Third edition of Artificial Intelligence: foundations of computational agents, Cambridge University Press, 2023 is now available (including the full text).

3.1 Problem Solving as Search

In the simplest case of an agent reasoning about what it should do, the agent has a state-based model of the world, with no uncertainty and with goals to achieve. This is either a flat (non-hierarchical) representation or a single level of a hierarchy. The agent can determine how to achieve its goals by searching in its representation of the world state space for a way to get from its current state to a goal state. It can find a sequence of actions that will achieve its goal before it has to act in the world.

This problem can be abstracted to the mathematical problem of finding a path from a start node to a goal node in a directed graph. Many other problems can also be mapped to this abstraction, so it is worthwhile to consider this level of abstraction. Most of this chapter explores various algorithms for finding such paths.

This notion of search is computation inside the agent. It is different from searching in the world, when it may have to act in the world, for example, an agent searching for its keys, lifting up cushions, and so on. It is also different from searching the web, which involves searching for information. Searching in this chapter means searching in an internal representation for a path to a goal.

The idea of search is straightforward: the agent constructs a set of potential partial solutions to a problem that can be checked to see if they truly are solutions or if they could lead to solutions. Search proceeds by repeatedly selecting a partial solution, stopping if it is a path to a goal, and otherwise extending it by one more arc in all possible ways.

Search underlies much of artificial intelligence. When an agent is given a problem, it is usually given only a description that lets it recognize a solution, not an algorithm to solve it. It has to search for a solution. The existence of NP-complete problems, with efficient means to recognize answers but no efficient methods for finding them, indicates that searching is, in many cases, a necessary part of solving problems.

It is often believed that humans are able to use intuition to jump to solutions to difficult problems. However, humans do not tend to solve general problems; instead they solve specific instances about which they may know much more than the underlying search space. Problems in which little structure exists or in which the structure cannot be related to the physical world are very difficult for humans to solve. The existence of public key encryption codes, where the search space is clear and the test for a solution is given - for which humans nevertheless have no hope of solving and computers cannot solve in a realistic time frame - demonstrates the difficulty of search.

The difficulty of search and the fact that humans are able to solve some search problems efficiently suggests that computer agents should exploit knowledge about special cases to guide them to a solution. This extra knowledge beyond the search space is heuristic knowledge. This chapter considers one kind of heuristic knowledge in the form of an estimate of the cost from a node to a goal.