To solve a problem with a computer, it is necessary to represent the problem in numerical or symbolic form and offer a specific procedure using a programming language. However, working with problem-solving in the artificial intelligence (AI) field, it is difficult to specify a formulation of a problem from the beginning. Therefore, the flexibility of choosing a solution procedure during the observation of state changes is highly required. Some problems can be represented by a graph or tree structure where each node represents a state of the problem. This kind of problem formulation method is called State-space representation.

State-space representation

In a state-space representation method, each state of the problem is represented by a node of a graph or tree structure. In this case, the problem is translated as a search problem to determine the goal under specific operators and restrains. In this post, I will introduce Traveling Salesman Problem (TSP) as an example.

Representation a problem with the state-space representation needs:

(1). A set of states of the problem

(2). A set of operators to operate between states of the problem

(3). Initial state and final state(goal)

Traveling Salesman Problem (TSP)

Consider the following situation. You are given a list of n cities with the distance between any two cities. Now, you have to start with your office and to visit all the cities only once each and return to your office. What is the shortest path can you take? This problem is called the Traveling Salesman Problem (TSP).

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