We presented a new hybrid method that combines cellular harmony search algorithms with the Smallest-Small-World theory. A harmony search (HS) algorithm is based on musical performance processes that occur when a musician searches for a better state of harmony. Harmony search has successfully been applied to a wide variety of practical optimization problems. Most of the previous researches have sought to improve the performance of the HS algorithm by changing the pitch adjusting rate and harmony memory considering rate. However, there has been a lack of studies to improve the performance of the algorithm by the formation of population structures. Therefore, we proposed an improved HS algorithm that uses the cellular automata formation and the topological structure of Smallest-Small-World network. The improved HS algorithm has a high clustering coefficient and a short characteristic path length, having good exploration and exploitation efficiencies. Nine benchmark functions were applied to evaluate the performance of the proposed algorithm. Unlike the existing improved HS algorithm, the proposed algorithm is expected to have improved algorithmic efficiency from the formation of the population structure.

Selecting the right set of features from data of high dimensionality for inducing an accurate classification model is a tough computational challenge. It is almost a NP-hard problem as the combinations of features escalate exponentially as the number of features increases. Unfortunately in data mining, as well as other engineering applications and bioinformatics, some data are described by a long array of features. Many feature subset selection algorithms have been proposed in the past, but not all of them are effective. Since it takes seemingly forever to use brute force in exhaustively trying every possible combination of features, stochastic optimization may be a solution. In this paper, we propose a new feature selection scheme called Swarm Search to find an optimal feature set by using metaheuristics. The advantage of Swarm Search is its flexibility in integrating any classifier into its fitness function and plugging in any metaheuristic algorithm to facilitate heuristic search. Simulation experiments are carried out by testing the Swarm Search over some high-dimensional datasets, with different classification algorithms and various metaheuristic algorithms. The comparative experiment results show that Swarm Search is able to attain relatively low error rates in classification without shrinking the size of the feature subset to its minimum.

We propose a novel heuristic algorithm based on the methods of advanced Harmony Search and Ant Colony Optimization (AHS-ACO) to effectively solve the Traveling Salesman Problem (TSP). The TSP, in general, is well known as an NP-complete problem, whose computational complexity increases exponentially by increasing the number of cities. In our algorithm, Ant Colony Optimization (ACO) is used to search the local optimum in the solution space, followed by the use of the Harmony Search to escape the local optimum determined by the ACO and to move towards a global optimum. Experiments were performed to validate the efficiency of our algorithm through a comparison with other algorithms and the optimum solutions presented in the TSPLIB. The results indicate that our algorithm is capable of generating the optimum solution for most instances in the TSPLIB; moreover, our algorithm found better solutions in two cases (kroB100 and pr144) when compared with the optimum solution presented in the TSPLIB.

This paper presents a heuristic method for electroencephalography (EEG) grouping and feature classification using harmony search (HS) for improving the accuracy of the brain-computer interface (BCI) system. EEG, a noninvasive BCI method, uses many electrodes on the scalp, and a large number of electrodes make the resulting analysis difficult. In addition, traditional EEG analysis cannot handle multiple stimuli. On the other hand, the classification method using the EEG signal has a low accuracy. To solve these problems, we use a heuristic approach to reduce the complexities in multichannel problems and classification. In this study, we build a group of stimuli using the HS algorithm. Then, the features from common spatial patterns are classified by the HS classifier. To confirm the proposed method, we perform experiments using 64-channel EEG equipment. The subjects are subjected to three kinds of stimuli: audio, visual, and motion. Each stimulus is applied alone or in combination with the others. The acquired signals are processed by the proposed method. The classification results in an accuracy of approximately 63%. We conclude that the heuristic approach using the HS algorithm on the BCI is beneficial for EEG signal analysis.

A technique has been developed for predicting road traffic noise for environmental assessment, taking into account traffic volume as well as road surface conditions. The ASJ model (ASJ Prediction Model for Road Traffic Noise, 1999), which is based on the sound power level of the noise emitted by the interaction between the road surface and tires, employs regression models for two road surface types: dense-graded asphalt (DGA) and permeable asphalt (PA). However, these models are not applicable to other types of road surfaces. Accordingly, this paper introduces a parameter estimation procedure for ASJ-based noise prediction models, utilizing a harmony search (HS) algorithm. Traffic noise measurement data for four different vehicle types were used in the algorithm to determine the regression parameters for several road surface types. The parameters of the traffic noise prediction models were evaluated using another measurement set, and good agreement was observed between the predicted and measured sound power levels.

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.

In this paper, a multilevel thresholding (MT) algorithm based on the harmony search algorithm (HSA) is introduced. HSA is an evolutionary method which is inspired in musicians improvising new harmonies while playing. Different to other evolutionary algorithms, HSA exhibits interesting search capabilities still keeping a low computational overhead. The proposed algorithm encodes random samples from a feasible search space inside the image histogram as candidate solutions, whereas their quality is evaluated considering the objective functions that are employed by the Otsu’s or Kapur’s methods. Guided by these objective values, the set of candidate solutions are evolved through the HSA operators until an optimal solution is found. Experimental results demonstrate the high performance of the proposed method for the segmentation of digital images.

A classical issue in many applied fields is to obtain an approximating surface to a given set of data points. This problem arises in Computer-Aided Design and Manufacturing (CAD/CAM), virtual reality, medical imaging, computer graphics, computer animation, and many others. Very often, the preferred approximating surface is polynomial, usually described in parametric form. This leads to the problem of determining suitable parametric values for the data points, the so-called surface parameterization. In real-world settings, data points are generally irregularly sampled and subjected to measurement noise, leading to a very difficult nonlinear continuous optimization problem, unsolvable with standard optimization techniques. This paper solves the parameterization problem for polynomial Bézier surfaces by applying the firefly algorithm, a powerful nature-inspired metaheuristic algorithm introduced recently to address difficult optimization problems. The method has been successfully applied to some illustrative examples of open and closed surfaces, including shapes with singularities. Our results show that the method performs very well, being able to yield the best approximating surface with a high degree of accuracy.

During the last two decades, Continuous Network Design Problem (CNDP) has received much more attention because of increasing trend of traffic congestion in road networks. In the CNDP, the problem is to find optimal link capacity expansions by minimizing the sum of total travel time and investment cost of capacity expansions in a road network. Considering both increasing traffic congestion and limited budgets of local authorities, the CNDP deserves to receive more attention in order to use available budget economically and to mitigate traffic congestion. The CNDP can generally be formulated as bilevel programming model in which the upper level deals with finding optimal link capacity expansions, whereas at the lower level, User Equilibrium (UE) link flows are determined by Wardrop’s first principle. In this paper, cuckoo search (CS) algorithm with Lévy flights is introduced for finding optimal link capacity expansions because of its recent successful applications in solving such complex problems. CS is applied to the 16-link and Sioux Falls networks and compared with available methods in the literature. Results show the potential of CS for finding optimal or near optimal link capacity expansions in a given road network.

Taking inspiration from an organizational evolutionary algorithm for numerical optimization, this paper designs a kind of dynamic population and combining evolutionary operators to form a novel algorithm, a cooperative coevolutionary cuckoo search algorithm (CCCS), for solving both unconstrained, constrained optimization and engineering problems. A population of this algorithm consists of organizations, and an organization consists of dynamic individuals. In experiments, fifteen unconstrained functions, eleven constrained functions, and two engineering design problems are used to validate the performance of CCCS, and thorough comparisons are made between the CCCS and the existing approaches. The results show that the CCCS obtains good performance in the solution quality. Moreover, for the constrained problems, the good performance is obtained by only incorporating a simple constraint handling technique into the CCCS. The results show that the CCCS is quite robust and easy to use.

The aircraft landing problem (ALP) is an NP-hard problem; the aim of ALP is to minimize the total cost of landing deviation from predefined target time under the condition of safe landing. In this paper, the multiple runways case of the static ALP is considered and a hybrid metaheuristic based on bat algorithm is presented to solve it. Moreover, four types of landing time assignment strategies are applied to allocate the scheduling time, and a constructed initialization is used to speed up the convergence rate. The computational results show that the proposed algorithm can obtain the high-quality and comparable solutions for instances up to 500 aircrafts, and also it is capable of finding the optimal solutions for many instances in a short time.

Since conventional methods are incapable of estimating the parameters of Photovoltaic (PV) models with high accuracy, bioinspired algorithms have attracted significant attention in the last decade. Cuckoo Search (CS) is invented based on the inspiration of brood parasitic behavior of some cuckoo species in combination with the Lévy flight behavior. In this paper, a CS-based parameter estimation method is proposed to extract the parameters of single-diode models for commercial PV generators. Simulation results and experimental data show that the CS algorithm is capable of obtaining all the parameters with extremely high accuracy, depicted by a low Root-Mean-Squared-Error (RMSE) value. The proposed method outperforms other algorithms applied in this study.

In differential evolution (DE) algorithm, depending on the characteristics of the problem at hand and the available computational resources, different strategies combined with a different set of parameters may be effective. In addition, a single, well-tuned combination of strategies and parameters may not guarantee optimal performance because different strategies combined with different parameter settings can be appropriate during different stages of the evolution. Therefore, various adaptive/self-adaptive techniques have been proposed to adapt the DE strategies and parameters during the course of evolution. In this paper, we propose a new parameter adaptation technique for DE based on ensemble approach and harmony search algorithm (HS). In the proposed method, an ensemble of parameters is randomly sampled which form the initial harmony memory. The parameter ensemble evolves during the course of the optimization process by HS algorithm. Each parameter combination in the harmony memory is evaluated by testing them on the DE population. The performance of the proposed adaptation method is evaluated using two recently proposed strategies (DE/current-to-pbest/bin and DE/current-to-gr_best/bin) as basic DE frameworks. Numerical results demonstrate the effectiveness of the proposed adaptation technique compared to the state-of-the-art DE based algorithms on a set of challenging test problems (CEC 2005).

This paper presents a mathematical programming model for optimal pavement rehabilitation planning. The model maximized the rehabilitation area through a newly developed permutation algorithm, based on the procedures outlined in the harmony search (HS) algorithm. Additionally, the proposed algorithm was based on an optimal solution method for the problem of multilocation rehabilitation activities on pavement structure, using empirical deterioration and rehabilitation effectiveness models, according to a limited maintenance budget. Thus, nonlinear pavement performance and rehabilitation activity decision models were used to maximize the objective functions of the rehabilitation area within a limited budget, through the permutation algorithm. Our results showed that the heuristic permutation algorithm provided a good optimum in terms of maximizing the rehabilitation area, compared with a method of the worst-first maintenance currently used in Seoul.

Economic dispatch is one of the popular energy system optimization problems. Recently, it has been solved by various phenomenon-mimicking metaheuristic algorithms such as genetic algorithm, tabu search, evolutionary programming, particle swarm optimization, harmony search, honey bee mating optimization, and firefly algorithm. However, those phenomenon-mimicking problems require a tedious and troublesome process of algorithm parameter value setting. Without a proper parameter setting, good results cannot be guaranteed. Thus, this study adopts a newly developed parameter-setting-free technique combined with the harmony search algorithm and applies it to the economic dispatch problem for the first time, obtaining good results. Hopefully more researchers in energy system fields will adopt this user-friendly technique in their own problems in the future.

Harmony search (HS) was introduced in 2001 as a heuristic population-based optimisation algorithm. Since then HS has become a popular alternative to other heuristic algorithms like simulated annealing and particle swarm optimisation. However, some flaws, like the need for parameter tuning, were identified and have been a topic of study for much research over the last 10 years. Many variants of HS were developed to address some of these flaws, and most of them have made substantial improvements. In this paper we compare the performance of three recent HS variants: exploratory harmony search, self-adaptive harmony search, and dynamic local-best harmony search. We compare the accuracy of these algorithms, using a set of well-known optimisation benchmark functions that include both unimodal and multimodal problems. Observations from this comparison led us to design a novel hybrid that combines the best attributes of these modern variants into a single optimiser called generalised adaptive harmony search.