# Domain-independent Heuristics

In this post, we look into domain-independent heuristic which can be used for domain-independent planning problems which we are interested in.

## Heuristic: Recap

We discussed in previous post about heuristic which is an estimate of the minimum cost from a state to goal state, to aid search algorithm in reducing the number of nodes it has to explore to find a solution plan, in the hope that it will reduce the runtime of the search algorithm and find optimal plan.

In other words, without heuristic, the search algorithms explore blindly to find a solution. With heuristic, the search algorithms are informed.

In this post, we look into domain-independent heuristic which can be used for domain-independent planning problems which we are interested in.

### Relaxation

We discussed a little bit about relaxation in the previous post which is the best known way to write heuristic function, by weakening some of the constraints that we use in our Planning Domain. We will see concrete examples of the relaxation in the sections below.

We look into two related algorithms in this post:

• Max-cost

## Max-cost Heuristic

A literal is either an atomic formula or its negation

and atomic formula, or atom is

An atomic formula is a logical expression

Definitions taken from here.

Basically we break down our goal state into literals. Using our example Pacman, as shown in the picture below, the goal is to eat all three foods.

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