- Introduction:
Decomposition representation is the process of solving complex problems by dividing them into simpler sub-problems, often structured in a hierarchical way. AND/OR graphs, widely used in artificial intelligence, optimization and operational research, are an effective approach for this decomposition.
2. Graph AND/OR: Definition
An AND/OR graph is an extension of the classical graphs used to model a complex problem and its subproblems. It contains:
Arcs AND: All child nodes must be resolved to resolve the parent.
Arcs OR: Only one child node is needed to solve the parent.
Nodes represent problems or sub-problems, and sheets are elementary solutions.
3. Structure of an AND/OR Graph
In a AND/OR graph:
AND Nodes: Conjunctive decomposition where all sub-problems must be solved (e.g. assembling a computer requires installing both the processor and memory).
OR nodes: Disjunctive decomposition where only one solution among several alternatives is sufficient (e.g. to go to the office, you can take the bus or the train).
4. Advantages of AND/OR Representation:
- Reduced complexity: The overall problem is divided into easier to solve sub-problems.
- Optimization: Possibility to choose between several solutions via the OR nodes.
- Parallelization: AND nodes allow to solve subproblems in parallel.
5. Application of AND/OR Graphs in Problem Solving
- Planning: Identify the best sequence of actions.
- Constraint-based reasoning: Solve a problem by breaking it down into simpler constraints.
- Expert systems: Use AND/OR nodes to represent rules and choose between several solutions.
- Combinatorial optimization: Explore different options in multi-path decision problems, such a in games.