#quantum
### Motivation
Mission planning --> Routing and scheduling problems are crucial, lead of combinatorial optimization because of the large search space.
> Plan the action of some agents to perform a set of tasks. TASK PLANNING/ WORKFLOW SCHEDULING
Satisfiability part:
- Can all the constraints be satisfied simultaneously?
- limited time / limited resources
### STRIPS representation
A way to describe planning problems: Stanford Research Institute Problem Solver.
- Finite set of binary variables
- State is described by the value of these variables at a given time.
- Special States: Initial and Final
- Initial State = Starting Values of all variables
- Actions = How to move from one state to another.
- Characterization of actions:
- A condition / boolean formula, action is allowed in a state if this state satisfies the condition. Usually, the condition only depends on a few variables.
- Action modifies the value of some variables
- Final / Target States
- Find a succession of actions that lead from the initial state to one of the target states. task must be completed whatever the final positions of the vehicles are
STRIPS is itself a solver, GraphPlan provides better performances for STRIPS-like problems.
GraphPlan has been improved and extended.
Existing Techniques to solve STRIPS-like problems with planning graphs.
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Use [[Erdos Renyi Model]] to generate random graphs to create STRIPS instances.
1. [[Hamiltonian Path]], Probability [[Parameters]] for the hardest instance is p = (log n + log logn) / n
1. STRIPS instance work be
1. Vertex U, ON or OFF
2. Edge Activation, with preconditions U is ON and v is OFF to make it work
3. [[Vertex Coloring]] 3 coloring, hardest asymptotical case is not known precisely, by p = 5/n
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