This work was initiated when Paraschool, the French leading e-learning company contacted the INRIA research center to conceive an automatic algorithm that would allow the relatively rigid albeit functional existing Paraschool software to behave differently depending on user specificities. After several brainstorming sessions where neural networks, evolutionary algorithms and other artificially intelligent techniques were considered, it appeared that swarm-like algorithms could be used, thanks to the great number of actual users (more than 10000) and more especially ant-based probabilistic optimisation that could easily be grafted on the existing pedagogical graph constituted by the Paraschool software.

Moreover, Ant Colony systems present the interesting property of exhibiting emergent behaviour that allow individuals to benefit from the dynamic experience acquired by the collectivity, which means, in pedagogic terms that a student could benefit from the pedagogic lessons drawn out of his peers’ successes and failures.

The implementation of these algorithms yields results that go beyond the requirements of the Paraschool company which will soon be experimenting in real size the automatic dynamic optimisation of the pedagogic graph (their set of interconnected lessons and exercises) implemented by their software. This paper successively presents a concise description of human-learning concepts and their software implementation, a short description of the technical implementation of the Ant-Colony based optimisation algorithm and a discussion on the use of various selection operators. A set of experiments is then conducted, showing that erroneous arc probabilities can be automatically corrected by the system.

II. ELEMENTS ON THE PHILOSOPHY OF LEARNING

The main concepts of teaching and learning used nowadays are still very old. The two main currents are Constructivism, that was elaborated by Kant and Behaviourism: a theory that came from Pavlov’s experiments.

A. Constructivism

In 1781, Kant tried to synthesize rationalist and empiricist viewpoints. Kant sees the mind as an active agent, that organizes and coordinates experiences. Along these lines, Piaget states that knowledge is not simply “acquired,” by children bit by bit, but constructed into coherent, robust frameworks called

“knowledge structures.” Children are not passive absorbers of experience and information, but active theory builders. Papert, a mathematician, and one of the early pioneers of Artificial Intelligence (he founded the Artificial Intelligence Laboratory at MIT), worked with Piaget at the University of Geneva

IV. IMPLEMENTATION OF THE ANT COLONY:

ALGORITHMIC OVERVIEW

All nodes (html pages) of the new Paraschool software now contain a new ACO-powered NEXT button that leads the user along an arc chosen by a selection algorithm (see section V), based on the probability associated with the arc. This probability is computed by taking several factors into account in the design of a weighted fitness function described in the next section. These factors are the following and play at both

the individual and collective levels:

A. Pedagogic Weights: W

This pedagogical weight is the main value of each arc. It is implemented as a static (i.e. “global”) variable (W), accessible to all ants. (W) is set by the Paraschool teachers and reflects the relative importance of the arcs that come out of a particular node. In other words, the teachers encourage the students to go toward such or such exercise after such or such lesson by giving the corresponding arc a higher weight. This valuation of the graph describes the pedagogic structure that will be optimized by the ACO algorithm

B. Pheromones: S and F

There are two kinds of pheromones that can be released on arcs to reflect students’ activity:

S: success pheromone.

This floating point value is incremented by ants/students on the adequate incoming arcs when

they are successful in completing the corresponding exercise.

F: failure pheromone.

This last value is S’s counterpart for failure. These pheromones are released not only on the arc that

led the ant to that node but also on previous ones in the ant’s history with decreasing amplitude.

This is meant to reflect the fact that the outcome of a particular node (exercise) is influenced by all the nodes (lessons, exercises) the ant went through before but with an influence that, of course, diminishes with time. For obvious pragmatical reasons, this “back propagation” of pheromone release is limited in scope (atypical value of 4 has been agreed upon). To illustrate this, let us consider an ant that went through nodes A,B,C,D,E,F and that reaches node G. When it validates node G with success, 1 unit of success pheromone is dropped on arc (F,G), 1/2 unit on arc (E,F), 1/3 of a unit on arc (D,E) and 1/4 on arc (C,D). In addition, to allow for dynamic adaptability of these pheromone amounts (S and F), evaporation is performed on a regular basis, usually every day, by reducing S and F in a given proportion _ typically around 0.999.

CONCLUSIONS AND PERSPECTIVE

Paraschool wanted a smart automatic system that could adapt to different users without manual intervention, which would be totally unrealistic to envisage on 10000 students. The ant-based system described in this paper not only offers such automatic features by gradually modifying pedagogic paths suggested by teachers using collective experience and by making the structure individual-specific thanks to variables such as H but also comes up with emergent informations that can be used as a refined auditing tool to help the pedagogical team identify the strengths and weaknesses of the software and pedagogic material.

From a more theoretical standpoint, this work can be seen as a new take on Interactive Evolutionary Computation where the solution to a problem is gradually constructed and modified by multiple interacting entities with different and possibly opposite goals. A creative and robust compromise can be reached that balances all the influences and constraints, which allows all participating entities to benefit from an emergent culture and to enhance their decision making processes accordingly. This suggest a great deal of new and exciting applications in the field of Collective Cognition Modelling and Collective Evolutionary Design.