Even simple problems can have very large problem spaces. A salesman has a list of cities to visit once. There are direct routes between each pair of cities on the list. Heuristics are rules of thumb which improve efficiency. Human problem solvers use heuristics all the time, e.g., choosing which part of the haystack to look in.
Heuristics are domain-specific knowledge, usually elicited from experts.
Note the example of the travelling salesman s nearest neighbour heuristic. Heuristics mean we accept reasonable rather than best solutions. Assessing solution options Heuristics are either embodied in problem space operators themselves, or applied by a heuristic function. A heuristic function evaluates individual problem states, determines how desirable the states are, invokes the heuristic, e.g., heuristic function for the travelling salesman determines the sum of distances travelled so far. Reasoning operates forwards from current state, and backwards from the goal state.