CeL as a Planning Problem

Therefore, with the process described above we ended up with a pool of suitable CeLLOs that will take part in the planning process. Formally, the Planning in CeL is a tuple:

P_CeL= (S_cel, A_cel, γcel, s0cel, gcel) (8.3)

where:

• Scel is the set of all possible propositions that describe the user profile, knowledge,

skills and desires

• Acel is the set of all CeLLOs

• γcel is the set of state transition functions which given a state of a learner and a CeLLO

returns a new state which includes new knowledge and skills that the learner has acquired through this CeLLO

• s0cel is the initial state of the learner

• g_cel is the set of goal states that include the desires in terms of skills and knowledge by the learner

As discussed in the papers [165–167], all recommended CeLLOs are offered as part of the planning problem and the CeLPLN synthesizes the right CeLLOs in the personalised sequence based on learners’ background and learners interest. The logic how the CeL planner is invoked is desribed using the pseudocode in Algorithm 1.

The CeLPLN has adapted the FF [168] planner, a planner inspired by HSP planner [169]. The FF planner relies on forward search, in the state space, guided by a heuristic function

Algorithm 1 Invoking Automate Planning to generate a personalised learning path Input: Recommended CeLLOs from the CeL and profile constraints of learner Output: Personalised Learning Path for the learner

1: if recommendedCeLLOs! = null then

2: Action 1: Select the relevant existing CeLLOs;

3: Action 2: Generate the personalised plan to the learner;

4: else

5: reInitiate the CeLRS;

6: end

which estimates the goal distance by ignoring the delete lists (the negative effects from all operators), as was proposed by Bonet and Geffner [169, 170].

The FF planner as a search strategy uses the enforced hill climbing algorithm which initiates the heuristic function and the relaxed graph-plan [168] respectively, to estimate the goal distance, which at the end generates either a solution or a fail plan.

Unlike FF, the CeLPLN uses the backward chaining algorithm, which starts from the goal up until to the prerequisite required to accomplish the goal state. Basically, it starts from the intended learning outcome of the desire, and aims to produce the necessary prerequisite of CeLLOs. It firstly builds a planning graph until all prerequisite are satisfied for achieving the intended learning outcome, which is stated as the main goal.

The graph consists of alternating CeLLOs and action layers as shown in Figure 8.4. The number of CeLLOs that deal with similar topics construct an action layer. The next layer is constructed based on the prerequisites of CeLLOs that are part of the previous layer.

To be more concrete, it first constructs the final layer (the "n" layer) which contains all CeLLOs that fulfill the intended learning outcome of the learner desire. All the CeLLOs within a layer are CeLLOs which target the same topic/subtopic but it could vary depending on the CeLLO attributes, such as: format, type, granularity etc. Then, it goes backward to the second layer (the "n-1" layer) which contains all the CeLLOs which are prerequisite for the final layer and the process of constructing layers and CeLLOs as part of particular layer goes on until no prerequisites are required. So, when this phase is fulfilled, the graph plan is designed, and then the learning path is constructed from the initial state up to the goal state as emphasized in Figure8.4, by adding successors based on their granularity.

In addition to the previous examples, there might be a need to define the duration of each action (watch, study, take test etc.) that the learner should do. In such case, we should specify the time frames as constraints for the action, precondition and effects [171]. If we consider the same actions with planning and scheduling techniques, beside the constraints, the action

8.3 Automated Planning as the final process of CeL 127

Fig. 8.4 The layered structure of states and CeLLOs

is specified with its resource requirements as well (which might be consumable or reusable resources) and three variables (starting time, ending time and duration).

Fig. 8.5 The CeL Planning Domain

To be more concrete, a visual examples is modelled in Figure 8.6, 8.7, and 8.8 using the itSimple tool [172] which emphasized a more technical architecture of Cloud eLearning through UML class diagram. The itSimple tool offers the possibility to model the planning environment and the planning problem through a graphical interface. Figure 8.6 expresses the concept of CeL. As depicted in Figure 8.6, Learners are defined by: type, knowledge level and desire attributes, whereas CeLLOs are defined throughs: type, format, granularity, topic, prerequisites and intended learning outcomes attributes. Each of the CeLLOs has a defined time to study, respectively to test the learners knowledge. The Match-making uses the learners profile and the existing CeLLOs to produce a personalised plan, specifically a personalised learning path, which is characterised through a number of CeLLOs and its defined sequence.

8.3 Automated Planning as the final process of CeL 129 Continuing with the Figure 8.7 as required by the Cloud eLearning Planner, the learner should have an initial and goal state. So, the initial state is represented using itSimple in Figure 8.7 and the goal state in Figure 8.8 which lists all objects that are related to learners, CeLLOs and related attributes associated with all the objects. So, starting with the representation of initial state in Figure 8.7, we have an instance of the learner, following with learner desire, and the instances of all required CeLLOs based on the learners desire and its background.

Fig. 8.7 The initial state in CeLPlanner

Following the Figure 8.8, the learner ends up with the desired goal, which defines the list of actions which needs to be followed in order to study the appropriate CeLLOs for satisfying the goal state.

8.3 Automated Planning as the final process of CeL 131