heuristics methods (MHSNH). To improve the initial harmony memory, we apply two heuristic techniques: nearest neighbor (NN) and constructive modified NEH (MNEH). A modified version of harmony search algorithm evolves to explore and generates a new solution. The newly generated solution is then enhanced by using neighboring heuristics. Lastly, another neighboring heuristic is applied to improve the obtained solution. The proposed algorithm is evaluated using 12 real-world problem instances each with 10 samples. The experimental evaluation is accomplished using two factors: CPU computational time and the number of iterations. For the first factor, comparative evaluation against six well-established methods shows that the proposed method achieves almost the best overall results in six problem instances out of the twelve and yields fruitful results for others. For the second factor, comparative evaluation against twelve well-regarded methods shows that the proposed method achieves the best overall results in three problem instances and obtains very good results in other instances. In a nutshell, the proposed MHSNH is an effective strategy for solving the job shop scheduling problem.

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Abstract

The multi-reservoir systems optimization problem requires defining a set of rules to recognize the water amount stored and released in accordance with the system constraints. Traditional methods are not suitable for complex multi-reservoir systems with high dimensionality. Recently, metaheuristic-based algorithms such as evolutionary algorithms and local search-based algorithms are successfully used to solve the multi-reservoir systems. β-hill climbing is a recent metaheuristic local search-based algorithm. In this paper, the multi-reservoir systems optimization problem is tackled using β-hill climbing. In order to validate the proposed method, four-reservoir systems used in the literature to evaluate the algorithm are utilized. A comparative evaluation is conducted to evaluate the proposed method against other methods found in the literature. The obtained results show the competitiveness of the proposed algorithm.

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β-hill climbing; optimization; multi-reservoir operation; partially and fully constrained; local search-based heuristic method.

Abstract

Artificial bee colony (ABC) algorithm is one of the most recent swarm intelligence-based algorithms simulate the foraging behavior of honey bees in their hive. ABC starts with a colony of artificial bees with sole aim of discovering the place of food sources with high nectar amount using the solution search equation in the employed bee and onlooker bee operators. However, the solution search equation is good in exploration and poor in exploitation. In this paper, the solution search equation of the onlooker bee is modified by using a value of the fittest food sources selected by a set of selection schemes inspired from the evolutionary algorithms. This is to guide the search process of onlooker bee toward the fittest food sources from the population in order to empower the exploitation capability and convergence. Four selection schemes are incorporated with the ABC algorithm to choose the fittest food sources in four versions as follows: global-best, tournament, linear rank, and exponential rank. For evaluation purposes, 10 classical benchmark optimization functions are used to study the sensitivity analysis of each ABC algorithm to its parameters. The performance of the proposed ABC versions is compared with the original ABC version in order to study the effectiveness of the modifications. In addition, a comparative evaluation of ABC algorithms is carried out against the state-of-the-art methods that worked on CEC2005 benchmark functions, CEC2015 benchmark functions, and two real-world cases of economic load dispatch problem. The experimental results show that the selection schemes incorporated within the search equation of the onlooker bee directly affects the performance of ABC algorithm.

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Abstract

This paper proposes a new enhanced algorithm called Modernized Genetic Algorithm for solving the Traveling Salesman Problem (MGA-TSP). Recently, the most successful evolutionary algorithm used to solve the TSP problem, is the GA algorithm. One of the main obstacles for GA is building its initial population. When initiating the GA with a strong initial population, the convergence rate and the diversity aspect will be more stronger. Therefore, in this paper, a new local search mechanism based on three neighborhood structure operators (Inverse, Insert, and Swap) along with 2-opt is utilized. This adapted neighborhood structure operators are employed to generate the initial population for GA algorithm. In addition to building powerful initial population for TSP, the main operators (i.e., crossover and mutation) of GA during the generation process should be also enhanced for TSP. Therefore, the recent and powerful crossover operator called EAX is utilized in the proposed MGA-TSP to enhance its convergence behavior. In order to validate the performance of the proposed algorithm we used TSP datasets, have different complexities and sizes. The sizes of the dataset-cities, range from 150 to 33810 cities. Initially, the impact of each neighboring operator on the performance of the proposed algorithm is studied. In conclusion, our proposed method achieved the best results. For comparative evaluation, the results obtained from our proposed MGA-TSP method is compared with those obtained by six well-regard methods using the same TSP instances. The proposed method is able to outperform other comparative methods in almost all TSP instances used.

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Abstract

In this paper, an adaptive version of β−hill climbing is proposed. In the original β−hill climbing, two control parameters are utilized to strike the right balance between a local-nearby exploitation and a global wide-range exploration during the search: N and β, respectively. Conventionally, these two parameters require an intensive study to find their suitable values. In order to yield an easy-to-use optimization method, this paper proposes an efficient adaptive strategy for these two parameters in a deterministic way. The proposed adaptive method is evaluated against 23 global optimization functions. The selectivity analysis to determine the optimal progressing values of N and β during the search is carried out. Furthermore, the behavior of the adaptive version is analyzed based on various problems with different complexity levels. For comparative evaluation, the adaptive version is initially compared with the original one as well as with other local search-based methods and other well-regarded methods using the same benchmark functions. Interestingly, the results produced are very competitive with the other methods. In a nutshell, the proposed adaptive β−hill climbing is able to achieve the best results on 10 out of 23 test functions. For more validation, the test functions established in IEEE-CEC2015 are used with various scaling values. The comparative results show the viability of the proposed adaptive method.

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Abstract

Flower pollination algorithm (FPA) is a recent swarm-based evolutionary algorithm that was inspired by the biological evolution of pollination of the flowers. It deals with a panmictic population of pollens (or solutions) at each generation, using global and local pollination operators, to improve the whole population at once. Like other evolutionary algorithms, FPA has a chronic shortcoming that lies in its inability to maturely converge. This is conventionally known as a premature convergence where the diversity of the population is loosed and thus the search is stagnated. Island model is one of the successful structured population techniques that were utilized in the theoretical characteristics of several evolutionary-based algorithms. In this model, the population is divided into a set of islands. The knowledge is distributed among those islands using a migration process that is controlled by migration rate, topology, frequency, and policy. In this paper, the island model is utilized in the evolution process of FPA to control diversity. The proposed approach is called IsFPA. The ability of IsFPA in maintaining the diversity during the search process, and in producing impressive results, can be interpreted by utilizing the island model in the FPA optimization framework. To assess the efficiency of IsFPA, 23 benchmark functions with various sizes and complexities were used. The best parameter configurations of IsFPA were investigated and analyzed. Comparing the results of IsFPA with those of state-of-the-art methods which are FPA, genetic algorithm (GA), particle swarm optimization (PSO), gravitational search algorithm (GSA), multi-verse optimizer (MVO), island bat algorithm (iBA), and island harmony search (iHS), the comparison results show that the IsFPA is able to control the diversity and improves the outcomes where IsFPA is ranked first followed by FPA, iBA, iHS, GSA, MVO, GA, PSO, respectively, based on the Friedman test with Holm and Hochberg as post hoc statistical test.

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Abstract

The patient admission scheduling (PAS) problem is an optimization problem in which we assign patients automatically to beds for a specific period of time while preserving their medical requirements and their preferences. In this paper, we present a novel solution to the PAS problem using the harmony search (HS) algorithm. We tailor the HS to solve the PAS problem by distributing patients to beds randomly in the harmony memory (HM) while respecting all hard constraints. The proposed algorithm uses five neighborhood strategies in the pitch adjustment stage. This technique helps in increasing the variations of the generated solutions by exploring more solutions in the search space. The PAS standard benchmark datasets are used in the evaluation. Initially, a sensitivity analysis of the HS algorithm is studied to show the effect of its control parameters on the HS performance. The proposed method is also compared with nine methods: non-linear great deluge (NLGD), simulated annealing with hyper-heuristic (HH-SA), improved with equal hyper-heuristic (HH-IE), simulated annealing (SA), tabu search (TS), simple random simulated annealing with dynamic heuristic (DHS-SA), simple random improvement with dynamic heuristic (DHS-OI), simple random great deluge with dynamic heuristic (DHS-GD), and biogeography-based optimization (BBO). The proposed HS algorithm is able to produce comparably competitive results when compared with these methods. This proves that the proposed HS is a very efficient alternative to the PAS problem, which can be efficiently used to solve many scheduling problems of a large-scale data.

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Abstract

Structured population in evolutionary algorithms is a vital strategy to control diversity during the search. One of the most popular structured population strategies is the island model in which the population is divided into several sub-populations (islands). The EA normally search for each island independently. After a number of predefined iterations, a migration process is activated to exchange specific migrants between islands. Recently, bat-inspired algorithm has been proposed as a population-based algorithm to mimic the echolocation system involved in micro-bat. The main drawback of bat-inspired algorithm is its inability to preserve the diversity during the search and thus the prematurity can take place. In this paper, the strategy of island model is adapted for bat-inspired algorithm to empower its capability in controlling its diversity concepts. The proposed island bat-inspired algorithm is evaluated using 25 IEEE-CEC2005 benchmark functions with different size and complexity. The sensitivity analysis for the main parameters of island bat-inspired algorithm is well-studied to show their effect on the convergence properties. For comparative evaluation, island bat-inspired algorithm is compared with 17 competitive methods and shows very successful outcomes. Furthermore, the proposed algorithm is applied for three real-world cases of economic load dispatch problem where the results obtained prove considerable efficiency in comparison with other state-of-the-art methods.

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Abstract

This paper proposed a new gene selection method based on modified Minimum Redundancy Maximum Relevancy (MRMR) as a filtering approach and hybrid bat algorithm with β-hill climbing as an efficient wrapper approach. The gene selection is a process of selecting the discriminative genes that aid in the development of efficient cancer diagnosis and classification. In general, the current filter-based approaches produced gene subset according to its discriminative power. However, one of the deficiencies of single filter approaches is that it has high variability of the classification results. Accordingly, this study aim to improve MRMR through incorporating its with ensemble of filters to increase the robustness and the stability of MRMR. The result of filtering-based approach is a set of discriminative genes. The wrapper-based approach considers the results from the filtering-based approach to formulate the gene selection search space. In wrapper approach, bat algorithm is tailored for gene selection problem and hybridized with a powerful local search method called beta hill climbing to further stress the deep learning side in the search space navigation and thus find a very robust and stable discriminative genes. Bat-inspired algorithm (BA) is a recent swarm-based optimization method while β-hill climbing is an exploratory local search. The proposed method is called Robust MRMR and Hybrid Bat-inspired Algorithm (rMRMR-HBA). To evaluate the proposed method, ten well-known microarray datasets are experimented with. These datasets are varies in terms of number of genes, samples, and classes. For performance evaluation, the proposed filtering-based approach (i.e., rMRMR) is initially tested against the standard MRMR and other well-regard filtering approaches. Thereafter, the wrapper-based approach (i.e., HBA) is evaluated by studying the convergence behavior of BA with and without β-hill climbing. For comparative evaluation, the results of the proposed rMRMR-HBA were compared with state-of-art methods using the same microarray datasets. The comparative results show that our proposed approach achieved outstanding results in two out of ten datasets in terms of clarification accuracy and minimum number of genes.

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Abstract

The selection process is the most attractive operator in the optimization algorithms. It normally mimics the natural selection of survival of the fittest principle. When the selection is too greedy, the selection pressure will be high and therefore the search becomes biased toward exploitation. In contrast, when the selection has a tendency to be random, the selection pressure will be low and thus the exploration is observed more. The selection process in Grey Wolf Optimizer (GWO) tends to be too greedy since the search is driven by the three best solutions. In this paper, different selection methods extracted from other evolutionary algorithms (EAs) are investigated for GWO. Along with the original selection method of GWO called greedy-based selection method, five others selection methods which are proportional, tournament, universal sampling, linear rank, and random selection methods are investigated. Accordingly, six versions of GWO are proposed which are Greedy-based GWO (GGWO), Proportional-based GWO (PGWO), Tournament-based GWO (TGWO), Universal sampling-based GWO (UGWO), Linear rank-based GWO (LGWO), Random-based GWO (RGWO). The six versions are evaluated using 23 test functions circulated in the literature with different characteristics and complexity. The sensitivity analysis of the control parameters of some new versions are discussed. Interestingly, TGWO achieved the best results for almost all benchmark functions. This proves that the selection methods have a high impact on the performance of GWO.

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Abstract

Maximum Satisfiability problem is an optimization variant of the Satisfiability problem (SAT) denoted as MAX-SAT. The aim of this problem is to find Boolean variable assignment that maximizes the number of satisfied clauses in the Boolean formula. In case the number of variables per clause is equal or greater than three, then this problem is considered NP-complete. Hence, many researchers have developed techniques to deal with MAX-SAT. In this paper, we investigate the impact of different hybrid versions of binary harmony search (HS) algorithm on solving MAX 3-SAT problem. Therefore, we propose two novel hybrid binary HS algorithms. The first hybridizes Flip heuristic with HS, and the second uses Tabu search combined with Flip heuristic. Furthermore, a distinguished feature of our proposed approaches is using an objective function that is updated dynamically based on the stepwise adaptation of weights (SAW) mechanism to evaluate the MAX-SAT solution using the proposed hybrid versions. The performance of the proposed approaches is evaluated over standard MAX-SAT benchmarks, and the results are compared with six evolutionary algorithms and three stochastic local search algorithms. The obtained results are competitive and show that the proposed novel approaches are effective.

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Maximum satisfiability problem; harmony search; local search; 3SAT problem; MAX-SAT problem.

Abstract

In this paper, the update process of harmony search (HS) algorithm is modified to improve its concept of diversity. The update process in HS is based on a greedy mechanism in which the new harmony solution, created in each generation, replaces the worst individual in the population, if better. This greedy process could be improved with other updates mechanisms in order to control the diversity perfectly. Three versions of HS have been proposed: (1) Natural Proportional HS ; (2) Natural Tournament HS; (3) Natural Rank HS. These three HS versions employed the natural selection principle of the ‘‘survival of the fittest’’. Instead of replacing the worst individual in population, any individual can be replaced based on certain criteria. Four versions of economic loading dispatch (ELD) problems with valve point have been used to measure the effect of the newly proposed HS versions. The results show that the new HS versions are very promising for ELD domain. This claim is proved based on the comparative evaluation process where the new HS versions are able to excel the state-of-the-art methods in almost ELD problems used.

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Economic dispatch; Valve point; Harmony search algorithm; Natural update process; Optimization

Abstract

In this paper, the problem of economic load dispatch (ELD) is tackled using a recently introduced local search-based method called β-hill climbing optimizer. In a power system, the ELD problem is tackled by arranging a set of generation units’ outputs in a specific order to minimize the cost of the operating fuel and to match the power system load demand. This goal is achieved by satisfying all the power balance equality constraints and power output inequality constraints. β-hill climbing algorithm is a new local search algorithm which uses an intelligent stochastic operator called β-operator to escape the trap of local optima. The proposed method is evaluated using five real-world ELD benchmarks which vary in terms of complexity and size. The sensitivity analysis to study the effect of the proposed method parameters is conducted based on eight different convergence cases. The evaluation results of the proposed method are compared with 45 state-of-the-art methods using the same tested ELD benchmarks. Interestingly, the proposed method is able to produce a very closed-to-optimum result for almost all the tested ELD systems and the best result for one of them.

Keywords:

Metaheuristics; Economic load dispatch; β-hill climbing optimizer; Optimization; Hill climbing 

Abstract

This paper introduces βHCWT, a hybrid of the β-hill climbing metaheuristic algorithm and wavelet transform (WT), as a new method for denoising electrocardiogram (ECG) signals. ECG signals are non-stationary signals that provide a graphical measure of electrical activities in human heart muscles. However, given their non-stationarity, these signals frequently encounter noise and a low signal-to-noise ratio (SNR). The selection of wavelet parameters is a challenging task that is usually performed based on empirical evidence or experience. Therefore, in this paper, β-hill climbing is applied to find the optimal wavelet parameters that can obtain the minimum mean square error (MSE) between the original and denoised ECG signals. The proposed method was tested on a standard ECG dataset from MIT-BIH while its performance was evaluated by using percentage root mean square difference (PRD) and SNR as criteria. Meanwhile, the effect of β-hill climbing on the performance of WT was tested by comparing the proposed method with WT. The proposed method was then compared with the genetic algorithm in consideration of the performance of the WT parameters and adaptive thresholding methods. The proposed method demonstrated an outstanding performance in removing noise from non-stationary signals, and the quality of the output signal was deemed favorable for medical diagnosis.

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Abstract

In this paper, alternative selection mechanisms in the bat-inspired algorithm for global optimization problems are studied. The bat-inspired algorithm is a recent swarm-based intelligent system which mimics the echolocation system of micro-bats. In the bat-inspired algorithm, the bats randomly fly around the best bat locations found during the search so as to improve their hunting of prey. In practice, one bat location from a set of best bat locations is selected. Thereafter, that best bat location is used by local search with a random walk strategy to inform other bats about the prey location. This selection mechanism can be improved using other natural selection mechanisms adopted from other advanced algorithms like Genetic Algorithm. Therefore, six selection mechanisms are studied to choose the best bat location: global-best, tournament, proportional, linear rank, exponential rank, and random. Consequently, six versions of bat-inspired algorithm are proposed and studied which are global-best bat-inspired algorithm (GBA), tournament bat-inspired algorithm (TBA), proportional bat-inspired algorithm (PBA), linear rank bat-inspired algorithm (LBA), exponential rank bat-inspired algorithm (EBA), and random bat-inspired algorithm (RBA). Using two sets of global optimization functions, the bat-inspired versions are evaluated and the sensitivity analyses of each version to its parameters studied. Our results suggest that there are positive effects of the selection mechanisms on the performance of the classical bat-inspired algorithm which is GBA. For comparative evaluation, eighteen methods are selected using 25 IEEE-CEC2005 functions. The results show that the bat-inspired versions with various selection schemes observing the “survival-of-the-fittest” principle are largely competitive to established methods.

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Abstract

This paper proposes a hybrid harmony search algorithm (HHSA) for solving the highly constrained nurse rostering problem (NRP). The NRP is a combinatorial optimization problem tackled by assigning a set of shifts to a set of nurses; each has specific skills and work contract, to a predefined rostering period according to a set of constraints. The harmony search is a metaheuristic approach, where the metaheuristics are the most successful methods for tackling this problem. In HHSA, the harmony search algorithm is hybridized with the hill climbing optimizer to empower its exploitation capability. Furthermore, the memory consideration operator of the HHSA is modified by replacing the random selection scheme with the global-best concept of particle swarm optimization to accelerate its convergence rate. The standard dataset published in the first international nurse rostering competition 2010 (INRC2010) was utilized to evaluate the proposed HHSA. Several convergence scenarios have been employed to study the effects of the two HHSA modifications. Finally, a comparative evaluation against twelve other methods that worked on the INRC2010 dataset is carried out. The experimental results show that the proposed method achieved five new best results, and 33 best published results out of 69 instances as achieved by other comparative methods.

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Metaheuristic; Harmony search; Nurse rostering; Hill climbing; Particle swarm optimization.

Abstract

Krill Herd (KH) algorithm is a class of nature-inspired algorithm, which simulates the herding behavior of krill individuals. It has been successfully utilized to tackle many optimization problems in different domains and found to be very efficient. As a result, the studies has expanded significantly in the last 3 years. This paper presents the extensive (not exhaustive) review of KH algorithm in the area of applications, modifications, and hybridizations across these fields. The description of how KH algorithm was used in the approaches for solving these kinds of problems and further research directions are also discussed.

Keywords:

Krill Herd algorithm;  Swarm intelligence algorithms;  Nature-inspired algorithms;  Metaheuristics

Abstract

For decades, image enhancement has been considered one of the most important aspects in computer science because of its influence on a number of fields including but not limited to medical, security, banking and financial sectors. In this paper, a new gray level image (edge preserving) enhancement method called the harmony search algorithm (HSA) is proposed. HSA is a recently introduced population-based algorithm stemmed by the musical improvisation process when a group of musicians play the pitches of their instruments seeking for pleasing harmony. Tremendous successful stories of HSA application to a wide variety of optimization problems have been passed on at a large scale. In order to evaluate the proposed HSA-based image enhancement method, 14 standard images from the literature are used. For comparative evaluation, the results of the 14 enhanced image produced by HSA are compared with two classical image enhancement methods (i.e., Histogram Equalization algorithm and Image Adjacent algorithm) and two advanced methods (i.e., genetic algorithm and particle swarm optimization). It is note worthy that all these methods employed the same criteria ( number of edges in an gray scaled images, summation intensity of edges detected using a Sobel filter and entropy measure) in order to evaluate their results. The HSA almost achieves the best results in comparison with the other classical and advanced image enhancement algorithms. Due to such achievements, we believe that the proposed method is very promising and has a potential to provide a substantial addition to the image enhancement domain.

Keywords:

Harmony Search;  Image enhancement;  Optimization; Intelligent Agent.

Abstract

This paper proposes a tournament-based harmony search (THS) algorithm for economic load dispatch (ELD) problem. The THS is an efficient modified version of the harmony search (HS) algorithm where the random selection process in the memory consideration operator is replaced by the tournament selection process to activate the natural selection of the survival-of-the-fittest principle and thus improve the convergence properties of HS. The performance THS is evaluated with ELD problem using five different test systems: 3-units generator system; two versions of 13-units generator system; 40-units generator system; and large-scaled 80-units generator system. The effect of tournament size (t) on the performance of THS is studied. A comparative evaluation between THS and other existing methods reported in the literature are carried out. The simulation results show that the THS algorithm is capable of achieving better quality solutions than many of the well-popular optimization methods.

Keywords:

Economic load dispatch
Harmony search algorithm
Tournament selection
Power systems
Global optimization

Abstract

The nurse rostering problem (NRP) is a combinatorial optimization problem tackled by assigning a set of shifts to a set of nurses, each has specific skills and work contract, to a predefined rostering period according to a set constraints. The metaheuristics are the most successful methods for tackling this problem. This paper proposes a metaheuristic technique called a hybrid artificial bee colony (HABC) for NRP. In HABC, the process of the employed bee operator is replaced with the hill climbing optimizer (HCO) to empower its exploitation capability and the usage of HCO is controlled by hill climbing rate (HCR) parameter. The performance of the proposed HABC is evaluated using the standard dataset published in the first international nurse rostering competition 2010 (INRC2010). This dataset consists of 69 instances which reflect this problem in many real-world cases that are varied in size and complexity. The experimental results of studying the effect of HCO using different value of HCR show that the HCO has a great impact on the performance of HABC. In addition, a comparative evaluation of HABC is carried out against other eleven methods that worked on INRC2010 dataset. The comparative results show that the proposed algorithm achieved two new best results for two problem instances, 35 best published results out of 69 instances as achieved by other comparative methods, and comparable results in the remaining instances of INRC2010 dataset.

Keywords:

Metaheuristics
Rostering
Artificial bee colony
Nurse rostering problem
Hill climbing

Abstract

Harmony search (HS) algorithm is a recent meta-heuristic algorithm that mimics the musical improvisation concepts. This algorithm has been widely used for solving optimization problems. Moreover, many modifications in this algorithm have been carried out in order to improve the performance of the search. Island model is a structured population mechanism used in evolutionary algorithms to preserve the diversity of the population and thus improve the performance. In this paper, the island model concepts are embedded into the main framework of HS algorithm to improve its convergence properties where the new method is refer to as island HS (iHS). In the proposed method, the individuals in population are distributed into separate sub-population named (islands). Then the breeding loop is separately involved in each island. After specific generations, a number of individuals run an exchange through a process called migration. This process is performed to keep the diversity of population and to allow islands to interact with each other. The experimental result using a set of benchmark function shows that the island model context is crucial to the performance of iHS. Finally the sensitivity analysis and the comparative study for iHS prove the efficiency of the island model.

Keywords:

Harmony search
Island model
Structured population
Diversity

Abstract

This article presents a Hybrid Artificial Bee Colony (HABC) for uncapacitated examination timetabling. The ABC algorithm is a recent metaheuristic population-based algorithm that belongs to the Swarm Intelligence technique. Examination timetabling is a hard combinatorial optimization problem of assigning examinations to timeslots based on the given hard and soft constraints. The proposed hybridization comes in two phases: the first phase hybridized a simple local search technique as a local refinement process within the employed bee operator of the original ABC, while the second phase involves the replacement of the scout bee operator with the random consideration concept of harmony search algorithm. The former is to empower the exploitation capability of ABC, whereas the latter is used to control the diversity of the solution search space. The HABC is evaluated using a benchmark dataset defined by Carter, including 12 problem instances. The results show that the HABC is better than exiting ABC techniques and competes well with other techniques from the literature.

Keywords:

Artificial Bee Colony algorithm
Swarm Intelligence
metaheuristics
timetabling problem
examination timetabling problem

Abstract

University course timetabling is concerned with assigning a set of courses to a set of rooms and timeslots according to a set of constraints. This problem has been tackled using metaheuristics techniques. Artificial bee colony (ABC) algorithm has been successfully used for tackling uncapaciated examination and course timetabling problems. In this paper, a novel hybrid ABC algorithm based on the integrated technique is proposed for tackling the university course timetabling problem. First of all, initial feasible solutions are generated using the combination of saturation degree (SD) and backtracking algorithm (BA). Secondly, a hill climbing optimizer is embedded within the employed bee operator to enhance the local exploitation ability of the original ABC algorithm while tackling the problem. Hill climbing iteratively navigates the search space of each population member in order to reach a local optima. The proposed hybrid ABC technique is evaluated using the dataset established by Socha including five small, five medium and one large problem instances. Empirical results on these problem instances validate the effectiveness and efficiency of the proposed algorithm. Our work also shows that a well-designed hybrid technique is a competitive alternative for addressing the university course timetabling problem.

Keywords:

Artificial bee colony
Timetabling problem
Nature-inspired computing
Swarm intelligence
Hybrid metaheuristic

Abstract

The selection methods of population-based metaheuristics provide the driving force to generate good solutions. These selection methods select the individuals with a higher fitness to be members of the population in the next iteration correspond to the natural rule of Darwin’s principle survival-of-the-fittest. Harmony search algorithm is a population-based metaheuristic, which mimicking the musical improvisation process where a group of musicians play the pitches of their musical instruments seeking for a pleasing harmony. It improvises the new harmony based on three rules: memory consideration, random consideration, and pitch adjustment. In this paper, we investigate the replacement of the original random selection of memory consideration with a set of selection methods in order to speed-up the convergence. These selection methods include tournament, proportional, and liner rank of Genetic Algorithm, and Global-best of Particle Swarm Optimization. The proposed harmony search with the different memory consideration selection methods evaluated using standard dataset published in the first International Nurse Rostering Competition INRC2010. Nurse rostering problem is a combinatorial optimization problem tackled by assigning a set of nurses with different skills to a set of shifts over predefined scheduling period. Experimentally, the tournament memory consideration selection method achieved the best rate of convergence as well as the best results in comparison with the other memory consideration selection methods.

Keywords:

Abstract

Structured population in evolutionary algorithms (EAs) is an important research track where an individual only interacts with its neighboring individuals in the breeding step. The main rationale behind this is to provide a high level of diversity to overcome the genetic drift. Cellular automata concepts have been embedded to the process of EA in order to provide a decentralized method in order to preserve the population structure. Harmony search (HS) is a recent EA that considers the whole individuals in the breeding step. In this paper, the cellular automata concepts are embedded into the HS algorithm to come up with a new version called cellular harmony search (cHS). In cHS, the population is arranged as a two-dimensional toroidal grid, where each individual in the grid is a cell and only interacts with its neighbors. The memory consideration and population update are modified according to cellular EA theory. The experimental results using benchmark functions show that embedding the cellular automata concepts with HS processes directly affects the performance. Finally, a parameter sensitivity analysis of the cHS variation is analyzed and a comparative evaluation shows the success of cHS.

Abstract

In this paper, the Harmony Search Algorithm (HSA) is proposed to tackle the Nurse Rostering Problem (NRP) using a dataset introduced in the First International Nurse Rostering Competition (INRC2010). NRP is a combinatorial optimization problem that is tackled by assigning a set of nurses with different skills and contracts to different types of shifts, over a predefined scheduling period. HSA is an approximation method which mimics the improvisation process that has been successfully applied for a wide range of optimization problems. It improvises the new harmony iteratively using three operators: memory consideration, random consideration, and pitch adjustment. Recently, HSA has been used for NRP, with promising results. This paper has made two major improvements to HSA for NRP: (i) replacing random selection with the Global-best selection of Particle Swarm Optimization in memory consideration operator to improve convergence speed. (ii) Establishing multi-pitch adjustment procedures to improve local exploitation. The result obtained by HSA is comparable with those produced by the five INRC2010 winners’ methods.

Keywords:

Nurse Rostering
Harmony Search
Approximation method
Population-based
Global-best

Abstract

This paper presents an analysis of some selection methods used in memory consideration of Harmony search (HS) Algorithm. The selection process in memory consideration entails selecting the value of the decision variable from any solution in the Harmony memory (HM). Quite recently, there has been a tendency to adopt novel selection methods that mimic the natural phenomena of the ‘survival of the fittest’ to replace the random selection method in memory consideration. Consequently, the value of decision variable selected using memory consideration is chosen from the higher promising solutions in HM. The adopted selection methods include: proportional, tournament, linear rank, and exponential rank. It has been demonstrated that experimenting with any of these methods in memory consideration directly affects the performance of HS. However, the success of these methods is based on choosing the optimal parameter value of each. The wrong parameter settings might affect the balance between exploration and exploitation of the search space. Accordingly, this paper studies the effect of the selection method parameters in order to show their effect on HS behavior. The evaluation is conducted using standard mathematical functions used in the literature for HS adoptions. The results suggest that the optimal setting of the selection method parameters is crucial to improve the HS performance.

Keywords:

Harmony search
Selection methods
Evolutionary algorithms
Selection pressure

Abstract

Artificial Bee Colony Algorithm (ABC) is nature-inspired metaheuristic, which imitates the foraging behavior of bees. ABC as a stochastic technique is easy to implement, has fewer control parameters, and could easily be modify and hybridized with other metaheuristic algorithms. Due to its successful implementation, several researchers in the optimization and artificial intelligence domains have adopted it to be the main focus of their research work. Since 2005, several related works have appeared to enhance the performance of the standard ABC in the literature, to meet up with challenges of recent research problems being encountered. Interestingly, ABC has been tailored successfully, to solve a wide variety of discrete and continuous optimization problems. Some other works have modified and hybridized ABC to other algorithms, to further enhance the structure of its framework. In this review paper, we provide a thorough and extensive overview of most research work focusing on the application of ABC, with the expectation that it would serve as a reference material to both old and new, incoming researchers to the field, to support their understanding of current trends and assist their future research prospects and directions. The advantages, applications and drawbacks of the newly developed ABC hybrids are highlighted, critically analyzed and discussed accordingly.

Keywords:

Artificial Bee Colony Algorithms
Nature-Inspired Metaheuristics
Swarm Intelligence Algorithms
Optimizations

Abstract

Recently, common selection schemes used in harmony search algorithm (HSA) are altered in memory consideration operation to imitate the natural selection principle of survival of the fittest. The selection schemes adopted include: random, proportional, tournament, and linear rank. In this paper, these selection schemes are analysed in order to evaluate their effect on the performance of HSA. The analysis considers takeover time and convergence rate to measure the effectiveness of each selection scheme. Furthermore, a scaled proportional selection scheme is proposed to replace the proportional selection scheme to overcome its shortcoming with negative fitness values. To study the effect of these different selection schemes we use eight global optimisation functions with different characteristics. An experimental evaluation show that linear rank selection provides the highest convergence speed and highest takeover time. On the other hand, scaled proportional selection provides the slowest convergence speed and slowest takeover time. This indicates the effect of the type of the selection method used in memory consideration in takeover time and convergence rate.

Keywords:

harmony search algorithm HSA,
evolutionary algorithms EA
selection mechanisms
meta-heuristic algorithm

Abstract

Selection is a vital component used in Evolutionary Algorithms (EA) where the fitness value of the solution has influence on the evolution process. Normally, any efficient selection method makes use of the Darwinian principle of natural selection (i.e., survival of the fittest). Harmony search (HS) is a recent EA inspired by musical improvisation process to seek a pleasing harmony. Originally, two selection methods are used in HS: (i) memory consideration selection method where the values of the decision variables are randomly selected from the population (or solutions stored in harmony memory (HM)) to generate a new harmony, and (ii) selecting a new solution in HM whereby a greedy selection is used to update the HM. The memory consideration selection, the focal point of this paper, is not based on natural selection principle which draws heavily on random selection. In this paper, novel selection schemes which replace the random selection scheme in memory consideration are investigated, comprising global-best, fitness-proportional, tournament, linear rank and exponential rank. The proposed selection schemes are individually altered and incorporated in the process of memory consideration and each adoption is realized as a new HS variation. The performance of the proposed HS variations are evaluated and a comparative study is conducted. The experimental results using benchmark functions show that the selection schemes incorporated in memory consideration directly affect the performance of HS algorithm. Finally, a parameter sensitivity analysis of the proposed HS variations is analyzed.

Keywords:

Harmony search algorithm
Selection schemes
Evolutionary Algorithm
Selective pressure
Memory consideration
Genetic Algorithm

Abstract

In this paper, a hybridization of Harmony Search Algorithm (HSA) with a greedy shuffle move is proposed for Nurse Rostering Problem (NRP). NRP is a combinatorial optimization problem that is tackled by assigning a set of nurses with different skills and contracts to different types of shifts, over a pre-determined scheduling period. HSA is a population-based method which mimics the improvisation process that has been successfully applied for a wide range of optimization problems. The performance of HSA is enhanced by hybridizing it with a greedy shuffle move. The proposed method is evaluated using a dataset defined in first International Nurse Rostering Competition (INRC2010). The hybrid HSA obtained the best results of the comparative methods in four datasets.

Keywords:

Harmony Search Algorithm (HSA)
Metaheuristic
Nurse Rostering Problem (NRP)
Population-Based
Shuffle Move

Abstract

This paper presents an artificial bee colony algorithm (ABC) for Education Timetabling Problem (ETP). It is aimed at developing a good-quality solution for the problem. The initial population of solutions was generated using Saturation Degree (SD) and Backtracking Algorithm (BA) to ensure the feasibility of the solutions. At the improvement stage in the solution method, ABC uses neighbourhood structures iteratively within the employed and onlooker bee operators, in order to rigorously navigate the UTP search space. The technique was evaluated using curriculum-based course timetabling (CB-CTT) and Uncapacitated Examination Timetabling Problem (UETP) problem instances. The experimental results on UETP showed that the technique is comparable with other state-of-the-art techniques and provides encouraging results on CB-CTT.

Keywords:

Artificial Bee Colony (ABC)
Course Timetabling
Examination Timetabling
Nature-Inspired Computing
Swarm Intelligence
Timetabling