Greedy randomized adaptive search procedure

{{short description|Metaheuristic commonly used for optimization problems}}

The greedy randomized adaptive search procedure (also known as GRASP) is a metaheuristic algorithm commonly applied to combinatorial optimization problems. GRASP typically consists of iterations made up from successive constructions of a greedy randomized solution and subsequent iterative improvements of it through a local search.{{cite journal |last1=Feo |first1=Thomas A. |last2=Resende |first2=Mauricio G. C. |title=Greedy Randomized Adaptive Search Procedures |journal=Journal of Global Optimization |date=1995 |volume=6 |issue=2 |pages=109–133 |doi=10.1007/BF01096763|s2cid=2110014 }} The greedy randomized solutions are generated by adding elements to the problem's solution set from a list of elements ranked by a greedy function according to the quality of the solution they will achieve. To obtain variability in the candidate set of greedy solutions, well-ranked candidate elements are often placed in a restricted candidate list (RCL), and chosen at random when building up the solution. This kind of greedy randomized construction method is also known as a semi-greedy heuristic, first described in Hart and Shogan (1987).{{cite journal |last1=Hart |first1=J. P. |last2=Shogan |first2=A. W. |title=Semi-greedy heuristics: An empirical study |journal=Operations Research Letters |date=July 1987 |volume=6 |issue=3 |pages=107–114 |doi=10.1016/0167-6377(87)90021-6}}

GRASP was first introduced in Feo and Resende (1989).{{cite journal |last1=Feo |first1=Thomas A. |last2=Resende |first2=Mauricio G. C. |title=A probabilistic heuristic for a computationally difficult set covering problem |journal=Operations Research Letters |date=April 1989 |volume=8 |issue=2 |pages=67–71 |doi=10.1016/0167-6377(89)90002-3}} Survey papers on GRASP include Feo and Resende (1995), and Resende and Ribeiro (2003).{{cite book |last1=Resende |first1=Mauricio G. C. |last2=Ribeiro |first2=Celso C. |title=Handbook of Metaheuristics |publisher=Springer |isbn=978-0-306-48056-0 |date=2003 |pages=219–249 |chapter=Greedy Randomized Adaptive Search Procedures}}

There are variations of the classical algorithm, such as the Reactive GRASP. In this variation, the basic parameter that defines the restrictiveness of the RCL during the construction phase is self-adjusted according to the quality of the solutions previously found.{{cite journal |last1=Prais |first1=Marcelo |last2=Ribeiro |first2=Celso C. |title=Reactive GRASP: An Application to a Matrix Decomposition Problem in TDMA Traffic Assignment |journal=INFORMS Journal on Computing |date=2000 |volume=12 |issue=3 |pages=164–176 |doi=10.1287/ijoc.12.3.164.12639}}

There are also techniques for search speed-up, such as cost perturbations, bias functions, memorization and learning, and local search on partially constructed solutions.