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Top1. Introduction
Web service technologies utilize Service-Oriented Architecture (SOA) as well as Service-Oriented Computing (SOC) (Lemos, Daniel, & Benatallah, 2015; Wagner, Ishikawa, & Honiden, 2016). The SOA framework contains the service provider, service registry and service consumer. The service provider develops and publishes web services in a standard format. The service registry contains service-related information, including the addresses of service providers and technical information. Service consumers use the information provided by the service registry and then, discover, bind, and invoke expected web services.
Service complementarity within a service class has attracted significant research attention (Garcia Llinas & Nagi, 2015; Liang, Qin, Tang, & Tan, 2019). To enable increasingly complex functionality, web software designers flexibly compose different services into composite ones, which benefit from the functionalities provided by single-component services, and then expose them as high-level composite services in a value-adding manner. This combination process is known as web service composition (WSC).
Using WSC, web software designers build executable business processes, including business logic and task execution orders, which are conducted from one party's perspective (Tbahriti, Ghedira, Medjahed, & Mrissa, 2014; Yan et al., 2016). However, in this study, we do not consider the technical processes of web services; rather, we focus on its economic properties. Multi-objective and many-objective optimization mathematical model are established to optimize the pricing behavior of all participators and the profits of each single service providers can be improved by considering pricing references provided in the Pareto front, which is more realistic.
We start by analyzing the economic behaviors of service providers. To implement a web service, the service provider may need to consider the economic feasibility of providing the service. This economic feasibility can be reflected in the benefits afforded to service providers, including service differentiation and profitability. Specifically, service profitability is investigated from the perspective of web services pricing in web service markets.
By formulating web services pricing as an optimization problem, the proposed model can serve as a decision-support tool for service providers. In real-life systems, this model can be competitive for investigating pricing in web service markets, which, as an economic behavior pattern, is often difficult or impossible to formulate accurately.
The contributions of the present study are as follows:
- a.
A multi-objective and many-objective optimization model is presented to formulate the web services pricing behaviors under the given assumptions.
- b.
The challenge associated with solving the model is demonstrated in terms of the NP-completeness of a single-objective version.
- c.
The model is solved using a multi-objective Genetic Algorithm Solver; Pareto front solutions are discussed based on the structure of the given composite web services network.
The remainder of this paper is structured as follows. Some preliminaries for the web services pricing framework are described in Section 2. Section 3 provides the background and assumptions of the studied problem. In Section 4, the problem is formulated and the complexity analysis presented. Numerical studies are described in Section 5 and a real world case study was conducted in section 6. Finally, conclusions are presented in Section 7.