Heuristic Techniques for Solving Large Combinatorial Problems on a Computer

Abstract

Many problems of optimization, search, or decision-making are combinatorial in nature and basically non-numerical. The advent of the modern high-speed digital computer has opened the way for us to solve many of these problems. Although virtually all of these problems are finite, it is well-known that their size grows extremely rapidly and we can usually expect the computer to do by exhaustive search just a few cases larger than what can be done by hand. Intelligent search procedures such as banach and bound (Little, Murty, Sweeney and Karel (1963), Lawles and Wood (1964)), back-track programming (Golomb and Baument (1965), Walker (1960)), linear or dynamic programming (Gomery (1963), Bellman (1962), Held and Karp (1962)), together with isomorphic rejection (Swift, 1960) help to reduce the total number of cases to be considered but more often than not, we are interested in the solution to problems which are still too large for these techniques. Here some sort of heuristics have to be employed, whereby we hope that the solution (in the instance where a solution when found may be readily verified), or a probably solution, or a useful partial or approximate solution may be obtained in reasonable computation time.