Ues advertised by the service provider but at last

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ues advertised by the service provider, but at last the composition optimization problem is also instantiated into an Integer Programming (IP) problem. How- ever, as pointed out by Berbner et al. in [1], the IP approach is hardly feasible in dynamic real-time scenarios when a large number of potential Web services are concerned. Canfora et al. [2] proposed the use of Genetic Algorithms (GAs) for the problem mentioned above. It has shown that GAs outperform integer
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310 A. Moustafa and M. Zhang programming used in [22] when a large number of services are available. More- over, GAs are more flexible than the MIP since GAs allow the consideration of nonlinear composition rules. Apparently, traditional GAs have some inherent limitations in solving QoS -aware composition problems as the the selection of the weights of characteristics is required in order to aggregate multi-objectives into a single objective function in GAs. All the above mentioned approaches, however, cannot solve Web service selec- tion with multiple QoS objectives and multi-constrain. They all assume multiple criteria, no matter whether they are competing or not, can be combined into a single criterion to be optimized, according to some utility functions. When mul- tiple quality criteria are considered, users are required to express their preference over different, and sometimes conflicting, quality attributes as numeric weights. This is a rather demanding task and an imprecise specification of the weights could miss user desired services. Despite the fact that the QoS optimization problem is multi-objective by na- ture few approaches based on multi-objective algorithms can be found in the literature [17,6,16]. Yu and Lin [21] studied multiple QoS constraints. The com- position problem is modelled as a Multi-dimension Multi-choice 0-1 Knapsack Problem (MMKP). A Multi-Constraint Optimal Path (MCOP) algorithm with heuristics is presented in [21]. However, the aggregation of parameters using the Min function is neglected. Maximilien and Singh [13] describe the Web Service Agent Framework (WSAF) to achieve service selection by considering the pref- erences of several service consumers as well as the trustworthiness of providers. Evolutionary Algorithms (EAs) are suitable to solve multi-objective optimiza- tion problems because they are able to produce a set of solutions in paral- lel. A growing interest in the application of EAs to the multi-objective Web service composition in recent years is evident. Claro et al. [5] discussed the advantages of Multi-Objective Genetic Algorithms (MOGA) in Web service selection and a popular multi-objective algorithm, NSGA-II [7], is used to find optimal sets of Web services. Other EAs that have been proposed to solve multi- objective service composition include, Multi-Objective Particle Swarm Opti- mizer (MOPSO) [3], and Multi-Objective Evolutionary Algorithm based on De- composition (MOEA/D) [14]. These EAs propose mathematical improvements to solve multi-objective service composition problems. However, as the dimensional-
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