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This paper proposes a novel optimization algorithm for grouping problems, the Grouping Coral Reefs Optimization algorithm, and describes its application to a Mobile Network Deployment Problem (MNDP) under four optimization criteria. These criteria include economical cost and coverage, and also electromagnetic pollution control and capacity constraints imposed at the base stations controllers, which are novel in this study. The Coral Reefs Optimization algorithm (CRO) is a recently-proposed bio-inspired approach for optimization, based on the simulation of the processes that occur in coral reefs, including reproduction, fight for space or depredation. This paper presents a grouping version of the CRO, which has not previously evaluated before. Grouping meta-heuristics are characterized by variable-length encoding solutions, and have been successfully applied to a number of different optimization and assignment problems. The GCRO proposed is a novel contribution to the intelligent systems field, which is able to improve results obtained by two alternative grouping algorithms such as grouping genetic algorithms and grouping Harmony Search. The performance of the proposed GCRO and the algorithms for comparison has been tested with real data in a case study of a MNDP in Alcalá de Henares, Madrid, Spain.

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... The spelling of "Salcedo-Sanz (2016)"has been changed to " Salcedo-Sanz et al. (2016)"to match the entry in the references list. Please provide revisions if this is incorrect. ...

... by Salcedo-Sanz et al. (2016). For both, every agent can be generated with different decision space Q22 ...

Some real-life optimization problems, apart from dependence on the combination of state variables, also show dependence on the complexity of the model describing the problem. Changing model complexity implies changing the number of decision space dimensions.
A new method called Particle Swarm Optimization for Variable Number of Dimensions is developed here. The well-known particle swarm optimization procedure is modified to handle spaces with a variable number of dimensions within a single run. Some well-known benchmark problems are modified to depend on the number of dimensions. Novel performance metrics are defined in the article to evaluate convergence properties of the method. Some recommendations for setting the optimization are made according to results of the method on the proposed benchmark test suite. The method is compared with conventional swarm strategies able to solve problems with variable number of dimensions.

... Moreover, [101] makes use of game theory for optimal placement of base stations within a wireless network, aiming at cost minimization and maximization of capacity and coverage under service demand constraints. Another solution [102] adopts the Grouping Coral Reefs Optimization algorithm for solving mobile network deployment problem optimizing economical cost, coverage, electromagnetic pollution control, and capacity constraints. ...

Efficient resource planning is recognized as one of the key enablers making the large-scale deployment of next-generation wireless networks available for mass usage. Modelling, planning, and software simulation tools reduce both the time needed and costs of their tuning and realization. In this paper, we propose a model-driven framework for proactive network planning relying on synergy of deep learning and multiobjective optimization. e predictions about service demand and energy consumption are taken into account. Also, the impact of degradations resulting from fading and cochannel interference (CCI) effects is also considered. e optimization task is treated as a component allocation problem (CAP) aiming to find the best possible base station allocation for the considered smart city locations with respect to performance and service demand constraints. e goal is to maximize Quality of Service (QoS) while keeping the costs and energy consumption as low as possible. e adoption of a model-driven approach in combination with model-to-model transformations and automated code generation does not only reduce the complexity, making experimentation more rapid and convenient at the same time, but also increase the overall reusability and expandability of the planning tool. According to the obtained results, the proposed solution seems to be promising not only due to achieved benefits but also regarding the execution time, which is shorter than that achieved in our previous works, especially for larger distances. Further, we adopt model-based representation of handover strategies within the planning tool, enabling examination of the dynamic behavior of user-created plan, which is not exploited in other similar works. e main contributions of the paper are (1) wireless network planning (WNP) metamodel, a modelling notation for network plans; (2) model-to-model transformation for conversion of WNP to generalized CAP metamodel; (3) prediction problem (PP) metamodel, high-level abstraction for representation of prediction-related regression and classification problems; (4) code generator that creates PyTorch neural network from PP representation; (5) service demand and energy consumption prediction modules performing regression; (6) multiobjective optimization model for base station allocation; (7) Handover Strategy (HS) metamodel used for description of dynamic aspects and adaptability relevant to network planning.

... This algorithm was first proposed in [29], and further described in [30]. It is based on a basic version of the CRO meta-heuristic proposed in [31] and successfully applied to different optimization problems [32,33]. The CRO-SL has been further applied to a large number alternative optimization problems, in different engineering fields [34][35][36][37]. ...

This paper deals with the problem of finding the optimal location and sizing of Energy Storage Systems in DC-electrified railway lines. These devices increment the use of the regenerated energy produced by the trains in the braking phases, as they store the energy to later provide to the catenary the excess of regenerated energy, that otherwise would be lost in the rheostats. However, these infrastructures require a high initial investment that, in some cases, may question their profitability. We propose a multi-method ensemble meta-heuristic to obtain the optimal solution to the problem, with a high level of accuracy. Specifically, the Coral Reefs Optimization with Substrate Layers (CRO-SL) is proposed, an evolutionary-type approach able to run different search procedures within the same population. We will evaluate the performance of the CRO-SL in the problem, and we will show that it performs better than the best known existing meta-heuristics for this problem.

... The Coral Reefs Optimization algorithm (CRO) is a type of evolutionary technique proposed in [34,35] that has been successfully applied in several optimization problems [36][37][38][39][40][41][42]. The CRO uses a n × m grid R (i.e., the coral reef), where each square (denoted by its coordinates (i,j)) can host a candidate solution to the problem x (i.e., a coral). ...

Hydro-power plants are able to produce electrical energy in a sustainable way. A known format for producing energy is through generation scheduling, which is a task usually established as a Unit Commitment problem. The challenge in this process is to define the amount of energy that each turbine-generator needs to deliver to the plant, to fulfill the requested electrical dispatch commitment, while coping with the operational restrictions. An optimal generation scheduling for turbine-generators in hydro-power plants can offer a larger amount of energy to be generated with respect to non-optimized schedules, with significantly less water consumption. This work presents an efficient mathematical modelling for generation scheduling in a real hydro-power plant in Brazil. An optimization method based on different versions of the Coral Reefs Optimization algorithm with Substrate Layers (CRO) is proposed as an effective method to tackle this problem. This approach uses different search operators in a single population to refine the search for an optimal scheduling for this problem. We have shown that the solution obtained with the CRO using Gaussian search in exploration is able to produce competitive solutions in terms of energy production. The results obtained show a huge savings of 13.98 billion (liters of water) monthly projected versus the non-optimized scheduling.

... Therefore, it becomes very important to achieve optimal deployment of cellular Base stations or wireless access points in order to minimize radiation levels. Compared to most optimization solutions in research [49]- [52], which have considered deployment cost, coverage level and base station capacity in the objective function, Salcedo-Sanz et al. [53] have considered an additional criterion, electromagnetic pollution. They have proposed a solution called Grouping Coral Reefs Optimization (GCRO) and demonstrated its effectiveness when applied to a Mobile Network Deplyment Problem (MNDP). ...

The electromagnetic radiation (EMR) emitted out of wireless communication modules in various IoT devices (especially used for healthcare applications due to their close proximity to the body) devices have been identified by researchers as biologically hazardous to humans as well as other living beings. Different countries have different regulations to limit the radiation density levels caused by these devices. The radiation absorbed by an individual depends on various factors such as the device they use, the proximity of use, the type of antenna, the relative orientation of the antenna on the device, and many more. Several standards exist which have tried to quantify the radiation levels and come up with safe limits of EMR absorption to prevent human harm. In this work, we determine the radiation concern levels in several scenarios using a handheld radiation meter by correlating the findings with several international standards, which are determined based on thorough scientific evidence. This study also analyzes the EMR from common devices used in day to day life such as smartphones, laptops, Wi-Fi routers, hotspots, wireless earphones, smartwatches, Bluetooth speakers and other wireless accessories using a handheld radio frequency radiation measurement device. The procedure followed in this paper is so presented that it can also be utilized by the general public as a tutorial to evaluate their own safety with respect to EMR exposure. We present a summary of the most prominent health hazards which have been known to occur due to EMR exposure. We also discuss some individual and collective human-centric protective and preventive measures that can be undertaken to reduce the risk of EMR absorption. This paper analyses radiation safety in pre-5G networks and uses the insight gained to raise valuable concerns regarding EMR safety in the upcoming 5G networks.

... This method can get better base station deployment, but for the management of large-scale network base stations the algorithm has a poor response speed. In 2014, Salcedo-Sanz optimized the goal of minimizing electromagnetic pollution, and proposed a coral reef optimization algorithm (CRO) to solve the problem of mobile network deployment [4]. Its convergence speed is obviously better than that of particle swarm algorithm and harmony search algorithm. ...

This paper proposes a green deployment method for micro base stations for ultra-dense heterogeneous cellular networks to balance network energy efficiency and electromagnetic radiation and meet certain user service quality. Firstly, a constrained multi-objective mathematical model for the green deployment of the micro base station is established for the two-dimensional communication scenario, with the user rate as the constraint, aiming at maximizing the network energy efficiency and minimizing the average electromagnetic radiation. Then, a multi-objective dolphin swarm algorithm which considering the evolutionary advantages of excellent infeasible solutions and feasible solutions, improving the individual search mechanism in the dolphin group algorithm, combined with the improved two-population strategy is proposed and tested on the CTP test set. It shows that compared with the other three methods, the method has certain advantages in convergence and distribution. Finally, a green deployment method for micro base stations based on constrained multi-objective dolphin swarm algorithm is established. Experiments on nine communication scenarios show that the proposed method can balance network energy efficiency and electromagnetic radiation.

... The CRO is an evolutionary-type algorithm which simulates the biological processes in a real coral reef. This metaheuristic has been applied in different areas such as energy problems [16,17] and telecommunications [18,19]. Moreover, the CRO algorithm has been used as a hybrid differential evolution for training extreme learning machines [20], for clustering [21] and for vehicle routing [22]. ...

This paper is focused on reducing the number of elements in time series with minimum information loss, with specific applications on time series segmentation. A modification of the coral reefs optimization metaheuristic (CRO) is proposed for this purpose, which is called statistical CRO (SCRO), where the main parameters of the algorithm are adjusted based on the mean and standard deviation associated with the fitness distribution. Moreover, the algorithm is combined with the Bottom-Up and Top-Down methodologies (traditional local search methods for time series segmentation), resulting in a hybrid methodology (HSCRO). We evaluate the performance of these algorithms using 16 time series from different application areas. The statistically-driven version of CRO is shown to improve the results of the standard CRO, eliminating the necessity of manually adjusting the main parameters of the algorithm and dynamically adjusting these parameters throughout the evolution. Moreover, when compared with other local search methods and metaheuristics from the state of the art, HSCRO shows robust segmentation results, consistently obtaining lower approximation errors.

... Fuzzy logic can be involved in adaptive GWO in order to exploit the advantages of the nonlinear input-output maps of fuzzy systems [46][47][48][49][50]. The hybridization with other algorithms is a good option because of the small numbers of GWO; metaheuristics or classical algorithms can be used with this regard in several applications [51][52][53][54]. ...

This paper proposes an easily understandable Grey Wolf Optimizer (GWO) applied to the optimal tuning of the parameters of Takagi-Sugeno proportional-integral fuzzy controllers (T-S PI-FCs). GWO is employed for solving optimization problems focused on the minimization of discrete-time objective functions defined as the weighted sum of the absolute value of the control error and of the squared output sensitivity function, and the vector variable consists of the tuning parameters of the T-S PI-FCs. Since the sensitivity functions are introduced with respect to the parametric variations of the process, solving these optimization problems is important as it leads to fuzzy control systems with a reduced process parametric sensitivity obtained by a GWO-based fuzzy controller tuning approach. GWO algorithms applied with this regard are formulated in easily understandable terms for both vector and scalar operations, and discussions on stability, convergence, and parameter settings are offered. The controlled processes referred to in the course of this paper belong to a family of nonlinear servo systems, which are modeled by second order dynamics plus a saturation and dead zone static nonlinearity. Experimental results concerning the angular position control of a laboratory servo system are included for validating the proposed method.

In this paper, we tackle a problem of frequency
assignment in Wi-Fi networks with a novel evolutionary-type algorithm. In this version of the problem, we consider the interferences originated by the access points, and also by the clients and all the 11 available channels in the 2.4 GHz Wi-Fi frequency band. The proposed evolutionary-type algorithm is the Coral Reefs Optimization approach with substrate layer (CRO-SL). It is a recently proposed algorithm, which simulates the processes which occur in real coral reefs, including the reproduction and fight for the space of living corals. This version of the algorithm includes a layer of “substrates” which allows using different search patterns jointly in the algorithm. This way, the CRO-SL is able to apply search patterns such as harmony search, differential evolution, Gaussian-based mutations and other traditional and novel search procedures, including local search algorithms, within a single population of solutions. We show the good performance of the proposed approach in a real case study of Wi-Fi frequency assignment, in the Polytechnic School building of the Universidad de Alcalá (Spain), where different realistic scenarios of the problem have been simulated and successfully
solved with the CRO-SL algorithm.

This Ph.D. thesis discusses advanced design issues of the evolutionary-based algorithm \textit{"Coral Reef Optimization"}, in its Substrate-Layer (CRO-SL) version, for optimization problems in Engineering Applications. The problems that can be tackled with meta-heuristic approaches is very wide and varied, and it is not exclusive of engineering. However we focus the Thesis on it area, one of the most prominent in our time. One of the proposed application is battery scheduling problem in Micro-Grids (MGs). Specifically, we consider an MG that includes renewable distributed generation and different loads, defined by its power profiles, and is equipped with an energy storage device (battery) to address its programming (duration of loading / discharging and occurrence) in a real scenario with variable electricity prices. Also, we discuss a problem of vibration cancellation over structures of two and four floors, using Tuned Mass Dampers (TMD's). The optimization algorithm will try to find the best solution by obtaining three physical parameters and the TMD location. As another related application, CRO-SL is used to design Multi-Input-Multi-Output Active Vibration Control (MIMO-AVC) via inertial-mass actuators, for structures subjected to human induced vibration. In this problem, we will optimize the location of each actuator and tune control gains. Finally, we tackle the optimization of a textile modified meander-line Inverted-F Antenna (IFA) with variable width and spacing meander, for RFID systems. Specifically, the CRO-SL is used to obtain an optimal antenna design, with a good bandwidth and radiation pattern, ideal for RFID readers. Radio Frequency Identification (RFID) has become one of the most numerous manufactured devices worldwide due to a reliable and inexpensive means of locating people. They are used in access and money cards and product labels and many other applications.

The simulation of biological processes has produced some of the most important meta-heuristics algorithms for optimization. Evolutionary algorithms were the first, and probably the most applied, algorithms coming from biological inspiration, but there have been many more, specially in the last few years. This paper describes a special class of evolutionary algorithms recently proposed, the coral reefs optimization algorithm (CRO), which simulates some specific biological processes that occur in real coral reefs. The simulation of these processes leads to an evolutionary algorithm in which similarities with Simulated Annealing have been introduced. Moreover, the inclusion of alternative processes occurring in coral reefs produces very effective co-evolution versions of the CRO algorithm, specially well suited for optimization problems with inherent variable length encodings, or able to co-evolve several exploration patterns within the same population. All these issues related to the CRO approach are thoroughly described in the paper, and also a fully description of the main applications of the algorithm in engineering optimization problems is given to close this first review on the CRO.

Coverage control is one of the most fundamental issues in directional sensor networks. In this paper, the coverage optimization problem in a directional sensor network is formulated as a multi-objective optimization problem. It takes into account the coverage rate of the network, the number of working sensor nodes and the connectivity of the network. The coverage problem considered in this paper is characterized by the geographical irregularity of the sensed events and heterogeneity of the sensor nodes in terms of sensing radius, field of angle and communication radius. To solve this multi-objective problem, we introduce a learning automata-based coral reef algorithm for adaptive parameter selection and use a novel Tchebycheff decomposition method to decompose the multi-objective problem into a single-objective problem. Simulation results show the consistent superiority of the proposed algorithm over alternative approaches.

Extreme learning machine (ELM) is a novel and fast learning method to train single layer feed-forward networks. However due to the demand for larger number of hidden neurons, the prediction speed of ELM is not fast enough. An evolutionary based ELM with differential evolution (DE) has been proposed to reduce the prediction time of original ELM. But it may still get stuck at local optima. In this paper, a novel algorithm hybridizing DE and metaheuristic coral reef optimization (CRO), which is called differential evolution coral reef optimization (DECRO), is proposed to balance the explorative power and exploitive power to reach better performance. The thought and the implement of DECRO algorithm are discussed in this article with detail. DE, CRO and DECRO are applied to ELM training respectively. Experimental results show that DECRO-ELM can reduce the prediction time of original ELM, and obtain better performance for training ELM than both DE and CRO.

Several clustering algorithms have been developed and applied to a great variety of problems in different fields. However, some of these algorithms have limitations. Bio-inspired algorithms have been applied to clustering problems aiming to overcome some of these limitations. In this paper, we apply the Coral Reefs Optimization (CRO) algorithm to clustering problems. The CRO algorithm has been originally proposed for classical optimization problems. In this paper, this algorithm will be adjusted to provide a good clustering partition for a dataset. In addition, we also propose three new modifications of this algorithm and an index to be used as objective function for the optimization techniques. In order to evaluate the effectiveness of
the CRO algorithm and the proposed extensions when dealing with real data, we conduct a comparison analysis with another bio-inspired algorithm, a hybrid genetic algorithm proposed for solving clustering problems. In this analysis, two clustering validiity measures are employed to measure the generated clusters by the bio-inspired algorithms. We also use two objective functions (TWCV and MX index) in the reproduction process of the analysed algorithms.

Clustering as a formal, systematic subject in dissertations can be considered the most influential unsupervised learning problem; so, as every other problem of this kind, it deals with finding the structure in a collection of unlabeled data. One of the matters associated with this subject is undoubtedly determination of the number of clusters. In this chapter, an efficient grouping genetic algorithm is proposed under the circumstances of an anonymous number of clusters. Concurrent clustering with different number of clusters is implemented on the same data in each chromosome of grouping genetic algorithm in order to discern the accurate number of clusters. In subsequent iterations of the algorithm, new solutions with different clusters number or distinct accuracy of clustering are produced by application of efficient crossover and mutation operators that led to significant improvement of clustering. Furthermore, a local search by a special probability is applied in each chromosome of each new population in order to increase the accuracy of clustering.These special operators will lead to the successful application of the proposed method in the big data analysis. To prove the accuracy and the efficiency of the algorithm, its tested on various artificial and real data sets in a comparable manner. Most of the datasets consisted of overlapping clusters, but the algorithm could detect the proper number of all data sets with high accuracy of clustering. The consequences make the best evidence of the algorithms successful performance of finding an appropriate number of clusters and accomplishment of the best clusterings quality in comparison with others.

In this study, the one-dimensional Bin Packing Problem (BPP) is approached. The BPP is a classical optimization problem that is known for its applicability and complexity. We propose a method that is referred to as the Grouping Genetic Algorithm with Controlled Gene Transmission (GGA-CGT) for Bin Packing. The proposed algorithm promotes the transmission of the best genes in the chromosomes without losing the balance between the selective pressure and population diversity. The transmission of the best genes is accomplished by means of a new set of grouping genetic operators, while the evolution is balanced with a new reproduction technique that controls the exploration of the search space and prevents premature convergence of the algorithm. The results obtained from an extensive computational study confirm that (1) promoting the transmission of the best genes improves the performance of each grouping genetic operator; (2) adding intelligence to the packing and rearrangement heuristics enhances the performance of a GGA; (3) controlling selective pressure and population diversity tends to lead to higher effectiveness; and (4) GGA-CGT is comparable to the best state-of-the-art algorithms, outperforming the published results for the class of instances Hard28, which appears to have the greatest degree of difficulty for BPP algorithms.
http://authors.elsevier.com/a/1Q0jQ15N8Rqrtq (Anyone who clicks on the link until January 1, 2015, will be taken to the final version of our article on ScienceDirect for free)

THIS PAPER PRESENTS A NOVEL BIOINSPIRED ALGORITHM TO TACKLE COMPLEX OPTIMIZATION PROBLEMS: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems.

This paper presents a novel fuzzy clustering technique based on grouping genetic algorithms (GGAs), which are a class of evolutionary algorithms especially modified to tackle grouping problems. Our approach hinges on a GGA devised for fuzzy clustering by means of a novel encoding of individuals (containing elements and clusters sections), a new fitness function (a superior modification of the Davies Bouldin index), specially tailored crossover and mutation operators, and the use of a scheme based on a local search and a parallelization process, inspired from an island-based model of evolution. The overall performance of our approach has been assessed over a number of synthetic and real fuzzy clustering problems with different objective functions and distance measures, from which it is concluded that the proposed approach shows excellent performance in all cases.

Many optimization problems in various fields have been solved using diverse optimization al gorithms. Traditional optimization techniques such as linear programming (LP), non-linear programming (NLP), and dynamic program ming (DP) have had major roles in solving these problems. However, their drawbacks generate demand for other types of algorithms, such as heuristic optimization approaches (simulated annealing, tabu search, and evolutionary algo rithms). However, there are still some possibili ties of devising new heuristic algorithms based on analogies with natural or artificial phenom ena. A new heuristic algorithm, mimicking the improvisation of music players, has been devel oped and named Harmony Search (HS). The performance of the algorithm is illustrated with a traveling salesman problem (TSP), a specific academic optimization problem, and a least-cost pipe network design problem.

In this work we explore the feasibility of applying a novel grouping genetic algorithm (GGA) to the problem of assigning resources to mobile terminals or users in Wideband Code Division Multiple Access (WCDMA) mobile networks. In particular, we propose: (1) A novel cost function (to be minimized) that contains, in addition to the common load factors, other utilization ratios for aggregate capacity, codes, power, and users without service. (2) A novel encoding scheme, and modifications for the crossover and mutation operators, tailored for resource assignment in WCDMA networks. The experimental work points out that our GGA approach exhibits a superior performance than that of the conventional method (which minimizes only the load factors), since all users receive the demanded service along with a minimum use of the assigned resources (aggregate capacity, power, and codes).

Mobile technology is currently one of the main pillars of worldwide economy. The constant evolution that mobile communications have undergone in the last decades, due to the appearance of new services and new technologies such as Universal Mobile Telecommunication Systems/High Speed Data Access and Long Term Evolution, has contributed to achieve this position in global economy. However, because of the crisis of the sector in the last 5years, mobile operator's revenues and investments have been reduced. Thus, mobile network operators tend to exploit the existing infrastructure at maximum possible, trying to use the existing network in the most efficient way. In this paper, a novel bio-inspired algorithm, the coral reef optimization algorithm (CRO) is introduced to minimise a network deployment investment cost problem. This is carried out by means of optimising the user demand of different services offered by mobile operators over the available technologies in the market, namely the optimal service distribution problem. The CRO is a recently proposed meta-heuristic based on the computer simulation of corals reproduction and reefs' formation. In this paper, this algorithm has been tested on several optimal service distribution problem scenarios in Spain, observing a significant reduction (up to 400 MEuro) on the total investment costs associated to the radio access network deployment. We compare the performance of the CRO approach with that of a classical (experience-based) services distribution, and with alternative meta-heuristics techniques, obtaining good results in all cases. Copyright (c) 2013 John Wiley & Sons, Ltd.

Many combinatorial optimization problems include a grouping (or assignment) phase wherein a set of items are partitioned into disjoint groups or sets. Introduced in 1994, the grouping genetic algorithm (GGA) is the most established heuristic for grouping problems which exploits the structural information along with the grouping nature of these problems to steer the search process. The aim of this paper is to evaluate the grouping version of the classic evolution strategies (ES) which originally maintain the well-known Gaussian mutation, recombination and selection operators for optimizing non-linear real-valued functions. Introducing the grouping evolution strategies (GES) to optimize the grouping problems that are intrinsically discrete, requests for developing a new mutation operator which works with groups of items rather than scalars and is respondent to the structure of grouping problems. As a source of variation, GES employs a mutation operator which shares a same rationale with the original ES mutation in the way that it works in continuous space while the consequences are used in discrete search space. A two phase heuristic procedure is developed to generate a complete feasible solution from the output of the mutation process. An extensive comparative study is conducted to evaluate the performance of GES versus GGA and GPSO (a recently proposed grouping particle swarm optimization algorithm) on test problem instances of the single batch-processing machine scheduling problem and the bin-packing problem. While these problems share exactly a same grouping structure and the performance of GES on both problems is reliable, switching from one problem to another deteriorates the performance of GGA. Though such a deficiency is not observed in the performance of GPSO, it is still inferior to GES on the single batch-processing machine scheduling test problem instances. Beside such empirical outcomes, the paper conveys a number of core strengths that the design of GES supports them but the design of GGA does not address them.

In this paper we present a hybrid discrete Particle Swarm Optimization (PSO) algorithm for the Mobile Network Deployment Problem (MNDP). First, we fully describe the MNDP, including a term for taking into account the Electromagnetic field produced by new locations of BTSs. We also describe the proposed PSO algorithm and some variations incorporated in order to cope with discrete search spaces, such as the one in the MNDP. We finally show the performance of the proposed discrete PSO in a real MNDP in a Spanish city near Madrid: Alcalá de Henares.

An important class of difficult optimization problems are grouping problems, where the aim is to group together members of a set (i.e. find a good partition of the set). In this paper, we present the grouping genetic algorithm (GGA), which is a genetic algorithm (GA) heavily modified to suit the structure of grouping problems. We first show why both the standard and the ordering GAs fare poorly in this domain, by pointing out their inherent difficulty to capture the regularities of the functional landscape of the grouping problems. We then propose a new encoding scheme and genetic operators adapted to these problems, embodied by the GGA. An experimental evaluation of the GGA on several different problems shows its superiority over standard GAs when applied to grouping problems. The potential of the algorithm is further illustrated by its application to the bin packing problem, where a hybridised GGA outperforms one of the best operations research techniques to date.

An important class of computational problems are grouping problems, where the aim is to group members of a set, i.e., to find a good partitioning of the set. We show why both the classic and the ordering GAs fare poorly in this domain by pointing out their inherent difficulty to capture the regularities of the “functional landscape” of grouping problems. We then propose a new encoding scheme and genetic operators adapted to these problems, yielding the Grouping Genetic Algorithm (GGA) paradigm. We illustrate the approach with three examples of important grouping problems successfully treated with the GGA: the problems of Bin Packing and Line Balancing, Economies of Scale, and Conjunctive Conceptual Clustering applied to the problem of creation of part families.

This paper thoroughly reviews and analyzes the main characteristics and application portfolio of the so-called Harmony Search algorithm, a meta-heuristic approach that has been shown to achieve excellent results in a wide range of optimization problems. As evidenced by a number of studies, this algorithm features several innovative aspects in its operational procedure that foster its utilization in diverse fields such as construction, engineering, robotics, telecommunications, health and energy. This manuscript will go through the most recent literature on the application of Harmony Search to the aforementioned disciplines towards a three-fold goal: (1) to underline the good behavior of this modern meta-heuristic based on the upsurge of related contributions reported to date; (2) to set a bibliographic basis for future research trends focused on its applicability to other areas; (3) to provide an insightful analysis of future research lines gravitating on this meta-heuristic solver.

Many combinatorial optimization problems comprise a grouping phase (the grouping problem) in which the task is to partition a set of items into disjoint sets. Introduced in 1994, grouping genetic algorithm (GGA) is the only evolutionary algorithm heavily modified to suit the structure of grouping problems. In this paper we adapt the structure of the well-known particle swarm optimization algorithm (PSO) for grouping problems. To propose the grouping version of the PSO algorithm, which is called GPSO algorithm, we develop new particle position and velocity updating equations which preserve the major characteristics of the original equations and are respondent to the structure of grouping problems. The new updating equations work with groups of items rather than items isolatedly. One of the main characteristics of the new equations is that they work in continuous space but their outcome is used in discrete space through a two phase procedure. Applications of GPSO algorithm are made to the single batch-machine scheduling problem and bin packing problem, and results are compared with the results reported by GGA. Computational results testify that our algorithm is efficient and can be regarded as a new solver for the wide class of grouping problems.

This paper discusses the performance of a novel Coral Reefs Optimization – Extreme Learning Machine (CRO–ELM) algorithm in a real problem of global solar radiation prediction. The work considers different meteorological data from the radiometric station at Murcia (southern Spain), both from measurements, radiosondes and meteorological models, and fully describes the hybrid CRO–ELM to solve the prediction of the daily global solar radiation from these data. The algorithm is designed in such a way that the ELM solves the prediction problem, whereas the CRO evolves the weights of the neural network, in order to improve the solutions obtained. The experiments carried out have shown that the CRO–ELM approach is able to obtain an accurate prediction of the daily global radiation, better than the classical ELM, and the Support Vector Regression algorithm.

In this paper we present a novel grouping genetic algorithm for clustering problems. Though there have been different approaches that have analyzed the performance of several genetic and evolutionary algorithms in clustering, the grouping-based approach has not been, to our knowledge, tested in this problem yet. In this paper we fully describe the grouping genetic algorithm for clustering, starting with the proposed encoding, different modifications of crossover and mutation operators, and also the description of a local search and an island model included in the algorithm, to improve the algorithm's performance in the problem. We test the proposed grouping genetic algorithm in several experiments in synthetic and real data from public repositories, and compare its results with that of classical clustering approaches, such as K-means and DBSCAN algorithms, obtaining excellent results that confirm the goodness of the proposed grouping-based methodology.

An empirical formula for propagation loss is derived from Okumura's report in order to put his propagation prediction method to computational use. The propagation loss in an urban area is presented in a simple form: A + B log10R, where A and B are frequency and antenna height functions and R is the distance. The introduced formula is applicable to system designs for UHF and VHF land mobile radio services, with a small formulation error, under the following conditions: frequency range 100-1500 MHz, distance 1-20 km, base station antenna height 30-200 m, and vehicular antenna height 1-10 m.

This paper presents a novel algorithm for wind farm design and layout optimization: the Coral Reefs Optimization algorithm (CRO). The CRO is a novel bio-inspired approach, based on the simulation of reef formation and coral reproduction. The CRO is fully described and detailed in this paper, and then applied to the design of a real offshore wind farm in northern Europe. It is shown that the CRO outperforms the results of alternative algorithms in this problem, such as Evolutionary Approaches, Differential Evolution or Harmony Search algorithms.

A number of different models have been suggested for detecting earnings management but the linear regression-based model presented by Jones (1991) is the most frequently used. The underlying assumption with the Jones model is that earnings are managed through accounting accruals. Typically, the companies for which earnings management is studied are grouped based on their industries. It is thus assumed that the accrual generating process for companies within a specific industry is similar. However, some studies have recently shown that this assumption does not necessarily hold. An alternative approach which returns a grouping which is, if not optimal, at least very close to optimal is the use of genetic algorithms. The purpose of this study is to assess the performance of the cross-sectional Jones accrual model when the data set firms are grouped using a grouping genetic algorithm. The results provide strong evidence that the grouping genetic algorithm method outperforms the various alternative grouping methods.

Electromagnetic pollution due to mobile telephony is one of the most concerning problems arising since the spreading of this technology. Different studies have shown the relationship between continuous exposition to electromagnetic fields and different kinds of pathologies. Despite this, the electromagnetic danger for exposition is not taken into account in recent mobile network deployments. In this paper we propose a novel evolutionary algorithm for mobile networks deployment, which takes into account the control of the electromagnetic emission from the base stations as one of the key design parameters. The proposed evolutionary approach is a variable-length algorithm, able to produce solutions with different number of base stations. We detail the encoding, operators and a repairing procedure applied to obtain good solutions in terms of coverage, cost and electromagnetic pollution. The algorithm has been tested in a real problem of mobile network deployment in Alcalá de Henares, Madrid, Spain, and compare with a greedy (constructive) approach and a meta-heuristic algorithm (Harmony Search), obtaining very good results.

Fuzzy data clustering plays an important role in practical use and has become a prerequisite step for decision-making in fuzzy environment. In this paper we propose a new algorithm, called FuzzyGES for unsupervised fuzzy clustering based on adaptation of the recently proposed Grouping Evolution Strategy (GES). To adapt GES for fuzzy clustering we devise a fuzzy counterpart of the grouping mutation operator typically used in GES, and employ it in a two phase procedure to generate a new clustering solution. Unlike conventional clustering algorithms which should get the number of clusters as an input, FuzzyGES tries to determine the true number of clusters as well as providing the optimal cluster centroids after several iterations. The proposed approach is validated through using several data sets and results are compared with those of fuzzy c-means algorithm, particle swarm optimization algorithm (PSO), differential evolution (DE) and league championship algorithm (LCA). We also investigate the performance of FuzzyGES through using different cluster validity indices. Our results indicate that FuzzyGES is fast and provides acceptable results in terms of both determining the correct number of clusters and the accurate cluster centroids.

Construction firms specializing in large commercial buildings often purchase large steel plates, cut them into pieces and then weld the pieces into H-beams and other construction components. We formalize the material ordering and cutting problem faced by this industry and propose a grouping genetic algorithm, called CPGEA, for efficiently controlling the relevant costs. We test the quality of CPGEA in various ways. Three sets of simulated problems with known optimal solutions are solved using CPGEA, and the gap between its solutions and optimal solutions is measured. The same problem sets are also solved with an expert system and a multi-start greedy heuristic. CPGEA solutions are found to be consistently lower cost than the competing methods. The difference in solution quality is most pronounced for difficult problems requiring multiple identical plates in the optimal solution. CPGEA is also tested using data from actual construction projects of a company faced with this problem. Since an optimal solution for the problems is not available, a lower bound is created. For the historical problems tested, the average percent difference between CPGEA solutions and the lower bound is 0.67%. To put this performance in context, the results of solving these problems with an expert system and using experienced engineers is also reported. Of these three methods, CPGEA achieves the best performance and the human experts the worst performance.

Modular products are products that fulfill various functions through the combination of distinct modules. These detachable modules are constructed both according to the maximum physical and functional relations among components and maximizing the similarity of specifically modular driving forces. Accordingly, a non-linear programming is proposed to identify separable modules and simultaneously optimize the number of modules. This paper presents a systematic approach to accomplish modular product design in four major phases. Phase 1 is by means of functional and physical interaction analysis to format a component-to-component correlation matrix. Phase 2 is the exploration of design requirements to evaluate the relative importance of each modular driver. In phase 3, non-linear programming is used to formulate the objective function. In the final phase, a heuristic grouping genetic algorithm is adopted to search for the optimal or near-optimal modular architecture. This process and its application are illustrated by a real case of an electrical consumer product provided by an Original Design Manufacturer. The results demonstrate that the designer could direct a new approach to establish product modules according to the relative importance of modular drivers and the interaction among components.

The layout problem arises in a production plant during the study of a new production system, but also during a possible restructuring. The main aim of layout design is to reduce transportation and maintenance, which simplifies management, shortens lead time, improves product quality and speeds up the response to market fluctuations. A principle of Group Technology (GT) advocates the division of a unity into small groups or cells. As it is most of the time impossible to design totally independent cells, the problem is to minimise traffic of items between the cells, for a fixed maximum cell size. This problem is known as cell formation problem (CFP). We propose here an original approach to solve this NP-hard problem. It is based on a Grouping Genetic Algorithm (GGA), a special class of genetic algorithms, heavily modified to suit the structure of grouping problems. The crucial advantage of this GGA is that it is able to deal with large instances of the problem thus becoming a powerful tool for an engineer determining a plant layout, allowing him or her to try several plant options, without the limitation of huge computation times. ©2000 IMACS/Elsevier Science B.V. All rights reserved.

This paper presents a new model for team formation based on group technology (TFPGT). Specifically, the model is applied as a generalization of the well-known Machine-Part Cell Formation problem, which has become a classical problem in manufacturing in the last few years. In this case, the model presented is especially well-suited for problems of team formation arising in R&D-oriented or teaching institutions. A parallel hybrid grouping genetic algorithm (HGGA) is also proposed in the paper to solve the TFPGT. The performance of the algorithm is shown in several synthetic TFPGT instances, and in a real problem: the formation of teaching groups at the Department of Signal Theory and Communications of the Universidad de Alcalá in Spain.

With the growing use of mobile communication devices, the management of such technologies is of increasing importance. The registration area planning (RAP) problem examines the grouping of cells comprising a personal communication services (PCS) network into contiguous blocks in an effort to reduce the cost of managing the location of the devices operating on the network, in terms of bandwidth. This study introduces a hybridized grouping genetic algorithm (HGGA) to obtain cell formations for the RAP problem. The hybridization is accomplished by adding a tabu search-based improvement operator to a traditional grouping genetic algorithm (GGA). Results indicate that significant performance gains can be realized by hybridizing the algorithm, especially for larger problem instances. The HGGA is shown to consistently outperform the traditional GGA on problems of size greater than 19 cells.

The grouping genetic algorithm (GGA), developed by Emmanuel Falkenauer, is a genetic algorithm whose encoding and operators are tailored to suit the special structure of grouping problems. In particular, the crossover operator for a GGA involves the development of heuristic procedures to restore group membership to any entities that may have been displaced by preceding actions of the operator. In this paper, we present evidence that the success of a GGA is heavily dependent on the replacement heuristic used as a part of the crossover operator. We demonstrate this by comparing the performance of a GGA that uses a naive replacement heuristic (GGA(0)) to a GGA that includes an intelligent replacement heuristic (GGA(CF)). We evaluate both the naive and intelligent approaches by applying each of the two GGAs to a well-known grouping problem, the machine-part cell formation problem. The algorithms are tested on problems from the literature as well as randomly generated problems. Using two measures of effectiveness, grouping efficiency and grouping efficacy, our tests demonstrate that adding intelligence to the replacement heuristic enhances the performance of a GGA, particularly on the larger problems tested. Since the intelligence of the replacement heuristic is highly dependent on the particular grouping problem being solved, our research brings into question the robustness of the GGA.

The number of wireless users has steadily increased over the last decade, leading to the need for methods that efficiently use the limited bandwidth available. Reducing the size of the cells in a cellular network increases the rate of frequency reuse or channel reuse, thus increasing the network capacity. The drawback of this approach is increased costs associated with installation and coordination of the additional base stations. A code-division multiple-access network where the base stations are connected to the central station by fiber has been proposed to reduce the installation costs. To reduce the coordination costs and the number of handoffs, sectorization (grouping) of the cells is suggested. We propose a dynamic sectorization of the cells, depending on the current sectorization and the time-varying traffic. A grouping genetic algorithm is proposed to find a solution which minimizes costs. The computational results demonstrate the effectiveness of the algorithm across a wide range of problems. The GGA is shown to be a useful tool to efficiently allocate the limited number of channels available.

The machine-part cell formation problem consists of constructing a set of machine cells and their corresponding product families with the objective of minimizing the inter-cell movement of the products while maximizing machine utilization. This paper presents a hybrid grouping genetic algorithm for the cell formation problem that combines a local search with a standard grouping genetic algorithm to form machine-part cells. Computational results using the grouping efficacy measure for a set of cell formation problems from the literature are presented. The hybrid grouping genetic algorithm is shown to outperform the standard grouping genetic algorithm by exceeding the solution quality on all test problems and by reducing the variability among the solutions found. The algorithm developed performs well on all test problems, exceeding or matching the solution quality of the results presented in previous literature for most problems.

Calculus has widespread applications in science and engineering. Optimization is one of its major subjects, where a problem can be mathematically formulated and its optimal solution is determined by using derivatives. However, this calculus-based derivative technique can only be applied to real-valued or continuous-valued functions rather than discrete-valued functions while there are many situations where design variables contain not continuous values but discrete values by nature. In order to consider these realistic design situations, this study proposes a novel derivative for discrete design variables based on a harmony search algorithm. Detailed analysis shows how this new stochastic derivative works in the bench-mark function and fluid-transport network design. Hopefully this new derivative, as a fundamental technology, will be utilized in various science and engineering problems.

An effective method based on the Genetic Algorithms is proposed to solve the Handicapped Person Transportation problem, which is a real-life application for pickup and delivery problems. In these problems, vehicles have to transport (clients, loads, etc.,) from their locations to different destinations (hospitals, shop centres, etc.). The objective of this paper is to implement Grouping Genetic Algorithm to find optimal (or close to optimal) routes for transporting handicapped people in terms of service quality and number of used vehicles. This algorithm is a stochastic search method based on randomized operators for combining solutions and producing better ones. The proposed algorithm has been applied on the handicapped persons transportation problem in the city of Brussels, Belgium. The obtained results are better than the manually generated solutions in terms of service quality and computational effort.

In this paper we present a novel grouping harmony search algorithm for the Access Node Location Problem (ANLP) with different types of concentrators. The ANLP is a NP-hard problem where a set of distributed terminals, with distinct rate demands, must be assigned to a variable number of concentrators subject to capacity constraints. We consider the possibility of choosing between different concentrator models is given in order to provide service demand at different cost. The ANLP is relevant in communication networks design, and has been considered before within the design of MPLS networks, for example. The approach we propose to tackle the ANLP problem consists of a hybrid Grouping Harmony Search (GHS) algorithm with a local search method and a technique for repairing unfeasible solutions. Moreover, the presented scheme also includes the adaptation of the GHS to a differential scheme, where each proposed harmony is obtained from the same harmony in the previous iteration. This differential scheme is perfectly adapted to the specifications of the ANLP problem, as it utilizes the grouping concept based on the proximity between nodes, instead of being only based on the grouping concept. This allows for a higher efficiency on the searching process of the algorithm. Extensive Monte Carlo simulations in synthetic instances show that this proposal provides faster convergence rate, less computational complexity and better statistical performance than alternative algorithms for the ANLP, such as grouping genetic algorithms, specially when the size of the scenario increases. We also include practical results for the application of GHS to a real wireless network deployment problem in Bizkaia, northern Spain.

This paper presents a novel application of the hybrid grouping genetic algorithm in a problem related to university timetabling. Specifically, the assignment of students to laboratory groups is tackled. This problem includes an important constraint of capacity, due to laboratories usually have a maximum number of equips or computers available, so the number of total students in a group is constrained to be equal or less than the capacity of the laboratory. In addition, our approach considers the case in which the students provide a sorted list of preferred laboratory groups, so the objective of the assignment must take this point into account. A variation of the problem in which a balanced number of students per group is required (lecturer preferences) is also studied in this paper. The performance of the approach is shown in different test problems and in a real application in a Spanish University.

This paper presents the application of a Hybrid Grouping Genetic Algorithm (HGGA) to solve the problem of deploying metropolitan wireless networks. In particular, the exploitation of the existing broadband infrastructure (e.g., ADSL networks) by “opening up” WiFi-enabled routers to third party users, is considered to produce a complex problem, henceforth call WiFi network Design Problem or WiFiDP. The application of a HGGA to this problem produces cost-effective network deployment plans, considering real life aspects such as budget (the total cost of deployment – i.e. the cost of opening all selected DSL routers for public use – should not exceed the allocated budget) and DSL router characteristics (coverage, DSL capacity at a specific location, unit price, etc.) The hybrid grouping genetic algorithm proposed incorporates a particular encoding to tackle the WiFiDP, in which the group part also includes the type of router to be installed. Also, a modification of this encoding to consider the working frequencies of routers is presented in this paper. Moreover, a repairing and local search procedures are added to the algorithm to obtain better performance and always find viable solutions. The performance and effectiveness of the proposed HGGA is evaluated using two randomly generated WiFiDP instances (considering 1000 and 2000 users), used to perform several experiments. The comparison of the proposed HGGA results against those of a greedy optimization algorithm (previously proposed to solve the WiFiDP) shows the better performance of this approach. Finally, the application of the HGGA to real datasets in the cities of Berlin (Germany) and Torrejón de Ardoz (Spain) is also reported in the experimental part. In real conditions, the HGGA keeps performing better than previous methods.

The advent of various real-time multimedia applications in high-speed networks creates a need for quality of service (QoS) based multicast routing. Two important QoS constraints are the bandwidth constraint and the end-to-end delay constraint. The QoS based multicast routing problem is a known NP-complete problem that depends on (1) bounded end-to-end delay and link bandwidth along the paths from the source to each destination, and (2) minimum cost of the multicast tree. In this paper, we presents novel centralized algorithms to solve the bandwidth-delay-constrained least-cost multicast routing problem based on the harmony search (HS) algorithm. Our first algorithm uses modified Prüfer number as Steiner tree representation that is called HSPR. Prüfer number has poor locality and heritability in evolutionary search, so, we describe a new representation, node parent index (NPI) representation, for representing trees and describe harmony operations accord to this representation. Our second algorithm is based on NPI representation that is called HSNPI, an empirical study to determine the impacts of different parameters of the HSNPI algorithm on the solution quality and convergence behavior was performed. We evaluate the performance and efficiency of our proposed methods with a GA-based algorithm and a modified version of the bounded shortest multicast algorithm (BSMA). Simulation results on randomly generated networks and real topologies indicate that HSNPI algorithm that we proposed has overcome other three algorithms on a variety of random generated networks considering average tree cost.

The genetic algorithm (GA) and a related procedure called the grouping genetic algorithm (GGA) are solution methodologies used to search for optimal solutions in constrained optimization problems. While the GA has been successfully applied to a range of problem types, the GGA was created specifically for problems involving the formation of groups. Falkenauer (JORBEL—Belg. J. Oper. Res. Stat. Comput. Sci. 33 (1992) 79), the originator of the GGA, and subsequent researchers have proposed reasons for expecting the GGA to perform more efficiently than the GA on grouping problems. Yet, there has been no research published to date which tests claims of GGA superiority. This paper describes empirical tests of the performance of GA and GGA in three domains which have substantial, practical importance, and which have been the subject of considerable academic research. Our purpose is not to determine which of these two approaches is better across an entire problem domain, but rather to begin to document practical differences between a standard off-the-shelf GA and a tailored GGA. Based on the level of solution quality desired, it may be the case that the additional time and resources required to design a tailored GGA may not be justified if the improvement in solution quality is only minor or non-existent.

European cooperation in the field of scientific and technical research EURO-COST 231. In Urban transmission loss models for mobile radio in the 900 and 1800 MHz bands

Euro COST 231 (1991). European cooperation in the field of scientific and technical
research EURO-COST 231. In Urban transmission loss models for mobile radio in
the 900 and 1800 MHz bands, revision 2. Euro COST.