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Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> An important class of computational problems are grouping problems, where the aim is to group together members of a set (i.e., find a good partition of the set). We 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, yielding the Grouping Genetic Algorithm (GGA). We give an experimental comparison of the GGA with the other GAs applied to grouping problems, and we illustrate the approach with two more examples of important grouping problems successfully treated with the GGA: the problems of Bin Packing and Economies of Scale. <s> BIB001 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> In this paper we present a genetic algorithm-based heuristic especially for the weighted maximum independent set problem (IS). The proposed approach treats also some equivalent combinatorial optimization problems. We introduce several modifications to the basic genetic algorithm, by (i) using a crossover called two-fusion operator which creates two new different children and (ii) replacing the mutation operator by the heuristic-feasibility operator tailored specifically for the weighted independent set. The performance of our algorithm was evaluated on several randomly generated problem instances for the weighted independent set and on some instances of the DIMACS Workshop for the particular case: the unweighted maximum clique problem. Computational results show that the proposed approach is able to produce high-quality solutions within reasonable computational times. This algorithm is easily parallelizable and this is one of its important features. <s> BIB002 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> Cellular network operators are dealing with complex problems when planning the network operation. In order to automate the planning process, the development of simulation and optimization tools are under research. In this paper genetic algorithms with three different approaches are studied in order to optimize the base station sites. This research shows that a proper approach in developing the individual structure and fitness function has crucial importance in solving practical base station siting problems with genetic algorithms. <s> BIB003 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> The cost and complexity of a network is closely related to the number of base-stations (BSs) required to achieve the system operator's service objectives. The location of BSs is not an easy task and there are numerous factors that must be taken into account when deciding the optimum position of BSs. This paper discusses the performance of three different algorithms developed to solve the BS location problem: the greedy algorithm (GR), the genetic algorithm (GA) and the combination algorithm for total optimisation (CAT). These three methods are compared and results are given for a typical test scenario. <s> BIB004 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> In this paper, the evolution of mobile radio network is presented. First of all, the network life cycle is considered. A mathematical modeling of these life periods is developed inside an optimization problem: optimal location of base stations. It is a combinatorial optimization problem. A multi-period model is built on a concentrator link approach. Finally, three different multi-period techniques are identified, they are based on using the genetic algorithm (GA) to tackle this problem of the design of microcellular networks. <s> BIB005 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> This paper presents an innovative algorithm for automatic base station placement and dimensioning. A highly efficient optimization strategy forms the core of the proposed algorithm that determines the number of base stations, their sites, and parameters to achieve a high-quality network that meets the requirements of area coverage, traffic capacity, and interference level, while trying to minimize system costs, including the frequency and financial costs. First, the hierarchical approach is outlined and it is applied to place base stations (BSs) for a large-scale network design. Also a fuzzy expert system is developed to exploit the expert experience to adjust BS parameters, e.g., the transmitted power, to improve the network performance. Simulation results are presented and analyzed. <s> BIB006 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> Engineering of mobile telecommunication networks endures two major problems: the design of the network and the frequency assignment. We address the first problem in this paper, which has been formulated as a multiobjective constrained combinatorial optimisation problem. We propose a genetic algorithm (GA) that aims to approximate the Pareto frontier of the problem. Advanced techniques have been used, such as Pareto ranking, sharing and elitism. The GA has been implemented in parallel on a network of workstations to speed up the search. To evaluate the performance of the GA, we have introduced two new quantitative indicators: the entropy and the contribution. Encouraging results are obtained on real-life problems. <s> BIB007 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> The cell planning problem with capacity expansion is examined in wireless communications. The problem decides the location and capacity of each new base station to cover expanded and increased traffic demand. The objective is to minimize the cost of new base stations. The coverage by the new and existing base stations is constrained to satisfy a proper portion of traffic demands. The received signal power at the base station also has to meet the receiver sensitivity. The cell planning is formulated as an integer linear programming problem and solved by a tabu search algorithm. In the tabu search intensification by add and drop move is implemented by short-term memory embodied by two tabu lists. Diversification is designed to investigate proper capacities of new base stations and to restart the tabu search from new base station locations. Computational results show that the proposed tabu search is highly effective. A 10% cost reduction is obtained by the diversification strategies. The gap from the optimal solutions is approximately 1/spl sim/5% in problems that can be handled in appropriate time limits. The proposed tabu search also outperforms the parallel genetic algorithm. The cost reduction by the tabu search approaches 10/spl sim/20% in problems: with 2500 traffic demand areas (TDAs) in code division multiple access (CDMA). <s> BIB008 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> With the imminent introduction of the 3G systems throughout the world precise cell planning in macrocell, microcell and picocell environments have become equally important. Beside coverage of the basic radio link quality parameter others such as rms delay spread and a measure of the system capacity have become increasingly important. Our contribution addresses the planning inside microcells based on a 3D deterministic ray-tracing propagation tool. It is based on the IHE model (Cichon, 1984) and a simple genetic algorithm (SGA) for the base station location optimization. At this stage the optimization is based on coverage and rms delay spread considerations. Our algorithm has as inputs the delay spread threshold and the minimum field strength. The cost function to be minimized is the number of locations in which the values of these parameters are above the threshold in the case of delay spread, and respectively below the threshold in the case of the field strength. <s> BIB009 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> In this paper, we find the best base station placement using a genetic approach. A new representation describing base station placement with a real number is proposed, and new genetic operators are introduced. This new representation can describe not only the locations of the base stations but also the number of those. Considering both coverage and economic efficiency, we also suggest a weighted objective function. Our algorithm is applied to an obvious optimization problem and then is verified. Moreover, our approach is tried in an inhomogeneous traffic density environment. The simulation result proves that the algorithm enables one to find near optimal base station placement and the efficient number of base stations. <s> BIB010 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> In this paper, the base station placement is automatically determined using genetic approach, and the transmit power is estimated considering the interference situation in the case of interference-dominant systems. For applying a genetic algorithm to the base station placement problem, a new representation scheme with real numbers is proposed. And, corresponding operators such as crossover and mutation are introduced. A weighted objective function is designed for performing the cell planning coverage, cost-effectively. To verify the proposed algorithm, the situation where the optimum positions and number of base stations are obvious is considered. The proposed algorithm is applied to an inhomogeneous traffic density environment, where a base station's coverage may be limited by offered traffic loads. Simulation result proves that the algorithm enables us to find near optimal base station placement and the efficient number of base stations. <s> BIB011 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> Summary form only given. Evolutionary algorithms (EAs) are applied to solve the radio network design problem (RND). The task is to find the best set of transmitter locations in order to cover a given geographical region at an optimal cost. Usually, parallel EAs are needed in order to cope with the high computational requirements of such a problem. Here, we try to develop and evaluate a set of sequential and parallel genetic algorithms (GAs) in order to solve efficiently the RND problem. The results show that our distributed steady state GA is an efficient and accurate tool for solving RND that even outperforms existing parallel solutions. The sequential algorithm performs very efficiently from a numerical point of view, although the distributed version is much faster, with an observed linear speedup. <s> BIB012 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> WCDMA is an interference-limited system and its coverage and data throughput are sensitive to background noise. The results of background noise measurements in urban Taipei city for the licence bands of 3G systems issued in Taiwan are presented. The measurements involve FDD mode uplink and downlink frequency bands measured on building tops and at street level, respectively. The severeness of spectrum pollution of these bands is evaluated by extracting three statistical parameters from the measurement data, and the impact of the background noise on coverage and throughput is analysed for WCDMA systems. Also, based on measurement results, a better solution using a genetic algorithm with the help of a propagation model and digitised building information is proposed for the deployment of the base stations of WCDMA systems, by which the required coverage can be met with a suitable number of base stations, locations, antenna heights and transmitting power. A system is obtained that suffers less impact from background noise and achieves a higher data throughput with minimum cost. <s> BIB013 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> It is increasingly important to optimally select base stations in the design of cellular networks, as customers demand cheaper and better wireless services. From a set of potential site locations, a subset needs to be selected which optimizes two critical objectives: service coverage and financial cost. As this is an NP-hard optimization problem, heuristic approaches are required for problems of practical size. Our approach consists of two phases which act upon a set of candidate site permutations at each generation. Firstly, a sequential greedy algorithm is designed to commission sites from an ordering of candidate sites, subject to satisfying an alterable constraint. Secondly, an evolutionary optimization technique, which is tested against a randomized approach, is used to search for orderings of candidate sites which optimize multiple objectives. The two-phase strategy is vigorously tested and the results delineated. <s> BIB014 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> In this article, evolutionary algorithms (EAs) are applied to solve the radio network design problem (RND). The task is to find the best set of transmitter locations in order to cover a given geographical region at an optimal cost. Usually, parallel EAs are needed to cope with the high computational requirements of such a problem. Here, we develop and evaluate a set of sequential and parallel genetic algorithms (GAs) to solve the RND problem efficiently. The results show that our distributed steady state GA is an efficient and accurate tool for solving RND that even outperforms existing parallel solutions. The sequential algorithm performs very efficiently from a numerical point of view, although the distributed version is much faster. <s> BIB015 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> The antenna placement problem, or cell planning problem, involves locating and configuring infrastructure for cellular wireless networks. From candidate site locations, a set needs to be selected against objectives relating to issues such as financial cost and service provision. This is an NP-hard optimization problem and consequently heuristic approaches are necessary for large problem instances. In this study, we use a greedy algorithm to select and configure base station locations. The performance of this greedy approach is dependent on the order in which the candidate sites are considered. We compare the ability of four state-of-the-art multiple objective genetic algorithms to find an optimal ordering of potential base stations. Results and discussion on the performance of the algorithms are provided. <s> BIB016 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> We focus on the dimensioning process of cellular networks that addresses the evaluation of equipment global costs to cover a city. To deal with frequency assignment, that constitutes the most critical resource in mobile systems, the network is usually modeled as a pattern of regular hexagonal cells. Each cell represents the area covered by the signal of a transmitter or base station (BS). Our work emphasizes on the design of irregular hexagonal cells in an adaptive way. Hexagons transform themselves and adapt their shapes according to a traffic density map and to geometrical constraints. This process, called adaptive meshing (AM), may be seen as a solution to minimize the required number of BS to cover a region and to propose a basis for transmitter positioning. The solution we present to the mesh generation problem for mobile network dimensioning is based on the use of an evolutionary algorithm. This algorithm, called hybrid island evolutionary strategy (HIES), performs distributed computation. It allows the user to tackle problem instances with large traffic density map requiring several hundreds of cells. HIES combines local search fast computation on individuals, incorporated into a global island-like strategy. Experiments are done on one real case representing the mobile traffic load of the second French city of Lyon and on several other traffic maps from urban fictive data sets. <s> BIB017 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> We propose a new solution to the problem of positioning base station transmitters of a mobile phone network and assigning frequencies to the transmitters, both in an optimal way. Since an exact solution cannot be expected to run in polynomial time for all interesting versions of this problem (they are all NP-hard), our algorithm follows a heuristic approach based on the evolutionary paradigm. For this evolution to be efficient, i.e., goal-oriented and sufficiently random at the same time, problem-specific knowledge is embedded in the operators. The problem requires both the minimization of the cost and of the channel interference. We examine and compare two standard multiobjective techniques and a new algorithm - the steady-state evolutionary algorithm with Pareto tournaments. One major finding of the empirical investigation is a strong influence of the choice of the multiobjective selection method on the utility of the problem-specific recombination leading to a significant difference in the solution quality. <s> BIB018 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> Radio network design (RND) is a fundamental problem in cellular networks for telecommunications. In these networks, the terrain must be covered by a set of base stations (or antennae), each of which defines a covered area called cell. The problem may be reduced to figure out the optimal placement of antennae out of a list of candidate sites trying to satisfy two objectives: to maximize the area covered by the radio signal and to reduce the number of used antennae. Consequently, RND is a bi-objective optimization problem. Previous works have solved the problem by using single-objective techniques which combine the values of both objectives. The used techniques have allowed to find optimal solutions according to the defined objective, thus yielding a unique solution instead of the set of Pareto optimal solutions. In this paper, we solve the RND problem using a multi-objective version of the algorithm CHC, which is the metaheuristic having reported the best results when solving the single-objective formulation of RND. This new algorithm, called MOCHC, is compared against a binary-coded NSGA-II algorithm and also against the provided results in the literature. Our experiments indicate that MOCHC outperfoms NSGA-II and, more importantly, it is more efficient finding the optimal solutions than single-objectives techniques. <s> BIB019 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Operators <s> The base station placement problem, with n potential candidate sites is NP-Hard with 2 n solutions (Mathar and Niessen, Wirel. Netw. 6, 421---428, 2000). When dimensioned on m unknown variable settings (e.g., number of power settings?+?number of tilt settings, etc.) the computational complexity becomes (m+1) n (Raisanen, PhD. thesis, 2006). We introduce a novel approach to reduce the computational complexity by dimensioning sites only once to guarantee traffic hold requirements are satisfied. This approach works by determining the maximum set of service test points candidate sites can handle without exceeding a hard traffic constraint, T MAX . Following this, the ability of two evolutionary strategies (binary and permutation-coded) to search for the minimum set cover are compared. This reverses the commonly followed approach of achieving service coverage first and then dimensioning to meet traffic hold. To test this approach, three realistic GSM network simulation environments are engineered, and a series of tests performed. Results indicate this approach can quickly meet network operator objectives. <s> BIB020

Several genetic operators have been investigated in the literature for solving ACP problems (Table 2 ). This section is only aimed at discussing the crossover and mutation operators since they are the ones which depend on the encoding schemes (selection and replacement operators are based on the fitness of the individuals). Downloaded by [UMA University of Malaga] at 03:59 04 October 2013 3.2.2.1. Crossover. The classical single point crossover (SPX) has been extensively used for solving ACP problems. Most of the existing work using binary encoding has adopted this approach (e.g. BIB003 BIB004 . With this encoding, other wellknown operators such as two point crossover BIB012 BIB015 and uniform crossover BIB009 BIB013 ) have been applied. It is also worth mentioning that algorithm-specific crossover operators also appear when particular algorithms have been used. The works of , BIB019 , Vega-Rodrŕguez et al. (2007a) and Vega-Rodrŕguez et al. (2007b) use the highly disruptive crossover (HUX) designed for the CHC algorithm, whereas the two-fusion crossover BIB002 ) is applied in BIB006 . In the case of the integer encoding scheme, the cycle crossover has been used in the works of BIB014 , Whitaker et al. (2004b,a) , BIB016 and BIB020 . Since their algorithms work on integer permutations, this crossover operator is aimed at preserving the permutation, and as a result no repair mechanism is required. It is important to remark here that using the decoder procedure that translates the permutation of BTSs into a cell plan avoids the main concern of this representation: different permutations represent the same solution in the objective space. Traditional recombination operators are not applied with the real encoding scheme since no pure real-valued strings have been used. Indeed, in the works of BIB010 and BIB011 this operator has to deal with the special NULL value used in any given position to indicate that the corresponding BTSs are not deployed. This way, given two parents p 1 and p 2 , the operator returns one single child, c, in which the position of the ith BTS is computed as follows. If p 1 (i) = NULL and p 2 (i) = NULL, then c(i) = NULL; if either p 1 (i) = NULL or p 2 (i) = NULL, c(i) receives the genetic material of the non-NULL parent; otherwise, the ith BTS is placed somewhere near the BTS positions of the parents (sampling a Gaussian distribution). The main disadvantages of all these crossover operators is that they just manipulate genes, without taking into account the links with other genes (epistasis). Indeed, as explained in the introduction, either activating, deactivating or redimensioning one given BTS in a cellular network will surely affect the influence of other BTSs in the ACP problem at hand. It is therefore worth giving particular attention to the development of operators specially designed for ACP problems that use classical encoding schemes in their resolution. When ACP-targeted encoding schemes are adopted, this crossover specialization is already addressed. Most of the works that use the network encoding (see previous section) apply the so-called geographical crossover defined in BIB007 . This operator is based on exchanging the configuration of the sites located within a given random radius around a randomly chosen site. Figure 4 shows an example of the working principles of the geographical crossover. The main advantage of this operator is that it considers somehow the connection between the sites in a topological way: only nearby sites are modified. However, under this encoding, the classical SPX crossover has also been used by BIB005 . Other specialized crossover operators have been defined for dealing with ACP-targeted encodings. BIB017 have proposed a mechanism that combines the vertices of the hexagonal cells used to cover the traffic demand in the cellular network. It works by selecting two individuals as follows. The first one, i 1 , is chosen by fitness-proportional probability (e.g. roulette-wheel selection), whereas the second, i 2 is picked randomly. Since it is assumed that the former will have a better fitness than the latter, the crossover operator generates a child in which i 1 attracts i 2 by using a weighted average sum. BIB008 , who have used the grouping GA, have adopted the grouping crossover operator defined by BIB001 . Finally, BIB018 have implemented a crossover operator based on the decomposition of the service area of the cellular network. Two halves along one of the dimensions are generated and then, for each half, the fitness of the parent individuals is evaluated. The offspring will inherit the configuration for each of the sub-areas from the fittest parent for that sub-area. this approach is that the operator may generate unfeasible individuals, therefore requiring that the authors apply a repair function.

Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Mutation. <s> An important class of computational problems are grouping problems, where the aim is to group together members of a set (i.e., find a good partition of the set). We 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, yielding the Grouping Genetic Algorithm (GGA). We give an experimental comparison of the GGA with the other GAs applied to grouping problems, and we illustrate the approach with two more examples of important grouping problems successfully treated with the GGA: the problems of Bin Packing and Economies of Scale. <s> BIB001 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Mutation. <s> Engineering of mobile telecommunication networks endures two major problems: the design of the network and the frequency assignment. We address the first problem in this paper, which has been formulated as a multiobjective constrained combinatorial optimisation problem. We propose a genetic algorithm (GA) that aims to approximate the Pareto frontier of the problem. Advanced techniques have been used, such as Pareto ranking, sharing and elitism. The GA has been implemented in parallel on a network of workstations to speed up the search. To evaluate the performance of the GA, we have introduced two new quantitative indicators: the entropy and the contribution. Encouraging results are obtained on real-life problems. <s> BIB002 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Mutation. <s> The cell planning problem with capacity expansion is examined in wireless communications. The problem decides the location and capacity of each new base station to cover expanded and increased traffic demand. The objective is to minimize the cost of new base stations. The coverage by the new and existing base stations is constrained to satisfy a proper portion of traffic demands. The received signal power at the base station also has to meet the receiver sensitivity. The cell planning is formulated as an integer linear programming problem and solved by a tabu search algorithm. In the tabu search intensification by add and drop move is implemented by short-term memory embodied by two tabu lists. Diversification is designed to investigate proper capacities of new base stations and to restart the tabu search from new base station locations. Computational results show that the proposed tabu search is highly effective. A 10% cost reduction is obtained by the diversification strategies. The gap from the optimal solutions is approximately 1/spl sim/5% in problems that can be handled in appropriate time limits. The proposed tabu search also outperforms the parallel genetic algorithm. The cost reduction by the tabu search approaches 10/spl sim/20% in problems: with 2500 traffic demand areas (TDAs) in code division multiple access (CDMA). <s> BIB003 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Mutation. <s> In this paper, we find the best base station placement using a genetic approach. A new representation describing base station placement with a real number is proposed, and new genetic operators are introduced. This new representation can describe not only the locations of the base stations but also the number of those. Considering both coverage and economic efficiency, we also suggest a weighted objective function. Our algorithm is applied to an obvious optimization problem and then is verified. Moreover, our approach is tried in an inhomogeneous traffic density environment. The simulation result proves that the algorithm enables one to find near optimal base station placement and the efficient number of base stations. <s> BIB004 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Mutation. <s> In this paper, the base station placement is automatically determined using genetic approach, and the transmit power is estimated considering the interference situation in the case of interference-dominant systems. For applying a genetic algorithm to the base station placement problem, a new representation scheme with real numbers is proposed. And, corresponding operators such as crossover and mutation are introduced. A weighted objective function is designed for performing the cell planning coverage, cost-effectively. To verify the proposed algorithm, the situation where the optimum positions and number of base stations are obvious is considered. The proposed algorithm is applied to an inhomogeneous traffic density environment, where a base station's coverage may be limited by offered traffic loads. Simulation result proves that the algorithm enables us to find near optimal base station placement and the efficient number of base stations. <s> BIB005 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Mutation. <s> We give a short introduction to the results of our theoretical analysis of evolutionary algorithms. These results are used to design an algorithm for a large real-world problem: the placement of antennas for mobile radio networks. Our model for the antenna placement problem (APP) addresses cover, traffic demand, interference, different parameterized antenna types, and the geometrical structure of cells. The resulting optimization problem is constrained and multi-objective. The evolutionary algorithm derived from our theoretical analysis is capable of dealing with more than 700 candidate sites in the working area. The results show that the APP is tractable. The automatically generated designs enable experts to focus their efforts on the difficult parts of a network design problem. <s> BIB006 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Mutation. <s> The antenna placement problem, or cell planning problem, involves locating and configuring infrastructure for cellular wireless networks. From candidate site locations, a set needs to be selected against objectives relating to issues such as financial cost and service provision. This is an NP-hard optimization problem and consequently heuristic approaches are necessary for large problem instances. In this study, we use a greedy algorithm to select and configure base station locations. The performance of this greedy approach is dependent on the order in which the candidate sites are considered. We compare the ability of four state-of-the-art multiple objective genetic algorithms to find an optimal ordering of potential base stations. Results and discussion on the performance of the algorithms are provided. <s> BIB007 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Mutation. <s> We focus on the dimensioning process of cellular networks that addresses the evaluation of equipment global costs to cover a city. To deal with frequency assignment, that constitutes the most critical resource in mobile systems, the network is usually modeled as a pattern of regular hexagonal cells. Each cell represents the area covered by the signal of a transmitter or base station (BS). Our work emphasizes on the design of irregular hexagonal cells in an adaptive way. Hexagons transform themselves and adapt their shapes according to a traffic density map and to geometrical constraints. This process, called adaptive meshing (AM), may be seen as a solution to minimize the required number of BS to cover a region and to propose a basis for transmitter positioning. The solution we present to the mesh generation problem for mobile network dimensioning is based on the use of an evolutionary algorithm. This algorithm, called hybrid island evolutionary strategy (HIES), performs distributed computation. It allows the user to tackle problem instances with large traffic density map requiring several hundreds of cells. HIES combines local search fast computation on individuals, incorporated into a global island-like strategy. Experiments are done on one real case representing the mobile traffic load of the second French city of Lyon and on several other traffic maps from urban fictive data sets. <s> BIB008 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Mutation. <s> We propose a new solution to the problem of positioning base station transmitters of a mobile phone network and assigning frequencies to the transmitters, both in an optimal way. Since an exact solution cannot be expected to run in polynomial time for all interesting versions of this problem (they are all NP-hard), our algorithm follows a heuristic approach based on the evolutionary paradigm. For this evolution to be efficient, i.e., goal-oriented and sufficiently random at the same time, problem-specific knowledge is embedded in the operators. The problem requires both the minimization of the cost and of the channel interference. We examine and compare two standard multiobjective techniques and a new algorithm - the steady-state evolutionary algorithm with Pareto tournaments. One major finding of the empirical investigation is a strong influence of the choice of the multiobjective selection method on the utility of the problem-specific recombination leading to a significant difference in the solution quality. <s> BIB009

The analysis of the mutation operators in the literature for solving ACP problems with EAs is similar to that performed for the crossover operators. It depends greatly on the encoding used. The classical bit flip mutation is the preferred operator for binary encoding schemes (see Section 3.2.1). In works using integer permutation encoding, a random swap that simply transposes two randomly chosen positions in the permutation is adopted (e.g. BIB007 . Again, this operator is safe and no repair function is needed. The two works categorized with real encoding, i.e. BIB004 and BIB005 , have to manage the NULL value which is used to represent that a BTS is not deployed in the network. This way, for each BTS, the mutation operator either randomly updates the current position of the deployed BTSs or it is assigned with a NULL value; otherwise, if the BTS is not deployed yet, it can remain where it is or it can be placed in an arbitrary position in the network. Using the network encoding (ACP-targeted encoding), the mutation operator usually works by first selecting a given site and then updating the configuration of this site. This is called multilevel mutation since it operates at different levels of the encoding. Depending on the parameters of each site, the mutation may affect the following. • Activation toggling. If the site is activated, then it is just deactivated. On the other hand, if L i is deactivated, then an entire random configuration for the site is generated. • BTS power tuning. It requires the site to be activated. It randomly chooses a BTS of the site and then the power is randomly changed to one of its discretized values. • BTS tilt tuning. The same as power tuning, but changing the tilt angle. • BTS azimuth tuning. The same as power and tilt tuning, but modifying the azimuth angle. • BTS diagram tuning. This mutation also requires the site to be activated. The goal of this operator is to change the BTS type, that is, from an omnidirectional BTS to several directive BTSs, or vice versa. The configuration for each newly generated BTS is randomly generated. This is the approach used in BIB002 , Altman et al. (2002a,b) On the other hand, the works of BIB006 have further detailed these mutations by defining more specialized search operators. The authors have distinguished between repair operators (RepairTraffic, RepairHole, DecreasePower, IncreasePower, ChangeAzimuth, ChangeTilt, DissipateTraffic) and climb operators (RemoveWeakAntenna, RemoveAntenna, RemoveWeakSite, RemoveSite, IncreaseCompactness, ReduceIrregularities and MinimizePower). They all are applied one at a time by randomly choosing one of them. Because unfeasible solutions may be generated, a repair phase is used. Other mutation operators used with ACP-targeted encoding schemes are described next. BIB008 have developed the macromutation operator. This is intended to perform simultaneous moves on the vertices of the cells that cover the cellular network, thus allowing these cells to exit or to reach traffic demand areas. BIB003 have adopted the grouping crossover operator defined by BIB001 for the grouping GA. Finally, Finally, BIB009 have applied both directed and random mutations. The former ones (six different operators) include problem knowledge, and feasibility is always guaranteed since several preconditions have to be met prior to their application. However, directed mutations find it difficult to explore the entire search space, so this is why random mutations have been used. The goal is to promote exploration, but the drawback is that feasibility is no longer guaranteed and a repair function has to be applied.

Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Local search <s> A new heuristic approach for minimizing possibly nonlinear and non differentiable continuous space functions is presented. By means of an extensive testbed, which includes the De Jong functions, it will be demonstrated that the new method converges faster and with more certainty than Adaptive Simulated Annealing as well as the Annealed Nelder&Mead approach, both of which have a reputation for being very powerful. The new method requires few control variables, is robust, easy to use and lends itself very well to parallel computation. ________________________________________ 1)International Computer Science Institute, 1947 Center Street, Berkeley, CA 94704-1198, Suite 600, Fax: 510-643-7684. E-mail: [email protected]. On leave from Siemens AG, ZFE T SN 2, OttoHahn-Ring 6, D-81739 Muenchen, Germany. Fax: 01149-636-44577, Email:[email protected]. 2)836 Owl Circle, Vacaville, CA 95687, [email protected]. <s> BIB001 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Local search <s> It is increasingly important to optimally select base stations in the design of cellular networks, as customers demand cheaper and better wireless services. From a set of potential site locations, a subset needs to be selected which optimizes two critical objectives: service coverage and financial cost. As this is an NP-hard optimization problem, heuristic approaches are required for problems of practical size. Our approach consists of two phases which act upon a set of candidate site permutations at each generation. Firstly, a sequential greedy algorithm is designed to commission sites from an ordering of candidate sites, subject to satisfying an alterable constraint. Secondly, an evolutionary optimization technique, which is tested against a randomized approach, is used to search for orderings of candidate sites which optimize multiple objectives. The two-phase strategy is vigorously tested and the results delineated. <s> BIB002 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Local search <s> We focus on the dimensioning process of cellular networks that addresses the evaluation of equipment global costs to cover a city. To deal with frequency assignment, that constitutes the most critical resource in mobile systems, the network is usually modeled as a pattern of regular hexagonal cells. Each cell represents the area covered by the signal of a transmitter or base station (BS). Our work emphasizes on the design of irregular hexagonal cells in an adaptive way. Hexagons transform themselves and adapt their shapes according to a traffic density map and to geometrical constraints. This process, called adaptive meshing (AM), may be seen as a solution to minimize the required number of BS to cover a region and to propose a basis for transmitter positioning. The solution we present to the mesh generation problem for mobile network dimensioning is based on the use of an evolutionary algorithm. This algorithm, called hybrid island evolutionary strategy (HIES), performs distributed computation. It allows the user to tackle problem instances with large traffic density map requiring several hundreds of cells. HIES combines local search fast computation on individuals, incorporated into a global island-like strategy. Experiments are done on one real case representing the mobile traffic load of the second French city of Lyon and on several other traffic maps from urban fictive data sets. <s> BIB003 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Local search <s> The antenna placement problem, or cell planning problem, involves locating and configuring infrastructure for cellular wireless networks. From candidate site locations, a set needs to be selected against objectives relating to issues such as financial cost and service provision. This is an NP-hard optimization problem and consequently heuristic approaches are necessary for large problem instances. In this study, we use a greedy algorithm to select and configure base station locations. The performance of this greedy approach is dependent on the order in which the candidate sites are considered. We compare the ability of four state-of-the-art multiple objective genetic algorithms to find an optimal ordering of potential base stations. Results and discussion on the performance of the algorithms are provided. <s> BIB004 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Local search <s> Cellular network design is a major issue in mobile telecommunication systems. In this paper, a model of the problem in its full practical complexity, based on multiobjective constrained combinatorial optimization, has been investigated. We adopted the Pareto approach at resolution in order to compute a set of diversified non-dominated networks, thus removing the need for the designer to rank or weight objectives a priori. We designed and implemented a ''ready-to-use'' platform for radio network optimization that is flexible regarding both the modeling of the problem (adding, removing, updating new antagonist objectives and constraints) and the solution methods. It extends the ''white-box'' ParadisEO framework for metaheuristics applied to the resolution of mono/multi-objective Combinatorial Optimization Problems requiring both the use of advanced optimization methods and the exploitation of large-scale parallel and distributed environments. Specific coding scheme and genetic and neighborhood operators have been designed and embedded. On the other side, we make use of many generic features related to advanced intensification and diversification search techniques, hybridization of metaheuristics and grid computing for the distribution of the computations. They aim at improving the quality of networks and their robustness. They also allow, to speed-up the search and obtain results in a tractable time, and so efficiently solving large instances of the problem. Using three realistic benchmarks, the computed networks and speed-ups on different parallel and/or distributed architectures show the efficiency and the scalability of hierarchical parallel hybrid models. <s> BIB005 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Local search <s> The base station placement problem, with n potential candidate sites is NP-Hard with 2 n solutions (Mathar and Niessen, Wirel. Netw. 6, 421---428, 2000). When dimensioned on m unknown variable settings (e.g., number of power settings?+?number of tilt settings, etc.) the computational complexity becomes (m+1) n (Raisanen, PhD. thesis, 2006). We introduce a novel approach to reduce the computational complexity by dimensioning sites only once to guarantee traffic hold requirements are satisfied. This approach works by determining the maximum set of service test points candidate sites can handle without exceeding a hard traffic constraint, T MAX . Following this, the ability of two evolutionary strategies (binary and permutation-coded) to search for the minimum set cover are compared. This reverses the commonly followed approach of achieving service coverage first and then dimensioning to meet traffic hold. To test this approach, three realistic GSM network simulation environments are engineered, and a series of tests performed. Results indicate this approach can quickly meet network operator objectives. <s> BIB006

Adding ACP problem knowledge to the exploration performed by EAs can be further promoted with the usage of local search algorithms. That is, engineering hybrid algorithms BIB001 . So far, this problem-specific knowledge has been added by using specific encoding schemes and genetic operators (as has been shown in the previous sections). However, there are several proposals in the literature in which EAs are endowed with highly tailored search methods, allowing the search to be intensified in promising regions of the search space. When adaptively meshing the cell shapes of a cellular network, BIB003 have used a local search algorithm based on a Lamarckian adaptive process. This process applies small mutations on isolated vertices of the hexagonal cells which makes an individual evolve to a local minimum. The mutation operator, called micromutation, performs a small move on some randomly chosen vertex. BIB005 have designed a multiobjective local search to be used with the network encoding explained above. It is an iterative process that starts from a set of non-dominated solutions (or network configurations). Then, for each activated BTS of any network, it successively tests its removal, the updating of the power, azimuth and tilt with any of the available discretized values. By using the newly generated solutions, the set of non-dominated solutions is continuously updated. Finally, the local search algorithm restarts from any newly inserted solution, and so on. Finally, the decoder approach of BIB002 , Whitaker et al. (2004a,b) , BIB004 and BIB006 for translating the integer permutation of BTSs into a cell plan can also be mentioned here. As its authors have indicated, this decoder can be considered a local search algorithm.

Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Parallelization <s> This paper uses a realistic combinatorial optimization problem as an example to show how a genetic algorithm can be parallelized in an efficient way. The problem considered is the selection of the best set of transmitter locations in order to cover a given geographical region at optimal cost. It is shown that it is possible to obtain good solutions to the problem even with a very low communication load. The parallel program is tested, first on an artificial example, then on a real-life case. <s> BIB001 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Parallelization <s> The cell planning problem with capacity expansion is examined in wireless communications. The problem decides the location and capacity of each new base station to cover expanded and increased traffic demand. The objective is to minimize the cost of new base stations. The coverage by the new and existing base stations is constrained to satisfy a proper portion of traffic demands. The received signal power at the base station also has to meet the receiver sensitivity. The cell planning is formulated as an integer linear programming problem and solved by a tabu search algorithm. In the tabu search intensification by add and drop move is implemented by short-term memory embodied by two tabu lists. Diversification is designed to investigate proper capacities of new base stations and to restart the tabu search from new base station locations. Computational results show that the proposed tabu search is highly effective. A 10% cost reduction is obtained by the diversification strategies. The gap from the optimal solutions is approximately 1/spl sim/5% in problems that can be handled in appropriate time limits. The proposed tabu search also outperforms the parallel genetic algorithm. The cost reduction by the tabu search approaches 10/spl sim/20% in problems: with 2500 traffic demand areas (TDAs) in code division multiple access (CDMA). <s> BIB002 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Parallelization <s> Engineering of mobile telecommunication networks endures two major problems: the design of the network and the frequency assignment. We address the first problem in this paper, which has been formulated as a multiobjective constrained combinatorial optimisation problem. We propose a genetic algorithm (GA) that aims to approximate the Pareto frontier of the problem. Advanced techniques have been used, such as Pareto ranking, sharing and elitism. The GA has been implemented in parallel on a network of workstations to speed up the search. To evaluate the performance of the GA, we have introduced two new quantitative indicators: the entropy and the contribution. Encouraging results are obtained on real-life problems. <s> BIB003 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Parallelization <s> This paper uses a realistic problem taken from the telecommunication world as the basis for comparing different combinatorial optimization algorithms. The problem recalls the minimum hitting set problem, and is solved with greedy-like, Darwinism and genetic algorithms. These three paradigms are described and analyzed with emphasis on the Darwinism approach, which is based on the computation of e-nets. <s> BIB004 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Parallelization <s> Summary form only given. Evolutionary algorithms (EAs) are applied to solve the radio network design problem (RND). The task is to find the best set of transmitter locations in order to cover a given geographical region at an optimal cost. Usually, parallel EAs are needed in order to cope with the high computational requirements of such a problem. Here, we try to develop and evaluate a set of sequential and parallel genetic algorithms (GAs) in order to solve efficiently the RND problem. The results show that our distributed steady state GA is an efficient and accurate tool for solving RND that even outperforms existing parallel solutions. The sequential algorithm performs very efficiently from a numerical point of view, although the distributed version is much faster, with an observed linear speedup. <s> BIB005 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Parallelization <s> In this article, evolutionary algorithms (EAs) are applied to solve the radio network design problem (RND). The task is to find the best set of transmitter locations in order to cover a given geographical region at an optimal cost. Usually, parallel EAs are needed to cope with the high computational requirements of such a problem. Here, we develop and evaluate a set of sequential and parallel genetic algorithms (GAs) to solve the RND problem efficiently. The results show that our distributed steady state GA is an efficient and accurate tool for solving RND that even outperforms existing parallel solutions. The sequential algorithm performs very efficiently from a numerical point of view, although the distributed version is much faster. <s> BIB006 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Parallelization <s> We focus on the dimensioning process of cellular networks that addresses the evaluation of equipment global costs to cover a city. To deal with frequency assignment, that constitutes the most critical resource in mobile systems, the network is usually modeled as a pattern of regular hexagonal cells. Each cell represents the area covered by the signal of a transmitter or base station (BS). Our work emphasizes on the design of irregular hexagonal cells in an adaptive way. Hexagons transform themselves and adapt their shapes according to a traffic density map and to geometrical constraints. This process, called adaptive meshing (AM), may be seen as a solution to minimize the required number of BS to cover a region and to propose a basis for transmitter positioning. The solution we present to the mesh generation problem for mobile network dimensioning is based on the use of an evolutionary algorithm. This algorithm, called hybrid island evolutionary strategy (HIES), performs distributed computation. It allows the user to tackle problem instances with large traffic density map requiring several hundreds of cells. HIES combines local search fast computation on individuals, incorporated into a global island-like strategy. Experiments are done on one real case representing the mobile traffic load of the second French city of Lyon and on several other traffic maps from urban fictive data sets. <s> BIB007 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Parallelization <s> Cellular network design is a major issue in second generation GSM mobile telecommunication systems. In this paper, a new model of the problem in its full practical complexity, based on multiobjective constrained combinatorial optimization, has been used. We propose an evolutionary algorithm that aims at approximating the Pareto frontier of the problem, which removes the need for a cellular network designer to rank or weight objectives a priori. Specific coding scheme and genetic operators have been designed. Advanced intensification and diversification search techniques, such as elitism and adaptive sharing, have been used. Three complementary hierarchical parallel models have been designed to improve the solution quality and robustness, to speed-up the search and to solve large instances of the problem. The obtained Pareto fronts and speed-ups on different parallel architectures show the efficiency and the scalability of the parallel model. Performance evaluation of the algorithm has been carried out on different realistic benchmarks. The obtained results show the impact of the proposed parallel models and the introduced search mechanisms. <s> BIB008 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Parallelization <s> Cellular network design is a major issue in mobile telecommunication systems. In this paper , a model of the problem in its full practical complexity, based on multiobjective constrained combinatorial optimization, has been investigated. We adopted the Pareto approach at resolution in order to compute a set of diversified non-dominated networks, thus removing the need for the designer to rank or weight objectives. We design an asynchronous steady-state evolutionary algorithm for its resolution. Specific coding scheme and genetic and neighborhood operators have been designed for the tackled problem. On the other side, we make use of many generic features related to advanced intensification and diversification search techniques, hybridization of metaheuristics and grid computing for the distribution of the computations. They aim at improving the quality of networks and robustness, at speeding-up the search, hence efficiently solving large instances of the problem. Using realistic benchmarks, the computed networks and speed-ups on parallel/distributed architectures show the efficiency and the scalability of hierarchical models of hybridization and parallelization used in conjunction. <s> BIB009 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Parallelization <s> Cellular network design is a major issue in mobile telecommunication systems. In this paper, a model of the problem in its full practical complexity, based on multiobjective constrained combinatorial optimization, has been investigated. We adopted the Pareto approach at resolution in order to compute a set of diversified non-dominated networks, thus removing the need for the designer to rank or weight objectives a priori. We designed and implemented a ''ready-to-use'' platform for radio network optimization that is flexible regarding both the modeling of the problem (adding, removing, updating new antagonist objectives and constraints) and the solution methods. It extends the ''white-box'' ParadisEO framework for metaheuristics applied to the resolution of mono/multi-objective Combinatorial Optimization Problems requiring both the use of advanced optimization methods and the exploitation of large-scale parallel and distributed environments. Specific coding scheme and genetic and neighborhood operators have been designed and embedded. On the other side, we make use of many generic features related to advanced intensification and diversification search techniques, hybridization of metaheuristics and grid computing for the distribution of the computations. They aim at improving the quality of networks and their robustness. They also allow, to speed-up the search and obtain results in a tractable time, and so efficiently solving large instances of the problem. Using three realistic benchmarks, the computed networks and speed-ups on different parallel and/or distributed architectures show the efficiency and the scalability of hierarchical parallel hybrid models. <s> BIB010

As early as in the first works published on EAs for solving the ACP problem, i.e. and BIB001 , it was soon understood that this optimization problem involved tasks demanding high computational resources. With the aim of not only speeding up the computation but also improving the solution quality, most of the parallel EAs analysed have adopted the coarse-grained scheme, also known as the island model (Alba and Tomassini Downloaded by [UMA University of Malaga] at 03:59 04 October 2013 2002). They have also used a unidirectional ring topology: BIB001 , , BIB002 , BIB004 , BIB005 and BIB006 . The work of BIB007 has also used the island model with a unidirectional ring topology but, instead of subpopulations, each island runs a hybrid evolution strategy. BIB003 have used a master/slave approach for the parallel implementation of the function evaluation, i.e. each function evaluation is distributed to different processors. BIB008 have extended this work by using the master/slave scheme not only for the parallel evaluation of the function evaluation, but also for evaluating each tentative solution of the EA asynchronously in parallel. They have also used the island model in this work. Finally, the works of BIB009 and BIB010 have again proposed extensions of these previous publications by deploying a parallel hybrid EA on a computational grid . This EA is hybrid because a local search is used to improve the solutions generated within the evolutionary loop. The parallelism is applied at different levels: the main EA model is an island model. Then, on each island, individuals undergo local search in parallel. The third level of parallelism considers each single function evaluation in parallel by decomposing the fitness function.

Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Future trends <s> A new heuristic approach for minimizing possibly nonlinear and non differentiable continuous space functions is presented. By means of an extensive testbed, which includes the De Jong functions, it will be demonstrated that the new method converges faster and with more certainty than Adaptive Simulated Annealing as well as the Annealed Nelder&Mead approach, both of which have a reputation for being very powerful. The new method requires few control variables, is robust, easy to use and lends itself very well to parallel computation. ________________________________________ 1)International Computer Science Institute, 1947 Center Street, Berkeley, CA 94704-1198, Suite 600, Fax: 510-643-7684. E-mail: [email protected]. On leave from Siemens AG, ZFE T SN 2, OttoHahn-Ring 6, D-81739 Muenchen, Germany. Fax: 01149-636-44577, Email:[email protected]. 2)836 Owl Circle, Vacaville, CA 95687, [email protected]. <s> BIB001 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Future trends <s> This paper contains a modern vision of the parallelization techniques used for evolutionary algorithms (EAs). The work is motivated by two fundamental facts: 1) the different families of EAs have naturally converged in the last decade while parallel EAs (PEAs) are still lack of unified studies; and 2) there is a large number of improvements in these algorithms and in their parallelization that raise the need for a comprehensive survey. We stress the differences between the EA model and its parallel implementation throughout the paper. We discuss the advantages and drawbacks of PEAs. Also, successful applications are mentioned and open problems are identified. We propose potential solutions to these problems and classify the different ways in which recent results in theory and practice are helping to solve them. Finally, we provide a highly structured background relating to PEAs in order to make researchers aware of the benefits of decentralizing and parallelizing an EA. <s> BIB002 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Future trends <s> Some designs are sufficiently creative that they are considered to be inventions. The invention process is typically characterized by a singular moment when the prevailing thinking concerning a long-standing problem is, in a “flash of genius,” overthrown and replaced by a new approach that could not have been logically deduced from what was previously known. This paper discusses such logical discontinuities using an example based on the history of one of the most important inventions of the 20th century in electrical engineering, namely, the invention of negative feedback by AT&T's Harold S. Black. This 1927 invention overthrew the then prevailing idiom of positive feedback championed by Westinghouse's Edwin Howard Armstrong. The paper then shows how this historically important discovery can be readily replicated by an automated design and invention technique patterned after the evolutionary process in nature, namely, genetic programming. Genetic programming employs Darwinian natural selection along with analogs of recombination (crossover), mutation, gene duplication, gene deletion, and mechanisms of developmental biology to breed an ever improving population of structures. Genetic programming rediscovers negative feedback by conducting an evolutionary search for a structure that satisfies Black's stated high-level goal (i.e., reduction of distortion in amplifiers). Like evolution in nature, genetic programming conducts its search probabilistically without resort to logic using a process that is replete with logical discontinuities. The paper then shows that genetic programming can routinely produce many additional inventive and creative results. In this regard, the paper discusses the automated rediscovery of numerous 20th-century patented inventions involving analog electrical circuits and controllers, the Sallen–Key filter, and six 21st-century patented inventions. <s> BIB003 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Future trends <s> We focus on the dimensioning process of cellular networks that addresses the evaluation of equipment global costs to cover a city. To deal with frequency assignment, that constitutes the most critical resource in mobile systems, the network is usually modeled as a pattern of regular hexagonal cells. Each cell represents the area covered by the signal of a transmitter or base station (BS). Our work emphasizes on the design of irregular hexagonal cells in an adaptive way. Hexagons transform themselves and adapt their shapes according to a traffic density map and to geometrical constraints. This process, called adaptive meshing (AM), may be seen as a solution to minimize the required number of BS to cover a region and to propose a basis for transmitter positioning. The solution we present to the mesh generation problem for mobile network dimensioning is based on the use of an evolutionary algorithm. This algorithm, called hybrid island evolutionary strategy (HIES), performs distributed computation. It allows the user to tackle problem instances with large traffic density map requiring several hundreds of cells. HIES combines local search fast computation on individuals, incorporated into a global island-like strategy. Experiments are done on one real case representing the mobile traffic load of the second French city of Lyon and on several other traffic maps from urban fictive data sets. <s> BIB004 </s> Evolutionary algorithms for solving the automatic cell planning problem : a survey <s> Future trends <s> Cellular network design is a major issue in mobile telecommunication systems. In this paper, a model of the problem in its full practical complexity, based on multiobjective constrained combinatorial optimization, has been investigated. We adopted the Pareto approach at resolution in order to compute a set of diversified non-dominated networks, thus removing the need for the designer to rank or weight objectives a priori. We designed and implemented a ''ready-to-use'' platform for radio network optimization that is flexible regarding both the modeling of the problem (adding, removing, updating new antagonist objectives and constraints) and the solution methods. It extends the ''white-box'' ParadisEO framework for metaheuristics applied to the resolution of mono/multi-objective Combinatorial Optimization Problems requiring both the use of advanced optimization methods and the exploitation of large-scale parallel and distributed environments. Specific coding scheme and genetic and neighborhood operators have been designed and embedded. On the other side, we make use of many generic features related to advanced intensification and diversification search techniques, hybridization of metaheuristics and grid computing for the distribution of the computations. They aim at improving the quality of networks and their robustness. They also allow, to speed-up the search and obtain results in a tractable time, and so efficiently solving large instances of the problem. Using three realistic benchmarks, the computed networks and speed-ups on different parallel and/or distributed architectures show the efficiency and the scalability of hierarchical parallel hybrid models. <s> BIB005

There are several research lines that can be explored to address the ACP problem with EAs further. At a lower algorithmic level, the design of new encodings and genetic operators for the problem, as well as the analysis of current existing ones, are of great interest. Concretely, the more complex encoding, the network encoding presented in Section 3.2, has only been evaluated with a few genetic operators (multilevel mutation and geographical crossover, mainly). Additional operator developments may take advantage of this ACP-targeted encoding. Evaluating this encoding and operators with the search engine of well-known algorithms such as NSGA-II or SPEA2 is also a matter for research. At a higher algorithmic level, a promising research line is targeted at hybridizing EAs BIB001 , especially with other EAs. Up to now, EAs have been hybridized in the literature with local search algorithms (e.g. see BIB004 BIB005 or Tabu Search to solve ACP problems, but hybrid algorithms involving two different EAs have not been found. The aim here would be to profit from the different search capabilities, for example, of Downloaded by [UMA University of Malaga] at 03:59 04 October 2013 Engineering Optimization 687 a GA (diversification) and an evolution strategy (intensification). In the context of multiobjective EAs, hybridization is underexplored in the literature. Checking whether other unused EAs can successfully address the ACP problem is a promising research topic as well. To the best of our knowledge, two main unused EAs have been left unexplored in the literature. On the one hand, no genetic programming approach has been found in the literature for ACP, even when this kind of EA performs well on other design problems BIB003 . On the other hand, the cellular model of structured EAs BIB002 has not been used either. Cellular EAs have been shown to be very effective in other domains , so evaluating their enhanced search engine may lead to an improvement in the current state-of-the-art algorithms. There are several additional studies whose conclusions may result in relevant outcomes especially for telecommunications engineers who use EAs to solve their ACP problems. The analysis of both the scalability and the convergence speed of EAs on this problem also requires more investigation. The increasing size of cellular networks means EAs are faced with problem instances with thousand of decision variables. Therefore, evaluating the algorithms that perform better on very large instances is of great interest for cellular operators, since they can afford larger and more efficient network deployments. The study of how quickly EAs converge towards optimal solutions would also be of interest to the telecommunications industry. Indeed, execution time becomes a critical constraint for the operators and mainly for the software companies that are developing software for the operators. Within commercial applications, reaching 'good' solutions in a very short time is usually essential in order to provide operators with competitive software tools. These studies have to pay special attention to the statistical analysis of the results, which must be rigorously performed in order to draw useful conclusions. However, the works analysed in this articles for the most part lack such thorough analyses.