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Top1. Introduction
Meeting Scheduling Problem (MSP) is a distributed task in which there are several participants, and they are looking for times and places to hold their meetings. Each of the participants has their own preference and calendar (Al-ani, 2007). Meeting scheduling is naturally a time consuming and iterative activity. Tsuruta and Shintani (2000) have defined an MSP as “the process of determining a starting time and an ending time of an event in which several people will participate.” Solving a meeting scheduling problem involves satisfying conflicted preferences between individuals. Constraints in the context of scheduling problem are divided into two kinds, hard and soft. Hard constraints are conditions that must be satisfied (like the availability of an individual), whereas soft constraints maybe violated. However, it would be better to satisfy them as much as possible (Abdennadher & Schlenker, 1999). Automated meeting scheduling has two important effects; it will reduce the time that users spend on scheduling, and it will also try to find an efficient schedule. Before we introduce the preference problem, we provide a closer look at the scheduling problem.
There are two main approaches in solving a meeting scheduling problem. The first approach is the centralized approach. In a centralized system each of the participants sends their preferences to the meeting scheduling manager. It is the manager’s job to search for a good feasible answer that satisfies all the participants (Ephrati et al., 1994). In this case, a meeting scheduling problem has been seen as a Constraint Satisfaction Problems (CSP) (Chun et al., 2003; BenHassine et al., 2006). However, in recent years many researchers have used distributed and multi-agent systems in order to find good solutions (Mishra & Mishra, 2010; Mazumdar & Mishra, 2010). There have been enormous attempts for solving the CSP in a distributed way such as Distributed CSPs or DCSPs (Maheswaran et al., 2006). Even so, there is another important distributed method in MSP solving, which is the multi-agent negotiation approach. In this method MSP is a treated as a multi-agent agreement problem, and each agent represents a user (Crawford & Veloso, 2004, 2005). Increasingly, software agents perform tasks on behalf of their human counterpart in a variety of application domains (Kuppuswamy & Chithralekha, 2010; Russell & Yoon, 2009).
In this paper, we formulate the MSP as a multi-agent problem and base it on the work discussed in Crawford (2009) and Ephrati et al. (1996). In Crawford (2009) the author introduces a semi-cooperative learning negotiation agent. This agent could develop a preference model of the user while it is watching the negotiation process. To accomplish this, the agent uses the system log (history). The drawback of this work is that the agent needs a time consuming learning process to understand a user's preference. In addition, there are no facilities for agents that have no information about the history of negotiation (or there exists no information). One solution to circumvent this problem is the use of Analytical Hierarchy Process (AHP) in order to make a prior model of the user’s preference. In essence, this research extends the prior work of Crawford (2009) and Ephrati et al. (1996). Our proposed method acquires pairwise preferences of choices from a user in the very first step, and this model can learn as well. This means that when the user negotiates with other participants, the model will update itself. And as times go by, this model will be dependent on learning data (experience), not on the prior knowledge required to be stored in the system. A simplified high level characterization of the MSP system preference modeling is shown in Figure 1.
Figure 1. Simplified components of the preference modeling system