In computer science, local search is a heuristic method for solving computationally complex optimization problems. The local search can be used in problems that can be formulated such as the search for a solution that maximizes a criterion among a series of candidate solutions. A local optimization algorithm, also called a local search algorithm, is an algorithm intended to locate a local optimal. It is suitable for going through a specific region of the search space and getting closer to (or finding exactly) the ends of the function in that region.
The algorithm's strategy guided by local search consists of using penalties to encourage a local search technique to escape the local optimal and discover the global optimal. A local search algorithm is executed until it gets stuck in a local optimal. The characteristics of local optimists are evaluated and penalized, including the results that are used in a cost-increasing function used by the local search procedure. The local search is repeated several times using the last local optimal discovered and the cost increase function, which prevents the exploration of solutions with characteristics present in the optimal place discovered.
For some brick-and-mortar businesses, all searches are local searches. Most of them are hyperlocal companies that only attract customers from a specific service area. Some examples are barbers, manicurists, dry cleaners, laundries, delicatessen stores, and sandwich shops. It is a fact that if someone is looking for these types of products or services, they intend to buy them in a nearby place.
Some types of businesses are very specific to each location, but the people looking for them are more likely to be in other places. While potential customers aren't currently in their immediate area, they expect to be in the future. Some examples are cruise lines, ski resorts, car rental agencies, campgrounds, and convention centers. Some companies attract customers both from near and far.
Examples include financial advisors, consultants, regional hospitals, moving companies, and mortgage companies. The presence of the local optimal is an important component of what defines the difficulty of a global optimization problem, since it can be relatively easy to locate a local optimal and relatively difficult to locate the global optimal. Local optimization, in which the algorithm can get stuck in a local optimal without finding a global optimal. If Google is pretty sure that the user is looking for a local business, but doesn't know which one is the most relevant, it will show some local results at the top of the lists with phone numbers and links to more information on Google Maps.
The global optimal may be the same as the local optimal, in which case it would be more appropriate to refer to the optimization problem as local optimization, rather than global optimization. The guided local search procedure may need to be performed over thousands or hundreds of thousands of iterations, each of which involves running a local search algorithm to converge. Google continuously tries to interpret local intent, and when it does, it wants to provide local search results.
