Basically, it’s Popular Search Algorithms. Also, a prospective solution. Further, moves to a neighboring solution. Moreover, returns a valid solution.
a. Hill-Climbing Search Algorithm

We can start this algorithm with an arbitrary solution to a problem. Also, it’s an iterative algorithm. Hence, the algorithm attempts to better solution by a single element of the solution. Although, we take an incremental change as a new solution. As if the change produces a better solution. Moreover, we have to repeat until there are no further improvements.
b. Local Beam Search Algorithm

In this algorithm, we have to hold k number of states at any given time. In the beginning, we have to generate states randomly.
Moreover, with the objective function, we have to compute successors of these k states. Also, this stop, if any of these successors is the maximum value of the objective function.
Otherwise, we have to put the (initial k states and k number of successors of the states = 2k) states in a pool. Also, a pool is then sorted numerically. Further, we have to select highest k states as new initial states. This process continues until a maximum value is reached.