Local search algorithms are useful for solving pure optimization problems, in which the aim is to find the best state according to an objective function
To understand local search, we find it useful to consider the state-space landscape . A landscape has both “location” (defined by the state) and “elevation” (defined by the value of the heuristic cost function or objective function). If elevation corresponds to cost, then the aim is to find the lowest valley—a global minimum; if elevation corresponds to an objective function, then the aim is to find the highest peak—a global maximum. Local search algorithms explore this landscape. A complete local search algorithm always finds a goal if one exists; an optimal algorithm always finds a global minimum/maximum
function HILL-CLIMBING(problem) returns a state that is a local maximum
current ← MAKE-NODE(problem.INITIAL-STATE)
loop do
neighbor ← a highest-valued successor of current
if neighbor.VALUE ≤ current.VALUE then return current.STATE
current ← neighbor