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Multi-Agent Interaction
We want to develop a multi-agent system whose role is to reconstruct a Puzzle according to the cognitive
approach. In the modeling that we propose to you, each agent represents a cell of this Puzzle whose size is n * n.
To simplify, in the first step, we will retain n = 5. Each box is numbered, from 1 to n * n, and occupies a space
in this Puzzle (see Fig1.). For example box number 4, represented below by a gray star (row 1 column 4),
should normally be found at the end of the game at position (1, 2), if we want the Puzzle to be correctly
reconstructed . Initially, this box can be at any position, for example (1,4), as shown in the figure below.
To move these boxes, each agent can perform jumps. For example, to go from position (1, 4) to position (1, 2)
several movements for the "star" cell are possible depending on whether or not its adjacent cells are occupied.
The following two figures (2 and 3) describe two possible movements of this box. In Figure 2, the star square
moves directly from right to left to reach its final position since no square is in front of it. FIG. 3 describes
another situation in which the star box is forced to bypass the “circled cross” box which is in its path, passing
through the box (2,4), in order to reach its final position.
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The first step is to model this system using the multi-agent approach.
1. We will start by defining, first, simple strategies in which agents move only on the basis of their perception
of the occupation of neighboring squares or not. For example :
1.1. An agent chooses directly to move if the path to his space is free.
1.2. He only moves after having identified the best path to take to his square.
2. In a purely cognitive approach, more sophisticated strategies would consist for an agent to choose to interact
with its neighbors before moving. The agent first asks his neighbor to free him from the neighboring square
before moving himself. It consists in sending a message to his neighbor who once his agreement and his trip
have been made, the agent will start his trip. The following three figures (4, 5 and 6) illustrate this succession of
displacements of for the “cross-circled” box to allow the “star” box to return to its position.
3. You are first asked to define the structure of the messages exchanged between the agents. We will define the
structures necessary to implement the model of interaction and exchange of messages between the agents.


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