his paper addresses the web service composition problem considering multi-criteria regarding quality of services (QoS). Three different scenarios of multi-criteria mathematical programming models are explored under the framework of network based analysis in web service composition. This work takes care of the issues pertaining to inputs and outputs matching of web services and Quality-of-Service (QoS) at the same time. The multi-criteria programming models are explored to select the desirable

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... rvice composition in a variety of categories in accordance with customers' preferences in three different scenarios: (1) Optimal, (2) Compromised optimal, and (3) Acceptable. This set of multi-criteria models have both advantages and disadvantages comparing with each other, and can be used as different solvers in the network based service composition framework. The proposed regular multi-criteria programming (MCP) models are used in Scenario (1): Optimal. The proposed multi-criteria goal programming for optimal composition (MCGPO) and multi-criteria goal programming for non-optimal solution (MCGPN) models are designed for Scenarios (2):Compromised optimal and (3)Acceptable respectively. And they can find a compromised composition based on the trade-off of customer's preference on the QoS goals in case that the optimal composition satisfying both functional and QoS constraints does not exist in the network.